TSTP Solution File: LAT270-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LAT270-1 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:26:22 EDT 2024
% Result : Unsatisfiable 5.51s 1.23s
% Output : Refutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3906
% Syntax : Number of formulae : 6640 (2542 unt; 0 def)
% Number of atoms : 14001 (2479 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 12592 (5231 ~;5329 |; 0 &)
% (2032 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2103 (2101 usr;2033 prp; 0-4 aty)
% Number of functors : 213 ( 213 usr; 52 con; 0-18 aty)
% Number of variables : 9085 (9085 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22712,plain,
$false,
inference(avatar_sat_refutation,[],[f3178,f3183,f3188,f3193,f3198,f3203,f3208,f3213,f3218,f3223,f3228,f3233,f3238,f3243,f3248,f3253,f3258,f3263,f3268,f3273,f3278,f3283,f3288,f3293,f3298,f3303,f3308,f3313,f3318,f3323,f3328,f3333,f3338,f3343,f3348,f3353,f3358,f3363,f3368,f3373,f3378,f3383,f3388,f3393,f3398,f3403,f3408,f3413,f3418,f3423,f3428,f3433,f3438,f3443,f3448,f3453,f3458,f3463,f3468,f3473,f3478,f3483,f3488,f3493,f3498,f3503,f3508,f3513,f3518,f3523,f3528,f3533,f3538,f3543,f3548,f3553,f3558,f3563,f3568,f3573,f3578,f3583,f3588,f3593,f3598,f3603,f3608,f3613,f3618,f3623,f3628,f3633,f3638,f3643,f3648,f3653,f3658,f3663,f3668,f3673,f3678,f3682,f3686,f3691,f3696,f3701,f3706,f3711,f3715,f3720,f3725,f3729,f3733,f3737,f3742,f3747,f3752,f3756,f3760,f3764,f3769,f3773,f3778,f3782,f3786,f3790,f3794,f3798,f3802,f3806,f3810,f3814,f3818,f3822,f3826,f3830,f3834,f3838,f3842,f3846,f3850,f3854,f3858,f3862,f3866,f3870,f3874,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3978,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4398,f4402,f4406,f4410,f4414,f4418,f4422,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4614,f4618,f4622,f4626,f4630,f4634,f4638,f4642,f4646,f4650,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f4774,f4778,f4782,f4786,f4790,f4794,f4798,f4802,f4806,f4810,f4814,f4818,f4822,f4826,f4830,f4834,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f4898,f4902,f4906,f4910,f4914,f4918,f4922,f4926,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4958,f4962,f4966,f4970,f4974,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5038,f5042,f5046,f5050,f5054,f5058,f5062,f5066,f5070,f5074,f5078,f5082,f5086,f5090,f5094,f5098,f5102,f5106,f5110,f5114,f5118,f5122,f5126,f5130,f5134,f5138,f5142,f5146,f5150,f5154,f5158,f5162,f5166,f5170,f5174,f5178,f5182,f5186,f5190,f5194,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5242,f5246,f5250,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5290,f5294,f5298,f5302,f5306,f5310,f5314,f5318,f5322,f5326,f5330,f5334,f5338,f5342,f5346,f5350,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5382,f5386,f5390,f5394,f5398,f5402,f5406,f5410,f5414,f5418,f5422,f5426,f5430,f5434,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5486,f5490,f5494,f5498,f5502,f5506,f5510,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5554,f5558,f5562,f5566,f5570,f5574,f5578,f5582,f5586,f5590,f5594,f5598,f5602,f5606,f5610,f5614,f5618,f5622,f5626,f5630,f5634,f5638,f5642,f5646,f5650,f5654,f5658,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5706,f5710,f5714,f5718,f5722,f5726,f5730,f5734,f5738,f5742,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5774,f5778,f5782,f5786,f5790,f5794,f5798,f5802,f5806,f5810,f5814,f5818,f5822,f5826,f5830,f5834,f5838,f5842,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5890,f5894,f5898,f5902,f5907,f5911,f5916,f5921,f5928,f5941,f6697,f6701,f6705,f6709,f6714,f6719,f6724,f6728,f6732,f6736,f6741,f6745,f6749,f6753,f6757,f6761,f6765,f6769,f6773,f6778,f6783,f6788,f6793,f6798,f6803,f6808,f6813,f6818,f6823,f6828,f6833,f6838,f6843,f6848,f6853,f6857,f6861,f6865,f6869,f6873,f6878,f6883,f6888,f6892,f6896,f6900,f6904,f6908,f6912,f6917,f6922,f6926,f6931,f6936,f6940,f6944,f6948,f6952,f6956,f6960,f6964,f6968,f6972,f6976,f6980,f6984,f6988,f6992,f6997,f7001,f7006,f7017,f7022,f7027,f7034,f7038,f7042,f7046,f7050,f7054,f7058,f7062,f7066,f7070,f7075,f7079,f7083,f7087,f7091,f7095,f7099,f7103,f7107,f7111,f7115,f7119,f7123,f7127,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7159,f7163,f7167,f7171,f7175,f7179,f7183,f7187,f7191,f7195,f7199,f7203,f7207,f7211,f7215,f7219,f7224,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7268,f7272,f7276,f7280,f7284,f7288,f7292,f7296,f7300,f7304,f7309,f7313,f7318,f7322,f7327,f7331,f7335,f7339,f7343,f7347,f7351,f7355,f7359,f7363,f7367,f7371,f7375,f7379,f7383,f7387,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7439,f7443,f7447,f7451,f7455,f7459,f7463,f7467,f7471,f7475,f7479,f7483,f7487,f7491,f7495,f7499,f7503,f7507,f7511,f7515,f7519,f7523,f7527,f7531,f7535,f7539,f7543,f7547,f7551,f7555,f7559,f7563,f7567,f7572,f7577,f7581,f7585,f7589,f7598,f7627,f7643,f7655,f7671,f7684,f7688,f7693,f7697,f7701,f7705,f7709,f7713,f7717,f7721,f7725,f7730,f7734,f7738,f7742,f7746,f7750,f7754,f7758,f7762,f7766,f7770,f7774,f7778,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7819,f7823,f7827,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7863,f7867,f7871,f7875,f7879,f7883,f7887,f7891,f7895,f7899,f7903,f7907,f7911,f7915,f7919,f7923,f7927,f7931,f7935,f7939,f7945,f7949,f7953,f7957,f7961,f7965,f7969,f7973,f7977,f7981,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8014,f8018,f8022,f8026,f8031,f8052,f8154,f8159,f8163,f8167,f8171,f8175,f8179,f8183,f8187,f8191,f8195,f8200,f8204,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8240,f8244,f8248,f8252,f8256,f8260,f8264,f8268,f8272,f8276,f8280,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8325,f8329,f8333,f8337,f8341,f8345,f8349,f8353,f8357,f8361,f8365,f8370,f8374,f8378,f8382,f8386,f8390,f8394,f8398,f8402,f8406,f8410,f8414,f8418,f8422,f8426,f8430,f8434,f8438,f8442,f8446,f8450,f8454,f8458,f8462,f8466,f8470,f8474,f8478,f8482,f8494,f8574,f8593,f8640,f8665,f8704,f8708,f8712,f8716,f8720,f8724,f8728,f8733,f8737,f8741,f8745,f8749,f8753,f8757,f8761,f8765,f8769,f8773,f8777,f8781,f8785,f8789,f8793,f8797,f8801,f8805,f8809,f8813,f8817,f8821,f8826,f8830,f8834,f8838,f8842,f8846,f8850,f8854,f8858,f8862,f8866,f8870,f8874,f8878,f8882,f8886,f8890,f8894,f8898,f8902,f8907,f8911,f8915,f8919,f8923,f8927,f8931,f8935,f8939,f8943,f8947,f8951,f8955,f8959,f8963,f8967,f8971,f8975,f8979,f8983,f8988,f8992,f8996,f9001,f9008,f9012,f9016,f9020,f9024,f9035,f9095,f9131,f9185,f9209,f9223,f9247,f9251,f9255,f9259,f9263,f9267,f9271,f9275,f9279,f9283,f9287,f9292,f9296,f9300,f9304,f9308,f9312,f9316,f9320,f9324,f9328,f9332,f9336,f9340,f9344,f9348,f9352,f9356,f9360,f9364,f9368,f9372,f9376,f9380,f9384,f9388,f9392,f9396,f9400,f9404,f9408,f9412,f9416,f9420,f9424,f9428,f9432,f9436,f9440,f9444,f9448,f9452,f9456,f9460,f9464,f9468,f9472,f9476,f9480,f9484,f9488,f9492,f9496,f9500,f9504,f9508,f9512,f9516,f9520,f9524,f9528,f9532,f9536,f9541,f9549,f9553,f9557,f9561,f9565,f9569,f9573,f9605,f9611,f9639,f9691,f9739,f9806,f9946,f9959,f9963,f9967,f9971,f9975,f9979,f9988,f9992,f9996,f10000,f10004,f10008,f10012,f10016,f10020,f10024,f10034,f10038,f10042,f10046,f10050,f10054,f10058,f10062,f10066,f10071,f10082,f10086,f10090,f10094,f10098,f10102,f10106,f10110,f10114,f10118,f10122,f10126,f10130,f10134,f10138,f10142,f10146,f10150,f10154,f10158,f10162,f10166,f10170,f10174,f10178,f10182,f10186,f10190,f10194,f10198,f10206,f10210,f10214,f10218,f10222,f10226,f10230,f10234,f10238,f10242,f10246,f10250,f10254,f10258,f10262,f10266,f10270,f10274,f10278,f10282,f10286,f10291,f10295,f10299,f10303,f10307,f10311,f10315,f10319,f10323,f10327,f10331,f10335,f10339,f10343,f10347,f10351,f10355,f10359,f10363,f10367,f10371,f10375,f10379,f10383,f10387,f10391,f10395,f10399,f10403,f10407,f10411,f10415,f10419,f10423,f10427,f10431,f10435,f10439,f10443,f10447,f10451,f10458,f10462,f10466,f10470,f10474,f10622,f10683,f10879,f10982,f11028,f11160,f11338,f11342,f11346,f11350,f11354,f11358,f11362,f11375,f11379,f11383,f11387,f11391,f11395,f11399,f11403,f11407,f11411,f11415,f11419,f11423,f11427,f11431,f11435,f11439,f11443,f11447,f11451,f11455,f11459,f11463,f11467,f11471,f11475,f11479,f11483,f11487,f11491,f11495,f11499,f11503,f11507,f11511,f11515,f11519,f11523,f11527,f11531,f11535,f11540,f11544,f11548,f11552,f11556,f11560,f11564,f11568,f11572,f11576,f11580,f11584,f11588,f11592,f11596,f11600,f11604,f11608,f11612,f11616,f11620,f11624,f11628,f11632,f11636,f11640,f11644,f11648,f11652,f11656,f11660,f11664,f11675,f11679,f11683,f11687,f11691,f11695,f11699,f11703,f11708,f11724,f11728,f11732,f11736,f11741,f11749,f11753,f11758,f11805,f11809,f11813,f11817,f11821,f11825,f11829,f12410,f12776,f12890,f12894,f12898,f12902,f12906,f12910,f12914,f12918,f12922,f12926,f12930,f12934,f12938,f12942,f12946,f12950,f12954,f12958,f12962,f12966,f12970,f12974,f12978,f12982,f12986,f12990,f12994,f12998,f13002,f13006,f13010,f13014,f13018,f13022,f13026,f13030,f13034,f13038,f13042,f13046,f13050,f13054,f13058,f13062,f13066,f13070,f13074,f13078,f13082,f13086,f13091,f13095,f13099,f13103,f13107,f13111,f13115,f13119,f13123,f13127,f13131,f13136,f13140,f13144,f13148,f13152,f13156,f13160,f13164,f13168,f13172,f13176,f13188,f13192,f13196,f13201,f13209,f13213,f13217,f13221,f13352,f13639,f14147,f14172,f14176,f14180,f14184,f14188,f14192,f14196,f14200,f14204,f14208,f14212,f14216,f14220,f14224,f14228,f14232,f14236,f14240,f14244,f14248,f14252,f14256,f14260,f14264,f14268,f14272,f14276,f14280,f14284,f14288,f14292,f14296,f14300,f14304,f14308,f14312,f14316,f14320,f14327,f14331,f14335,f14339,f14343,f14347,f14351,f14355,f14359,f14363,f14364,f14368,f14372,f14376,f14380,f14384,f14388,f14392,f14396,f14400,f14404,f14421,f14445,f14450,f14468,f14473,f14493,f14497,f14502,f14506,f14510,f14514,f14518,f14522,f14526,f14530,f14534,f14538,f14761,f15290,f15482,f15486,f15490,f15494,f15498,f15502,f15506,f15510,f15514,f15518,f15522,f15526,f15530,f15534,f15538,f15543,f15547,f15551,f15555,f15559,f15563,f15567,f15571,f15576,f15580,f15586,f15590,f15594,f15598,f15602,f15606,f15610,f15614,f15618,f15622,f15627,f15631,f15635,f15639,f15643,f15647,f15651,f15655,f15659,f15663,f15669,f15673,f15677,f15681,f15685,f15689,f15693,f15697,f15701,f15705,f15710,f15714,f15718,f15722,f15726,f15730,f15735,f15760,f15765,f15832,f15837,f15932,f15937,f16036,f16041,f16071,f16077,f16081,f16098,f16103,f16111,f16116,f16124,f16130,f16135,f16140,f16144,f16148,f16154,f16160,f16164,f16168,f16172,f16176,f16182,f16187,f16222,f16226,f16240,f17337,f17341,f17345,f17349,f17353,f17357,f17361,f17365,f17369,f17373,f17377,f17392,f17396,f17400,f17404,f17408,f17412,f17416,f17420,f17424,f17428,f17432,f17436,f17440,f17444,f17448,f17452,f17456,f17460,f17464,f17468,f17472,f17487,f17491,f17495,f17499,f17503,f17507,f17511,f17515,f17519,f17523,f17527,f17531,f17535,f17539,f17543,f17547,f17551,f17555,f17559,f17563,f17567,f17573,f17577,f17581,f17587,f17613,f17619,f17704,f17709,f17713,f17736,f17740,f17744,f17749,f17754,f17759,f17764,f17781,f17786,f17790,f17794,f17798,f17803,f17823,f17827,f17831,f17835,f17840,f17845,f17850,f17855,f17860,f17865,f17872,f17880,f17884,f17889,f17897,f17901,f17905,f17909,f17913,f17917,f17995,f18199,f18483,f18778,f18782,f18786,f18790,f18791,f18795,f18799,f18803,f18809,f18815,f18819,f18823,f18827,f18831,f18835,f18839,f18843,f18847,f18851,f18855,f18859,f18863,f18867,f18871,f18875,f18881,f18885,f18889,f18893,f18897,f18901,f18905,f18909,f18913,f18919,f18923,f19244,f19248,f19914,f19918,f19922,f19926,f19931,f19935,f19939,f19943,f19948,f19952,f19956,f19960,f19964,f19968,f19972,f19976,f19982,f19986,f19990,f19994,f20055,f20087,f20501,f20505,f20509,f20513,f20517,f20521,f20525,f20529,f20533,f20537,f20541,f20545,f20549,f20553,f20557,f20561,f20565,f20569,f20573,f20577,f20582,f20587,f20593,f20614,f20619,f20631,f20635,f20639,f20643,f20648,f20668,f20673,f20693,f20697,f20724,f20729,f20878,f21010,f21014,f21018,f21111,f21115,f21138,f21142,f21146,f21150,f21154,f21158,f21162,f21166,f21170,f21174,f21195,f21199,f21203,f21207,f21211,f21215,f21219,f21223,f21227,f21231,f21235,f21239,f21243,f21247,f21251,f21255,f21259,f21263,f21267,f21271,f21275,f21279,f21283,f21287,f21291,f21295,f21299,f21303,f21307,f21311,f21315,f21319,f21323,f21327,f21331,f21335,f21339,f21343,f21347,f21351,f21355,f21359,f21363,f21407,f21411,f21415,f21419,f21423,f21427,f21434,f21452,f21459,f21464,f21487,f21491,f21495,f21499,f21505,f21581,f21585,f21589,f21609,f21613,f21617,f21621,f21625,f21630,f21657,f21663,f21678,f21896,f21900,f22502,f22506,f22510,f22520,f22524,f22528,f22532,f22536,f22540,f22544,f22548,f22552,f22556,f22560,f22564,f22568,f22572,f22576,f22580,f22584,f22588,f22592,f22596,f22600,f22604,f22608,f22612,f22616,f22620,f22624,f22628,f22632,f22711]) ).
fof(f22711,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_3
| ~ spl0_99
| ~ spl0_2001 ),
inference(avatar_split_clause,[],[f22640,f22500,f3665,f3185,f3195,f3180]) ).
fof(f3180,plain,
( spl0_2
<=> c_in(v_a,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f3195,plain,
( spl0_5
<=> c_lessequals(v_S,v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f3185,plain,
( spl0_3
<=> c_in(v_b,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f3665,plain,
( spl0_99
<=> c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f22500,plain,
( spl0_2001
<=> ! [X2,X0,X7] :
( ~ c_in(X2,v_A,t_a)
| ~ c_in(X7,v_A,t_a)
| c_lessequals(X0,v_A,tc_set(t_a))
| ~ c_lessequals(X0,c_Tarski_Ointerval(v_r,X2,X7,t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f22640,plain,
( ~ c_in(v_b,v_A,t_a)
| c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(v_a,v_A,t_a)
| ~ spl0_99
| ~ spl0_2001 ),
inference(resolution,[],[f22501,f3667]) ).
fof(f3667,plain,
( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f3665]) ).
fof(f22501,plain,
( ! [X2,X0,X7] :
( ~ c_lessequals(X0,c_Tarski_Ointerval(v_r,X2,X7,t_a),tc_set(t_a))
| ~ c_in(X7,v_A,t_a)
| c_lessequals(X0,v_A,tc_set(t_a))
| ~ c_in(X2,v_A,t_a) )
| ~ spl0_2001 ),
inference(avatar_component_clause,[],[f22500]) ).
fof(f22632,plain,
spl0_2032,
inference(avatar_split_clause,[],[f2950,f22630]) ).
fof(f22630,plain,
( spl0_2032
<=> ! [X80,X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X80)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).
fof(f2950,plain,
! [X40,X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X80)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f721,f994]) ).
fof(f994,axiom,
! [X39] : c_Numeral_Obin__minus(X39) = c_Numeral_Obin__mult(c_Numeral_OMin,X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f721,axiom,
! [X40,X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__minus(X80)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
fof(f22628,plain,
spl0_2031,
inference(avatar_split_clause,[],[f2949,f22626]) ).
fof(f22626,plain,
( spl0_2031
<=> ! [X80,X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X80)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f2949,plain,
! [X40,X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X80)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f722,f994]) ).
fof(f722,axiom,
! [X40,X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__minus(X80)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
fof(f22624,plain,
spl0_2030,
inference(avatar_split_clause,[],[f2922,f22622]) ).
fof(f22622,plain,
( spl0_2030
<=> ! [X30,X29,X19] :
( ~ c_lessequals(c_plus(X29,X30,tc_nat),X19,tc_nat)
| c_List_Oupt(X29,c_plus(X29,X30,tc_nat)) = c_List_Osublist(c_List_Oupt(X29,X19),c_SetInterval_OlessThan(X30,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f2922,plain,
! [X29,X19,X30] :
( ~ c_lessequals(c_plus(X29,X30,tc_nat),X19,tc_nat)
| c_List_Oupt(X29,c_plus(X29,X30,tc_nat)) = c_List_Osublist(c_List_Oupt(X29,X19),c_SetInterval_OlessThan(X30,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f642,f631]) ).
fof(f631,axiom,
! [X19,X77,X5] : c_List_Osublist(X77,c_SetInterval_OlessThan(X19,tc_nat),X5) = c_List_Otake(X19,X77,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
fof(f642,axiom,
! [X29,X19,X30] :
( ~ c_lessequals(c_plus(X29,X30,tc_nat),X19,tc_nat)
| c_List_Otake(X30,c_List_Oupt(X29,X19),tc_nat) = c_List_Oupt(X29,c_plus(X29,X30,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
fof(f22620,plain,
spl0_2029,
inference(avatar_split_clause,[],[f2812,f22618]) ).
fof(f22618,plain,
( spl0_2029
<=> ! [X82,X5] : c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f2812,plain,
! [X82,X5] : c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1577,f1581,f1581]) ).
fof(f1581,axiom,
! [X6,X5] : c_Transitive__Closure_Ortrancl(X6,X5) = c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f1577,axiom,
! [X82,X5] : c_Transitive__Closure_Ortrancl(X82,X5) = c_Transitive__Closure_Ortrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f22616,plain,
spl0_2028,
inference(avatar_split_clause,[],[f1713,f22614]) ).
fof(f22614,plain,
( spl0_2028
<=> ! [X5,X7,X6,X2] :
( ~ c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(X2,X7,X5,X5),c_Transitive__Closure_Otrancl(X6,X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).
fof(f1713,axiom,
! [X2,X6,X7,X5] :
( ~ c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(X2,X7,X5,X5),c_Transitive__Closure_Otrancl(X6,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f22612,plain,
spl0_2027,
inference(avatar_split_clause,[],[f1666,f22610]) ).
fof(f22610,plain,
( spl0_2027
<=> ! [X6,X23,X7,X5,X2,X1] :
( ~ c_in(X2,X1,X5)
| c_in(X7,c_Relation_OImage(X6,X1,X5,X23),X23)
| ~ c_in(c_Pair(X2,X7,X5,X23),X6,tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).
fof(f1666,axiom,
! [X2,X1,X6,X7,X5,X23] :
( ~ c_in(X2,X1,X5)
| c_in(X7,c_Relation_OImage(X6,X1,X5,X23),X23)
| ~ c_in(c_Pair(X2,X7,X5,X23),X6,tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f22608,plain,
spl0_2026,
inference(avatar_split_clause,[],[f1427,f22606]) ).
fof(f22606,plain,
( spl0_2026
<=> ! [X5,X29,X19,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X29,X19,X5)
| c_minus(c_SetInterval_OatLeastLessThan(X29,X30,X5),c_SetInterval_OatLeastLessThan(X29,X19,X5),tc_set(X5)) = c_SetInterval_OatLeastLessThan(X19,X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f1427,axiom,
! [X29,X19,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X29,X19,X5)
| c_minus(c_SetInterval_OatLeastLessThan(X29,X30,X5),c_SetInterval_OatLeastLessThan(X29,X19,X5),tc_set(X5)) = c_SetInterval_OatLeastLessThan(X19,X30,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
fof(f22604,plain,
( spl0_2025
| ~ spl0_1707
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f21602,f21461,f16142,f22602]) ).
fof(f22602,plain,
( spl0_2025
<=> ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(v_A,t_a),X0,t_a,t_a)
| ~ c_in(v_a,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).
fof(f16142,plain,
( spl0_1707
<=> ! [X35,X5,X2,X1] :
( ~ c_in(X2,X35,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X2,X1,X5),X5),X35,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f21461,plain,
( spl0_1981
<=> v_A = c_insert(v_a,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f21602,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(v_A,t_a),X0,t_a,t_a)
| ~ c_in(v_a,X0,t_a) )
| ~ spl0_1707
| ~ spl0_1981 ),
inference(superposition,[],[f16143,f21463]) ).
fof(f21463,plain,
( v_A = c_insert(v_a,v_A,t_a)
| ~ spl0_1981 ),
inference(avatar_component_clause,[],[f21461]) ).
fof(f16143,plain,
( ! [X2,X1,X5,X35] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X2,X1,X5),X5),X35,X5,X5)
| ~ c_in(X2,X35,X5) )
| ~ spl0_1707 ),
inference(avatar_component_clause,[],[f16142]) ).
fof(f22600,plain,
spl0_2024,
inference(avatar_split_clause,[],[f1221,f22598]) ).
fof(f22598,plain,
( spl0_2024
<=> ! [X4,X7,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X4,X8,tc_nat)
| ~ c_less(c_1,X7,X5)
| c_less(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f1221,axiom,
! [X8,X7,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X4,X8,tc_nat)
| ~ c_less(c_1,X7,X5)
| c_less(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f22596,plain,
spl0_2023,
inference(avatar_split_clause,[],[f1220,f22594]) ).
fof(f22594,plain,
( spl0_2023
<=> ! [X4,X7,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X7,X5)
| c_less(X4,X8,tc_nat)
| ~ c_less(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f1220,axiom,
! [X8,X7,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X7,X5)
| c_less(X4,X8,tc_nat)
| ~ c_less(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f22592,plain,
spl0_2022,
inference(avatar_split_clause,[],[f1216,f22590]) ).
fof(f22590,plain,
( spl0_2022
<=> ! [X4,X7,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X4,X8,tc_nat)
| ~ c_less(c_1,X7,X5)
| c_lessequals(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f1216,axiom,
! [X8,X7,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X4,X8,tc_nat)
| ~ c_less(c_1,X7,X5)
| c_lessequals(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
fof(f22588,plain,
spl0_2021,
inference(avatar_split_clause,[],[f1215,f22586]) ).
fof(f22586,plain,
( spl0_2021
<=> ! [X4,X7,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X7,X5)
| c_lessequals(X4,X8,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f1215,axiom,
! [X8,X7,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X7,X5)
| c_lessequals(X4,X8,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X7,X4,X5),c_Nat_Opower(X7,X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
fof(f22584,plain,
spl0_2020,
inference(avatar_split_clause,[],[f1201,f22582]) ).
fof(f22582,plain,
( spl0_2020
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X4,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f1201,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X4,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f22580,plain,
spl0_2019,
inference(avatar_split_clause,[],[f1198,f22578]) ).
fof(f22578,plain,
( spl0_2019
<=> ! [X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f1198,axiom,
! [X39,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f22576,plain,
spl0_2018,
inference(avatar_split_clause,[],[f1195,f22574]) ).
fof(f22574,plain,
( spl0_2018
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X4,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f1195,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X4,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f22572,plain,
spl0_2017,
inference(avatar_split_clause,[],[f1193,f22570]) ).
fof(f22570,plain,
( spl0_2017
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X4,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f1193,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X4,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f22568,plain,
spl0_2016,
inference(avatar_split_clause,[],[f1190,f22566]) ).
fof(f22566,plain,
( spl0_2016
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X4,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f1190,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X4,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f22564,plain,
spl0_2015,
inference(avatar_split_clause,[],[f1184,f22562]) ).
fof(f22562,plain,
( spl0_2015
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X4,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).
fof(f1184,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X4,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f22560,plain,
( spl0_2014
| ~ spl0_1706
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f21601,f21461,f16138,f22558]) ).
fof(f22558,plain,
( spl0_2014
<=> ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,t_a),v_A,t_a,t_a)
| ~ c_in(v_a,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).
fof(f16138,plain,
( spl0_1706
<=> ! [X35,X7,X5,X1] :
( ~ c_in(X7,X1,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X1,X5),c_insert(X7,X35,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f21601,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,t_a),v_A,t_a,t_a)
| ~ c_in(v_a,X0,t_a) )
| ~ spl0_1706
| ~ spl0_1981 ),
inference(superposition,[],[f16139,f21463]) ).
fof(f16139,plain,
( ! [X1,X7,X5,X35] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X1,X5),c_insert(X7,X35,X5),X5,X5)
| ~ c_in(X7,X1,X5) )
| ~ spl0_1706 ),
inference(avatar_component_clause,[],[f16138]) ).
fof(f22556,plain,
spl0_2013,
inference(avatar_split_clause,[],[f1033,f22554]) ).
fof(f22554,plain,
( spl0_2013
<=> ! [X5,X40,X9,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X40,X5),c_times(c_Numeral_Onumber__of(X39,X5),X9,X5),X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X40,X39),X5),X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).
fof(f1033,axiom,
! [X40,X39,X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X40,X5),c_times(c_Numeral_Onumber__of(X39,X5),X9,X5),X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X40,X39),X5),X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f22552,plain,
spl0_2012,
inference(avatar_split_clause,[],[f973,f22550]) ).
fof(f22550,plain,
( spl0_2012
<=> ! [X5,X40,X9,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X40,X5),c_plus(c_Numeral_Onumber__of(X39,X5),X9,X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,X39),X5),X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).
fof(f973,axiom,
! [X40,X39,X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X40,X5),c_plus(c_Numeral_Onumber__of(X39,X5),X9,X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,X39),X5),X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f22548,plain,
spl0_2011,
inference(avatar_split_clause,[],[f726,f22546]) ).
fof(f22546,plain,
( spl0_2011
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).
fof(f726,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f22544,plain,
spl0_2010,
inference(avatar_split_clause,[],[f700,f22542]) ).
fof(f22542,plain,
( spl0_2010
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) != c_Numeral_Onumber__of(X80,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f700,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) != c_Numeral_Onumber__of(X80,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).
fof(f22540,plain,
spl0_2009,
inference(avatar_split_clause,[],[f690,f22538]) ).
fof(f22538,plain,
( spl0_2009
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_plus(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).
fof(f690,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_plus(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f22536,plain,
spl0_2008,
inference(avatar_split_clause,[],[f500,f22534]) ).
fof(f22534,plain,
( spl0_2008
<=> ! [X5,X44,X4,X29,X8] :
( ~ c_less(X29,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X44,X29,X4,X5),X29,X8,X5) = c_List_Olist__update(X44,X29,X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f500,axiom,
! [X29,X8,X44,X4,X5] :
( ~ c_less(X29,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X44,X29,X4,X5),X29,X8,X5) = c_List_Olist__update(X44,X29,X8,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
fof(f22532,plain,
spl0_2007,
inference(avatar_split_clause,[],[f499,f22530]) ).
fof(f22530,plain,
( spl0_2007
<=> ! [X44,X4,X8,X5,X45] : c_List_Olist__update(c_append(X44,c_List_Olist_OCons(X4,X45,X5),X5),c_Nat_Osize(X44,tc_List_Olist(X5)),X8,X5) = c_append(X44,c_List_Olist_OCons(X8,X45,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f499,axiom,
! [X8,X44,X45,X4,X5] : c_List_Olist__update(c_append(X44,c_List_Olist_OCons(X4,X45,X5),X5),c_Nat_Osize(X44,tc_List_Olist(X5)),X8,X5) = c_append(X44,c_List_Olist_OCons(X8,X45,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
fof(f22528,plain,
spl0_2006,
inference(avatar_split_clause,[],[f220,f22526]) ).
fof(f22526,plain,
( spl0_2006
<=> ! [X4,X8] :
( X4 = X8
| c_IntDef_OAbs__Integ(X4) != c_IntDef_OAbs__Integ(X8)
| ~ c_in(X4,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
fof(f220,axiom,
! [X8,X4] :
( X4 = X8
| c_IntDef_OAbs__Integ(X4) != c_IntDef_OAbs__Integ(X8)
| ~ c_in(X4,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
fof(f22524,plain,
spl0_2005,
inference(avatar_split_clause,[],[f159,f22522]) ).
fof(f22522,plain,
( spl0_2005
<=> ! [X1,X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X8,X1,X23)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Orderings_Omax(X8,c_Finite__Set_OMin(X1,X23),X23) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).
fof(f159,axiom,
! [X1,X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X8,X1,X23)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Orderings_Omax(X8,c_Finite__Set_OMin(X1,X23),X23) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f22520,plain,
spl0_2004,
inference(avatar_split_clause,[],[f158,f22518]) ).
fof(f22518,plain,
( spl0_2004
<=> ! [X1,X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X8,X1,X23)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Orderings_Omin(X8,c_Finite__Set_OMax(X1,X23),X23) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
fof(f158,axiom,
! [X1,X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X8,X1,X23)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Orderings_Omin(X8,c_Finite__Set_OMax(X1,X23),X23) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f22510,plain,
spl0_2003,
inference(avatar_split_clause,[],[f87,f22508]) ).
fof(f22508,plain,
( spl0_2003
<=> ! [X30,X18,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_plus(X18,c_div(X30,X19,tc_nat),tc_nat) = c_div(c_plus(X30,c_times(X19,X18,tc_nat),tc_nat),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).
fof(f87,axiom,
! [X18,X19,X30] :
( ~ c_less(c_0,X19,tc_nat)
| c_plus(X18,c_div(X30,X19,tc_nat),tc_nat) = c_div(c_plus(X30,c_times(X19,X18,tc_nat),tc_nat),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
fof(f22506,plain,
spl0_2002,
inference(avatar_split_clause,[],[f85,f22504]) ).
fof(f22504,plain,
( spl0_2002
<=> ! [X30,X18,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_plus(X30,c_times(X18,X19,tc_nat),tc_nat),X19,tc_nat) = c_plus(X18,c_div(X30,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f85,axiom,
! [X18,X19,X30] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_plus(X30,c_times(X18,X19,tc_nat),tc_nat),X19,tc_nat) = c_plus(X18,c_div(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
fof(f22502,plain,
spl0_2001,
inference(avatar_split_clause,[],[f8,f22500]) ).
fof(f8,axiom,
! [X2,X0,X7] :
( ~ c_in(X2,v_A,t_a)
| ~ c_in(X7,v_A,t_a)
| c_lessequals(X0,v_A,tc_set(t_a))
| ~ c_lessequals(X0,c_Tarski_Ointerval(v_r,X2,X7,t_a),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) ).
fof(f21900,plain,
( spl0_2000
| ~ spl0_1333
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f21595,f21461,f10405,f21898]) ).
fof(f21898,plain,
( spl0_2000
<=> ! [X0] :
( v_A != c_insert(X0,c_emptyset,t_a)
| v_a = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f10405,plain,
( spl0_1333
<=> ! [X7,X5,X2,X1] :
( X2 = X7
| c_insert(X2,X1,X5) != c_insert(X7,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f21595,plain,
( ! [X0] :
( v_A != c_insert(X0,c_emptyset,t_a)
| v_a = X0 )
| ~ spl0_1333
| ~ spl0_1981 ),
inference(superposition,[],[f10406,f21463]) ).
fof(f10406,plain,
( ! [X2,X1,X7,X5] :
( c_insert(X2,X1,X5) != c_insert(X7,c_emptyset,X5)
| X2 = X7 )
| ~ spl0_1333 ),
inference(avatar_component_clause,[],[f10405]) ).
fof(f21896,plain,
( spl0_1999
| ~ spl0_1332
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f21594,f21461,f10401,f21894]) ).
fof(f21894,plain,
( spl0_1999
<=> ! [X0] :
( ~ c_lessequals(v_A,X0,tc_set(t_a))
| c_in(v_a,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f10401,plain,
( spl0_1332
<=> ! [X35,X4,X5,X1] :
( c_in(X4,X35,X5)
| ~ c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f21594,plain,
( ! [X0] :
( ~ c_lessequals(v_A,X0,tc_set(t_a))
| c_in(v_a,X0,t_a) )
| ~ spl0_1332
| ~ spl0_1981 ),
inference(superposition,[],[f10402,f21463]) ).
fof(f10402,plain,
( ! [X1,X4,X5,X35] :
( ~ c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5))
| c_in(X4,X35,X5) )
| ~ spl0_1332 ),
inference(avatar_component_clause,[],[f10401]) ).
fof(f21678,plain,
( ~ spl0_1998
| ~ spl0_801
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f21590,f21461,f7298,f21675]) ).
fof(f21675,plain,
( spl0_1998
<=> c_emptyset = v_A ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).
fof(f7298,plain,
( spl0_801
<=> ! [X2,X5,X1] : c_emptyset != c_insert(X2,X1,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f21590,plain,
( c_emptyset != v_A
| ~ spl0_801
| ~ spl0_1981 ),
inference(superposition,[],[f7299,f21463]) ).
fof(f7299,plain,
( ! [X2,X1,X5] : c_emptyset != c_insert(X2,X1,X5)
| ~ spl0_801 ),
inference(avatar_component_clause,[],[f7298]) ).
fof(f21663,plain,
( spl0_1997
| ~ spl0_771
| ~ spl0_780
| ~ spl0_1851
| ~ spl0_1996 ),
inference(avatar_split_clause,[],[f21659,f21655,f18917,f7213,f7177,f21661]) ).
fof(f21661,plain,
( spl0_1997
<=> ! [X30] :
( c_1 = c_Divides_Oop_Amod(X30,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X30,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).
fof(f7177,plain,
( spl0_771
<=> ! [X8] : c_plus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f7213,plain,
( spl0_780
<=> ! [X8] : c_plus(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f18917,plain,
( spl0_1851
<=> ! [X19] : c_plus(X19,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,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f21655,plain,
( spl0_1996
<=> ! [X30] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X30,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(X30,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_1996])]) ).
fof(f21659,plain,
( ! [X30] :
( c_1 = c_Divides_Oop_Amod(X30,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X30,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_771
| ~ spl0_780
| ~ spl0_1851
| ~ spl0_1996 ),
inference(forward_demodulation,[],[f21658,f19005]) ).
fof(f19005,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_771
| ~ spl0_780
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f18926,f7178]) ).
fof(f7178,plain,
( ! [X8] : c_plus(X8,c_0,tc_nat) = X8
| ~ spl0_771 ),
inference(avatar_component_clause,[],[f7177]) ).
fof(f18926,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_780
| ~ spl0_1851 ),
inference(superposition,[],[f18918,f7214]) ).
fof(f7214,plain,
( ! [X8] : c_plus(c_0,X8,tc_nat) = X8
| ~ spl0_780 ),
inference(avatar_component_clause,[],[f7213]) ).
fof(f18918,plain,
( ! [X19] : c_plus(X19,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,X19,tc_nat),tc_nat)
| ~ spl0_1851 ),
inference(avatar_component_clause,[],[f18917]) ).
fof(f21658,plain,
( ! [X30] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X30,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_771
| ~ spl0_780
| ~ spl0_1851
| ~ spl0_1996 ),
inference(forward_demodulation,[],[f21656,f19005]) ).
fof(f21656,plain,
( ! [X30] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X30,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(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_1996 ),
inference(avatar_component_clause,[],[f21655]) ).
fof(f21657,plain,
spl0_1996,
inference(avatar_split_clause,[],[f3116,f21655]) ).
fof(f3116,plain,
! [X30] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X30,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(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3115,f1021]) ).
fof(f1021,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(f3115,plain,
! [X30] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X30,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(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3114,f1019]) ).
fof(f1019,axiom,
! [X39] : c_Numeral_Obin__succ(c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X39),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3114,plain,
! [X30] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X30,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(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3113,f1021]) ).
fof(f3113,plain,
! [X30] :
( c_1 = c_Divides_Oop_Amod(X30,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(X30,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,[],[f3112,f1021]) ).
fof(f3112,plain,
! [X30] :
( c_1 = c_Divides_Oop_Amod(X30,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(X30,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,[],[f3111,f1019]) ).
fof(f3111,plain,
! [X30] :
( c_1 = c_Divides_Oop_Amod(X30,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(X30,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,[],[f840,f1021]) ).
fof(f840,axiom,
! [X30] :
( c_1 = c_Divides_Oop_Amod(X30,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(X30,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(f21630,plain,
( spl0_1995
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1994 ),
inference(avatar_split_clause,[],[f21626,f21623,f10445,f10140,f6747,f3739,f21628]) ).
fof(f21628,plain,
( spl0_1995
<=> ! [X18,X19,X30] : c_minus(X30,c_plus(X19,X18,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X19,X30,tc_nat),tc_nat),c_plus(c_1,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).
fof(f3739,plain,
( spl0_115
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f6747,plain,
( spl0_673
<=> ! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f10140,plain,
( spl0_1267
<=> ! [X30,X19] : c_IntDef_Oint(c_plus(X30,X19,tc_nat)) = c_plus(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f10445,plain,
( spl0_1343
<=> ! [X30] : c_plus(c_1,c_IntDef_Oint(X30),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f21623,plain,
( spl0_1994
<=> ! [X30,X18,X19] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X19,X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) = c_minus(X30,c_plus(X19,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).
fof(f21626,plain,
( ! [X18,X19,X30] : c_minus(X30,c_plus(X19,X18,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X19,X30,tc_nat),tc_nat),c_plus(c_1,X18,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1994 ),
inference(forward_demodulation,[],[f21624,f11255]) ).
fof(f11255,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343 ),
inference(forward_demodulation,[],[f11254,f6748]) ).
fof(f6748,plain,
( ! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8
| ~ spl0_673 ),
inference(avatar_component_clause,[],[f6747]) ).
fof(f11254,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_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343 ),
inference(forward_demodulation,[],[f11216,f10711]) ).
fof(f10711,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_115
| ~ spl0_1267 ),
inference(superposition,[],[f10141,f3741]) ).
fof(f3741,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f3739]) ).
fof(f10141,plain,
( ! [X19,X30] : c_IntDef_Oint(c_plus(X30,X19,tc_nat)) = c_plus(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint)
| ~ spl0_1267 ),
inference(avatar_component_clause,[],[f10140]) ).
fof(f11216,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_673
| ~ spl0_1343 ),
inference(superposition,[],[f6748,f10446]) ).
fof(f10446,plain,
( ! [X30] : c_plus(c_1,c_IntDef_Oint(X30),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat))
| ~ spl0_1343 ),
inference(avatar_component_clause,[],[f10445]) ).
fof(f21624,plain,
( ! [X18,X19,X30] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X19,X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) = c_minus(X30,c_plus(X19,X18,tc_nat),tc_nat)
| ~ spl0_1994 ),
inference(avatar_component_clause,[],[f21623]) ).
fof(f21625,plain,
spl0_1994,
inference(avatar_split_clause,[],[f3022,f21623]) ).
fof(f3022,plain,
! [X18,X19,X30] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X19,X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) = c_minus(X30,c_plus(X19,X18,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3021,f902]) ).
fof(f902,axiom,
! [X29,X18,X55] : c_minus(c_minus(X29,X55,tc_nat),X18,tc_nat) = c_minus(X29,c_plus(X55,X18,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f3021,plain,
! [X18,X19,X30] : c_minus(c_minus(X30,X19,tc_nat),X18,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X19,X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2846,f2815]) ).
fof(f2815,plain,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X41,tc_nat),tc_nat),X77,tc_nat),
inference(definition_unfolding,[],[f1405,f1409]) ).
fof(f1409,axiom,
! [X41] : c_Suc(X41) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X41,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f1405,axiom,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),tc_nat) = c_minus(c_Suc(X41),X77,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f2846,plain,
! [X18,X19,X30] : c_minus(c_minus(X30,X19,tc_nat),X18,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X19,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f883,f1409,f1409]) ).
fof(f883,axiom,
! [X18,X19,X30] : c_minus(c_minus(c_Suc(X30),X19,tc_nat),c_Suc(X18),tc_nat) = c_minus(c_minus(X30,X19,tc_nat),X18,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
fof(f21621,plain,
spl0_1993,
inference(avatar_split_clause,[],[f2971,f21619]) ).
fof(f21619,plain,
( spl0_1993
<=> ! [X4,X5,X8] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X4)),X5),X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).
fof(f2971,plain,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X4)),X5),X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ),
inference(definition_unfolding,[],[f1005,f994]) ).
fof(f1005,axiom,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(X4)),X5),X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f21617,plain,
spl0_1992,
inference(avatar_split_clause,[],[f2970,f21615]) ).
fof(f21615,plain,
( spl0_1992
<=> ! [X4,X5,X8] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).
fof(f2970,plain,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f1013,f994]) ).
fof(f1013,axiom,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f21613,plain,
spl0_1991,
inference(avatar_split_clause,[],[f2969,f21611]) ).
fof(f21611,plain,
( spl0_1991
<=> ! [X4,X5,X8] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f2969,plain,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ),
inference(definition_unfolding,[],[f1014,f994]) ).
fof(f1014,axiom,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(X8)),X5),X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f21609,plain,
spl0_1990,
inference(avatar_split_clause,[],[f2968,f21607]) ).
fof(f21607,plain,
( spl0_1990
<=> ! [X4,X5,X8] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X4)),X5),X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).
fof(f2968,plain,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,X4)),X5),X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ),
inference(definition_unfolding,[],[f1004,f994]) ).
fof(f1004,axiom,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(X4)),X5),X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_Numeral_Onumber__of(X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f21589,plain,
spl0_1989,
inference(avatar_split_clause,[],[f2948,f21587]) ).
fof(f21587,plain,
( spl0_1989
<=> ! [X35,X5,X1,X83] :
( ~ c_lessequals(X83,X35,tc_set(X5))
| ~ c_lessequals(X83,X1,tc_set(X5))
| c_lessequals(X83,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1989])]) ).
fof(f2948,plain,
! [X83,X1,X35,X5] :
( ~ c_lessequals(X83,X35,tc_set(X5))
| ~ c_lessequals(X83,X1,tc_set(X5))
| c_lessequals(X83,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)) ),
inference(definition_unfolding,[],[f1476,f1238]) ).
fof(f1238,axiom,
! [X1,X35,X5] : c_inter(X1,X35,X5) = c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f1476,axiom,
! [X83,X1,X35,X5] :
( ~ c_lessequals(X83,X35,tc_set(X5))
| ~ c_lessequals(X83,X1,tc_set(X5))
| c_lessequals(X83,c_inter(X1,X35,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
fof(f21585,plain,
spl0_1988,
inference(avatar_split_clause,[],[f2919,f21583]) ).
fof(f21583,plain,
( spl0_1988
<=> ! [X2,X5,X1,X35] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X2,X1,X5),X5),X35,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f2919,plain,
! [X2,X1,X5,X35] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X2,X1,X5),X5),X35,X5,X5) ),
inference(definition_unfolding,[],[f1546,f1238,f1238]) ).
fof(f1546,axiom,
! [X2,X1,X35,X5] :
( c_emptyset = c_inter(X1,X35,X5)
| c_emptyset != c_inter(c_insert(X2,X1,X5),X35,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
fof(f21581,plain,
spl0_1987,
inference(avatar_split_clause,[],[f2917,f21579]) ).
fof(f21579,plain,
( spl0_1987
<=> ! [X35,X7,X5,X1] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X1,X5),c_insert(X7,X35,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f2917,plain,
! [X1,X7,X5,X35] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X1,X5),c_insert(X7,X35,X5),X5,X5) ),
inference(definition_unfolding,[],[f1530,f1238,f1238]) ).
fof(f1530,axiom,
! [X1,X7,X35,X5] :
( c_emptyset = c_inter(X1,X35,X5)
| c_emptyset != c_inter(X1,c_insert(X7,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
fof(f21505,plain,
( spl0_1986
| ~ spl0_115
| ~ spl0_673
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1696
| ~ spl0_1985 ),
inference(avatar_split_clause,[],[f21501,f21497,f16039,f10445,f10140,f7177,f7153,f6747,f3739,f21503]) ).
fof(f21503,plain,
( spl0_1986
<=> ! [X29,X55] :
( c_List_Oupt(X29,c_plus(c_1,X55,tc_nat)) = c_append(c_List_Oupt(X29,X55),c_List_Oreplicate(c_1,X55,tc_nat),tc_nat)
| ~ c_lessequals(X29,X55,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).
fof(f7153,plain,
( spl0_765
<=> ! [X4,X21] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X4,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f16039,plain,
( spl0_1696
<=> ! [X4,X21,X19] : c_List_Olist_OCons(X4,c_List_Oreplicate(X19,X4,X21),X21) = c_List_Oreplicate(c_plus(c_1,X19,tc_nat),X4,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f21497,plain,
( spl0_1985
<=> ! [X29,X55] :
( ~ c_lessequals(X29,X55,tc_nat)
| c_append(c_List_Oupt(X29,X55),c_List_Olist_OCons(X55,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X29,c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).
fof(f21501,plain,
( ! [X29,X55] :
( c_List_Oupt(X29,c_plus(c_1,X55,tc_nat)) = c_append(c_List_Oupt(X29,X55),c_List_Oreplicate(c_1,X55,tc_nat),tc_nat)
| ~ c_lessequals(X29,X55,tc_nat) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1696
| ~ spl0_1985 ),
inference(forward_demodulation,[],[f21500,f16065]) ).
fof(f16065,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696 ),
inference(forward_demodulation,[],[f16042,f7178]) ).
fof(f16042,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_765
| ~ spl0_1696 ),
inference(superposition,[],[f16040,f7154]) ).
fof(f7154,plain,
( ! [X21,X4] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X4,X21)
| ~ spl0_765 ),
inference(avatar_component_clause,[],[f7153]) ).
fof(f16040,plain,
( ! [X21,X19,X4] : c_List_Olist_OCons(X4,c_List_Oreplicate(X19,X4,X21),X21) = c_List_Oreplicate(c_plus(c_1,X19,tc_nat),X4,X21)
| ~ spl0_1696 ),
inference(avatar_component_clause,[],[f16039]) ).
fof(f21500,plain,
( ! [X29,X55] :
( c_append(c_List_Oupt(X29,X55),c_List_Olist_OCons(X55,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X29,c_plus(c_1,X55,tc_nat))
| ~ c_lessequals(X29,X55,tc_nat) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1985 ),
inference(forward_demodulation,[],[f21498,f11255]) ).
fof(f21498,plain,
( ! [X29,X55] :
( ~ c_lessequals(X29,X55,tc_nat)
| c_append(c_List_Oupt(X29,X55),c_List_Olist_OCons(X55,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X29,c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat)) )
| ~ spl0_1985 ),
inference(avatar_component_clause,[],[f21497]) ).
fof(f21499,plain,
spl0_1985,
inference(avatar_split_clause,[],[f2887,f21497]) ).
fof(f2887,plain,
! [X29,X55] :
( ~ c_lessequals(X29,X55,tc_nat)
| c_append(c_List_Oupt(X29,X55),c_List_Olist_OCons(X55,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X29,c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f647,f1409]) ).
fof(f647,axiom,
! [X29,X55] :
( ~ c_lessequals(X29,X55,tc_nat)
| c_List_Oupt(X29,c_Suc(X55)) = c_append(c_List_Oupt(X29,X55),c_List_Olist_OCons(X55,c_List_Olist_ONil,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).
fof(f21495,plain,
spl0_1984,
inference(avatar_split_clause,[],[f2848,f21493]) ).
fof(f21493,plain,
( spl0_1984
<=> ! [X5,X1,X35] : c_union(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),X5) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f2848,plain,
! [X1,X5,X35] : c_union(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),X5) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)),
inference(definition_unfolding,[],[f1440,f1238]) ).
fof(f1440,axiom,
! [X1,X35,X5] : c_uminus(c_inter(X1,X35,X5),tc_set(X5)) = c_union(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
fof(f21491,plain,
spl0_1983,
inference(avatar_split_clause,[],[f2847,f21489]) ).
fof(f21489,plain,
( spl0_1983
<=> ! [X5,X1,X35] : c_uminus(c_union(X1,X35,X5),tc_set(X5)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X1,tc_set(X5)),X5),c_uminus(X35,tc_set(X5)),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f2847,plain,
! [X1,X35,X5] : c_uminus(c_union(X1,X35,X5),tc_set(X5)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X1,tc_set(X5)),X5),c_uminus(X35,tc_set(X5)),X5,X5),
inference(definition_unfolding,[],[f1442,f1238]) ).
fof(f1442,axiom,
! [X1,X35,X5] : c_uminus(c_union(X1,X35,X5),tc_set(X5)) = c_inter(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
fof(f21487,plain,
spl0_1982,
inference(avatar_split_clause,[],[f2841,f21485]) ).
fof(f21485,plain,
( spl0_1982
<=> ! [X44,X5,X19,X30] : c_List_Osublist(c_List_Osublist(X44,c_SetInterval_OlessThan(X30,tc_nat),X5),c_SetInterval_OlessThan(X19,tc_nat),X5) = c_List_Osublist(X44,c_SetInterval_OlessThan(c_Orderings_Omin(X19,X30,tc_nat),tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f2841,plain,
! [X44,X19,X5,X30] : c_List_Osublist(c_List_Osublist(X44,c_SetInterval_OlessThan(X30,tc_nat),X5),c_SetInterval_OlessThan(X19,tc_nat),X5) = c_List_Osublist(X44,c_SetInterval_OlessThan(c_Orderings_Omin(X19,X30,tc_nat),tc_nat),X5),
inference(definition_unfolding,[],[f641,f631,f631,f631]) ).
fof(f641,axiom,
! [X19,X44,X5,X30] : c_List_Otake(X19,c_List_Otake(X30,X44,X5),X5) = c_List_Otake(c_Orderings_Omin(X19,X30,tc_nat),X44,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).
fof(f21464,plain,
( spl0_1981
| ~ spl0_798
| ~ spl0_1913
| ~ spl0_1939 ),
inference(avatar_split_clause,[],[f21387,f21233,f20876,f7286,f21461]) ).
fof(f7286,plain,
( spl0_798
<=> ! [X5,X8] : c_union(X8,X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f20876,plain,
( spl0_1913
<=> ! [X0] : c_union(c_insert(v_a,X0,t_a),v_A,t_a) = c_union(X0,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f21233,plain,
( spl0_1939
<=> ! [X0] : c_union(X0,v_A,t_a) = c_union(X0,c_insert(v_a,v_A,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f21387,plain,
( v_A = c_insert(v_a,v_A,t_a)
| ~ spl0_798
| ~ spl0_1913
| ~ spl0_1939 ),
inference(forward_demodulation,[],[f21386,f7287]) ).
fof(f7287,plain,
( ! [X8,X5] : c_union(X8,X8,X5) = X8
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f7286]) ).
fof(f21386,plain,
( c_insert(v_a,v_A,t_a) = c_union(v_A,v_A,t_a)
| ~ spl0_798
| ~ spl0_1913
| ~ spl0_1939 ),
inference(forward_demodulation,[],[f21364,f20877]) ).
fof(f20877,plain,
( ! [X0] : c_union(c_insert(v_a,X0,t_a),v_A,t_a) = c_union(X0,v_A,t_a)
| ~ spl0_1913 ),
inference(avatar_component_clause,[],[f20876]) ).
fof(f21364,plain,
( c_insert(v_a,v_A,t_a) = c_union(c_insert(v_a,v_A,t_a),v_A,t_a)
| ~ spl0_798
| ~ spl0_1939 ),
inference(superposition,[],[f21234,f7287]) ).
fof(f21234,plain,
( ! [X0] : c_union(X0,v_A,t_a) = c_union(X0,c_insert(v_a,v_A,t_a),t_a)
| ~ spl0_1939 ),
inference(avatar_component_clause,[],[f21233]) ).
fof(f21459,plain,
( spl0_1980
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1979 ),
inference(avatar_split_clause,[],[f21455,f21450,f10445,f10140,f6747,f3739,f21457]) ).
fof(f21457,plain,
( spl0_1980
<=> ! [X30,X19] : c_plus(c_1,c_Orderings_Omin(X30,X19,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X30,tc_nat),c_plus(c_1,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).
fof(f21450,plain,
( spl0_1979
<=> ! [X30,X19] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X30,X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).
fof(f21455,plain,
( ! [X19,X30] : c_plus(c_1,c_Orderings_Omin(X30,X19,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X30,tc_nat),c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21454,f11255]) ).
fof(f21454,plain,
( ! [X19,X30] : c_plus(c_1,c_Orderings_Omin(X30,X19,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21453,f11255]) ).
fof(f21453,plain,
( ! [X19,X30] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X30,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21451,f11255]) ).
fof(f21451,plain,
( ! [X19,X30] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X30,X19,tc_nat),tc_nat),tc_nat)
| ~ spl0_1979 ),
inference(avatar_component_clause,[],[f21450]) ).
fof(f21452,plain,
spl0_1979,
inference(avatar_split_clause,[],[f2817,f21450]) ).
fof(f2817,plain,
! [X19,X30] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X30,X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f920,f1409,f1409,f1409]) ).
fof(f920,axiom,
! [X19,X30] : c_Orderings_Omin(c_Suc(X30),c_Suc(X19),tc_nat) = c_Suc(c_Orderings_Omin(X30,X19,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
fof(f21434,plain,
( spl0_1978
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f21430,f21425,f10445,f10140,f6747,f3739,f21432]) ).
fof(f21432,plain,
( spl0_1978
<=> ! [X30,X19] : c_plus(c_1,c_Orderings_Omax(X30,X19,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X30,tc_nat),c_plus(c_1,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f21425,plain,
( spl0_1977
<=> ! [X30,X19] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X30,X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f21430,plain,
( ! [X19,X30] : c_plus(c_1,c_Orderings_Omax(X30,X19,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X30,tc_nat),c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1977 ),
inference(forward_demodulation,[],[f21429,f11255]) ).
fof(f21429,plain,
( ! [X19,X30] : c_plus(c_1,c_Orderings_Omax(X30,X19,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1977 ),
inference(forward_demodulation,[],[f21428,f11255]) ).
fof(f21428,plain,
( ! [X19,X30] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X30,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1977 ),
inference(forward_demodulation,[],[f21426,f11255]) ).
fof(f21426,plain,
( ! [X19,X30] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X30,X19,tc_nat),tc_nat),tc_nat)
| ~ spl0_1977 ),
inference(avatar_component_clause,[],[f21425]) ).
fof(f21427,plain,
spl0_1977,
inference(avatar_split_clause,[],[f2816,f21425]) ).
fof(f2816,plain,
! [X19,X30] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X30,X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f917,f1409,f1409,f1409]) ).
fof(f917,axiom,
! [X19,X30] : c_Orderings_Omax(c_Suc(X30),c_Suc(X19),tc_nat) = c_Suc(c_Orderings_Omax(X30,X19,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
fof(f21423,plain,
spl0_1976,
inference(avatar_split_clause,[],[f1671,f21421]) ).
fof(f21421,plain,
( spl0_1976
<=> ! [X5,X1,X31] :
( ~ c_in(X31,c_Relation_Odiag(X1,X5),tc_prod(X5,X5))
| c_Pair(c_Main_OdiagE__1(X1,X31,X5),c_Main_OdiagE__1(X1,X31,X5),X5,X5) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f1671,axiom,
! [X31,X1,X5] :
( ~ c_in(X31,c_Relation_Odiag(X1,X5),tc_prod(X5,X5))
| c_Pair(c_Main_OdiagE__1(X1,X31,X5),c_Main_OdiagE__1(X1,X31,X5),X5,X5) = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f21419,plain,
spl0_1975,
inference(avatar_split_clause,[],[f1667,f21417]) ).
fof(f21417,plain,
( spl0_1975
<=> ! [X5,X23,X6,X7] :
( ~ c_in(X7,c_Relation_ORange(X6,X23,X5),X5)
| c_in(c_Pair(c_Main_ORangeE__1(X7,X6,X5,X23),X7,X23,X5),X6,tc_prod(X23,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).
fof(f1667,axiom,
! [X6,X7,X5,X23] :
( ~ c_in(X7,c_Relation_ORange(X6,X23,X5),X5)
| c_in(c_Pair(c_Main_ORangeE__1(X7,X6,X5,X23),X7,X23,X5),X6,tc_prod(X23,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f21415,plain,
spl0_1974,
inference(avatar_split_clause,[],[f1661,f21413]) ).
fof(f21413,plain,
( spl0_1974
<=> ! [X5,X23,X6,X2] :
( ~ c_in(X2,c_Relation_ODomain(X6,X5,X23),X5)
| c_in(c_Pair(X2,c_Main_ODomainE__1(X2,X6,X5,X23),X5,X23),X6,tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).
fof(f1661,axiom,
! [X2,X6,X5,X23] :
( ~ c_in(X2,c_Relation_ODomain(X6,X5,X23),X5)
| c_in(c_Pair(X2,c_Main_ODomainE__1(X2,X6,X5,X23),X5,X23),X6,tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f21411,plain,
spl0_1973,
inference(avatar_split_clause,[],[f1652,f21409]) ).
fof(f21409,plain,
( spl0_1973
<=> ! [X77,X5,X2,X1] :
( ~ c_in(X2,X1,X5)
| ~ c_in(X77,c_List_Olists(X1,X5),tc_List_Olist(X5))
| c_in(c_List_Olist_OCons(X2,X77,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).
fof(f1652,axiom,
! [X2,X1,X77,X5] :
( ~ c_in(X2,X1,X5)
| ~ c_in(X77,c_List_Olists(X1,X5),tc_List_Olist(X5))
| c_in(c_List_Olist_OCons(X2,X77,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f21407,plain,
spl0_1972,
inference(avatar_split_clause,[],[f1614,f21405]) ).
fof(f21405,plain,
( spl0_1972
<=> ! [X35,X23,X5,X25,X1] :
( ~ c_in(X25,X35,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Datatype__Universe_OIn1(X25,X5,X23),c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f1614,axiom,
! [X1,X35,X25,X5,X23] :
( ~ c_in(X25,X35,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Datatype__Universe_OIn1(X25,X5,X23),c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f21363,plain,
spl0_1971,
inference(avatar_split_clause,[],[f1613,f21361]) ).
fof(f21361,plain,
( spl0_1971
<=> ! [X24,X23,X5,X35,X1] :
( ~ c_in(X24,X1,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Datatype__Universe_OIn0(X24,X5,X23),c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).
fof(f1613,axiom,
! [X1,X24,X5,X35,X23] :
( ~ c_in(X24,X1,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Datatype__Universe_OIn0(X24,X5,X23),c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f21359,plain,
spl0_1970,
inference(avatar_split_clause,[],[f1431,f21357]) ).
fof(f21357,plain,
( spl0_1970
<=> ! [X5,X55,X29,X19,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X30,X29,X5)
| ~ c_lessequals(X55,X19,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f1431,axiom,
! [X29,X19,X55,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X30,X29,X5)
| ~ c_lessequals(X55,X19,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
fof(f21355,plain,
spl0_1969,
inference(avatar_split_clause,[],[f1429,f21353]) ).
fof(f21353,plain,
( spl0_1969
<=> ! [X5,X55,X29,X19,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X55,X29,X5)
| c_lessequals(X55,X19,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f1429,axiom,
! [X29,X19,X55,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X55,X29,X5)
| c_lessequals(X55,X19,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
fof(f21351,plain,
spl0_1968,
inference(avatar_split_clause,[],[f1428,f21349]) ).
fof(f21349,plain,
( spl0_1968
<=> ! [X5,X55,X29,X19,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X55,X29,X5)
| c_lessequals(X30,X29,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).
fof(f1428,axiom,
! [X29,X19,X55,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X55,X29,X5)
| c_lessequals(X30,X29,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
fof(f21347,plain,
spl0_1967,
inference(avatar_split_clause,[],[f1241,f21345]) ).
fof(f21345,plain,
( spl0_1967
<=> ! [X5,X23,X6,X2,X7] :
( ~ c_in(c_Pair(X2,X7,X23,X5),X6,tc_prod(X23,X5))
| c_in(X7,c_Relation_OImage(X6,c_insert(X2,c_emptyset,X23),X23,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f1241,axiom,
! [X2,X6,X7,X5,X23] :
( ~ c_in(c_Pair(X2,X7,X23,X5),X6,tc_prod(X23,X5))
| c_in(X7,c_Relation_OImage(X6,c_insert(X2,c_emptyset,X23),X23,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
fof(f21343,plain,
spl0_1966,
inference(avatar_split_clause,[],[f1240,f21341]) ).
fof(f21341,plain,
( spl0_1966
<=> ! [X5,X23,X6,X2,X7] :
( c_in(c_Pair(X2,X7,X23,X5),X6,tc_prod(X23,X5))
| ~ c_in(X7,c_Relation_OImage(X6,c_insert(X2,c_emptyset,X23),X23,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f1240,axiom,
! [X2,X6,X7,X5,X23] :
( c_in(c_Pair(X2,X7,X23,X5),X6,tc_prod(X23,X5))
| ~ c_in(X7,c_Relation_OImage(X6,c_insert(X2,c_emptyset,X23),X23,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
fof(f21339,plain,
spl0_1965,
inference(avatar_split_clause,[],[f1200,f21337]) ).
fof(f21337,plain,
( spl0_1965
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X4
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
fof(f1200,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X4
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f21335,plain,
spl0_1964,
inference(avatar_split_clause,[],[f1183,f21333]) ).
fof(f21333,plain,
( spl0_1964
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X4
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f1183,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X4
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f21331,plain,
spl0_1963,
inference(avatar_split_clause,[],[f1039,f21329]) ).
fof(f21329,plain,
( spl0_1963
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_plus(c_HOL_Oabs(X2,X5),c_HOL_Oabs(X7,X5),X5) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X2,X5),c_HOL_Oabs(X7,X5),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).
fof(f1039,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_plus(c_HOL_Oabs(X2,X5),c_HOL_Oabs(X7,X5),X5) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X2,X5),c_HOL_Oabs(X7,X5),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f21327,plain,
spl0_1962,
inference(avatar_split_clause,[],[f986,f21325]) ).
fof(f21325,plain,
( spl0_1962
<=> ! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_HOL_Oabs(c_Numeral_Onumber__of(X4,X5),X5) = c_uminus(c_Numeral_Onumber__of(X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f986,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_HOL_Oabs(c_Numeral_Onumber__of(X4,X5),X5) = c_uminus(c_Numeral_Onumber__of(X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f21323,plain,
( spl0_1961
| ~ spl0_1026
| ~ spl0_1914 ),
inference(avatar_split_clause,[],[f21179,f21008,f8400,f21321]) ).
fof(f21321,plain,
( spl0_1961
<=> ! [X0] :
( c_emptyset != c_union(v_A,X0,t_a)
| c_emptyset = c_insert(v_a,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f8400,plain,
( spl0_1026
<=> ! [X5,X1,X35] :
( c_emptyset = X35
| c_emptyset != c_union(X1,X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f21008,plain,
( spl0_1914
<=> ! [X0] : c_union(v_A,c_insert(v_a,X0,t_a),t_a) = c_union(v_A,X0,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f21179,plain,
( ! [X0] :
( c_emptyset != c_union(v_A,X0,t_a)
| c_emptyset = c_insert(v_a,X0,t_a) )
| ~ spl0_1026
| ~ spl0_1914 ),
inference(superposition,[],[f8401,f21009]) ).
fof(f21009,plain,
( ! [X0] : c_union(v_A,c_insert(v_a,X0,t_a),t_a) = c_union(v_A,X0,t_a)
| ~ spl0_1914 ),
inference(avatar_component_clause,[],[f21008]) ).
fof(f8401,plain,
( ! [X1,X35,X5] :
( c_emptyset != c_union(X1,X35,X5)
| c_emptyset = X35 )
| ~ spl0_1026 ),
inference(avatar_component_clause,[],[f8400]) ).
fof(f21319,plain,
spl0_1960,
inference(avatar_split_clause,[],[f675,f21317]) ).
fof(f21317,plain,
( spl0_1960
<=> ! [X5,X19,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_lessequals(X19,X30,tc_nat)
| c_NatArith_Oof__nat(c_minus(X30,X19,tc_nat),X5) = c_minus(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f675,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_lessequals(X19,X30,tc_nat)
| c_NatArith_Oof__nat(c_minus(X30,X19,tc_nat),X5) = c_minus(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
fof(f21315,plain,
spl0_1959,
inference(avatar_split_clause,[],[f537,f21313]) ).
fof(f21313,plain,
( spl0_1959
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X8,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f537,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X68,X8,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X8,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).
fof(f21311,plain,
spl0_1958,
inference(avatar_split_clause,[],[f536,f21309]) ).
fof(f21309,plain,
( spl0_1958
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X8,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble7,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f536,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X8,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble7,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).
fof(f21307,plain,
spl0_1957,
inference(avatar_split_clause,[],[f535,f21305]) ).
fof(f21305,plain,
( spl0_1957
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X32,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X8,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble6,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f535,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X74,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X8,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble6,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).
fof(f21303,plain,
spl0_1956,
inference(avatar_split_clause,[],[f534,f21301]) ).
fof(f21301,plain,
( spl0_1956
<=> ! [X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X64,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X8,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f534,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X8,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble5,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).
fof(f21299,plain,
spl0_1955,
inference(avatar_split_clause,[],[f533,f21297]) ).
fof(f21297,plain,
( spl0_1955
<=> ! [X64,X32,X33,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X8,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble4,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f533,axiom,
! [X74,X75,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X8,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble4,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).
fof(f21295,plain,
spl0_1954,
inference(avatar_split_clause,[],[f532,f21293]) ).
fof(f21293,plain,
( spl0_1954
<=> ! [X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X8,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble3,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f532,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X67,X33,X74] : c_List_Onibble_Onibble__rec(X33,X32,X63,X8,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble3,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).
fof(f21291,plain,
spl0_1953,
inference(avatar_split_clause,[],[f531,f21289]) ).
fof(f21289,plain,
( spl0_1953
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X8,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble2,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f531,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X8,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble2,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).
fof(f21287,plain,
spl0_1952,
inference(avatar_split_clause,[],[f530,f21285]) ).
fof(f21285,plain,
( spl0_1952
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X8,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble1,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f530,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X67,X74,X33,X64] : c_List_Onibble_Onibble__rec(X33,X8,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble1,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).
fof(f21283,plain,
spl0_1951,
inference(avatar_split_clause,[],[f529,f21281]) ).
fof(f21281,plain,
( spl0_1951
<=> ! [X64,X32,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X8,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f529,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X67,X64,X74] : c_List_Onibble_Onibble__rec(X8,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble0,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).
fof(f21279,plain,
( spl0_1950
| ~ spl0_1025
| ~ spl0_1913 ),
inference(avatar_split_clause,[],[f21120,f20876,f8396,f21277]) ).
fof(f21277,plain,
( spl0_1950
<=> ! [X0] :
( c_emptyset != c_union(X0,v_A,t_a)
| c_emptyset = c_insert(v_a,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f8396,plain,
( spl0_1025
<=> ! [X5,X1,X35] :
( c_emptyset = X1
| c_emptyset != c_union(X1,X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f21120,plain,
( ! [X0] :
( c_emptyset != c_union(X0,v_A,t_a)
| c_emptyset = c_insert(v_a,X0,t_a) )
| ~ spl0_1025
| ~ spl0_1913 ),
inference(superposition,[],[f8397,f20877]) ).
fof(f8397,plain,
( ! [X1,X35,X5] :
( c_emptyset != c_union(X1,X35,X5)
| c_emptyset = X1 )
| ~ spl0_1025 ),
inference(avatar_component_clause,[],[f8396]) ).
fof(f21275,plain,
spl0_1949,
inference(avatar_split_clause,[],[f528,f21273]) ).
fof(f21273,plain,
( spl0_1949
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X32] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X8,c_List_Onibble_ONibbleF,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f528,axiom,
! [X74,X65,X72,X70,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X8,c_List_Onibble_ONibbleF,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).
fof(f21271,plain,
spl0_1948,
inference(avatar_split_clause,[],[f527,f21269]) ).
fof(f21269,plain,
( spl0_1948
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X32,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X8,X75,c_List_Onibble_ONibbleE,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f527,axiom,
! [X75,X65,X72,X70,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X8,X75,c_List_Onibble_ONibbleE,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).
fof(f21267,plain,
spl0_1947,
inference(avatar_split_clause,[],[f526,f21265]) ).
fof(f21265,plain,
( spl0_1947
<=> ! [X64,X32,X33,X65,X72,X70,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X8,X74,X75,c_List_Onibble_ONibbleD,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f526,axiom,
! [X74,X75,X65,X72,X70,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X8,X74,X75,c_List_Onibble_ONibbleD,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).
fof(f21263,plain,
spl0_1946,
inference(avatar_split_clause,[],[f525,f21261]) ).
fof(f21261,plain,
( spl0_1946
<=> ! [X64,X32,X33,X65,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X8,X73,X74,X75,c_List_Onibble_ONibbleC,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f525,axiom,
! [X74,X75,X65,X70,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X8,X73,X74,X75,c_List_Onibble_ONibbleC,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).
fof(f21259,plain,
spl0_1945,
inference(avatar_split_clause,[],[f524,f21257]) ).
fof(f21257,plain,
( spl0_1945
<=> ! [X64,X32,X33,X65,X72,X70,X73,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X8,X72,X73,X74,X75,c_List_Onibble_ONibbleB,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f524,axiom,
! [X74,X75,X65,X72,X70,X73,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X8,X72,X73,X74,X75,c_List_Onibble_ONibbleB,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).
fof(f21255,plain,
spl0_1944,
inference(avatar_split_clause,[],[f523,f21253]) ).
fof(f21253,plain,
( spl0_1944
<=> ! [X64,X32,X33,X65,X72,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X8,X71,X72,X73,X74,X75,c_List_Onibble_ONibbleA,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f523,axiom,
! [X74,X75,X65,X72,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X8,X71,X72,X73,X74,X75,c_List_Onibble_ONibbleA,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).
fof(f21251,plain,
spl0_1943,
inference(avatar_split_clause,[],[f522,f21249]) ).
fof(f21249,plain,
( spl0_1943
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X69,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X8,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble9,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f522,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X68,X8,X69,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__rec(X33,X32,X63,X64,X65,X66,X67,X68,X69,X8,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble9,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).
fof(f21247,plain,
spl0_1942,
inference(avatar_split_clause,[],[f521,f21245]) ).
fof(f21245,plain,
( spl0_1942
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X8,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f521,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X68,X8,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X8,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).
fof(f21243,plain,
spl0_1941,
inference(avatar_split_clause,[],[f520,f21241]) ).
fof(f21241,plain,
( spl0_1941
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X8,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble7,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f520,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X8,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble7,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).
fof(f21239,plain,
spl0_1940,
inference(avatar_split_clause,[],[f519,f21237]) ).
fof(f21237,plain,
( spl0_1940
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X32,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X8,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble6,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f519,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X74,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X8,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble6,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).
fof(f21235,plain,
( spl0_1939
| ~ spl0_1614
| ~ spl0_1913 ),
inference(avatar_split_clause,[],[f21119,f20876,f14495,f21233]) ).
fof(f14495,plain,
( spl0_1614
<=> ! [X35,X5,X2,X83] : c_union(c_insert(X2,X35,X5),X83,X5) = c_union(X35,c_insert(X2,X83,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f21119,plain,
( ! [X0] : c_union(X0,v_A,t_a) = c_union(X0,c_insert(v_a,v_A,t_a),t_a)
| ~ spl0_1614
| ~ spl0_1913 ),
inference(superposition,[],[f20877,f14496]) ).
fof(f14496,plain,
( ! [X2,X83,X35,X5] : c_union(c_insert(X2,X35,X5),X83,X5) = c_union(X35,c_insert(X2,X83,X5),X5)
| ~ spl0_1614 ),
inference(avatar_component_clause,[],[f14495]) ).
fof(f21231,plain,
spl0_1938,
inference(avatar_split_clause,[],[f518,f21229]) ).
fof(f21229,plain,
( spl0_1938
<=> ! [X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X64,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X8,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f518,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X8,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble5,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).
fof(f21227,plain,
spl0_1937,
inference(avatar_split_clause,[],[f517,f21225]) ).
fof(f21225,plain,
( spl0_1937
<=> ! [X64,X32,X33,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X8,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble4,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f517,axiom,
! [X74,X75,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X8,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble4,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).
fof(f21223,plain,
spl0_1936,
inference(avatar_split_clause,[],[f516,f21221]) ).
fof(f21221,plain,
( spl0_1936
<=> ! [X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X8,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble3,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f516,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X67,X33,X74] : c_List_Onibble_Onibble__case(X33,X32,X63,X8,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble3,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).
fof(f21219,plain,
spl0_1935,
inference(avatar_split_clause,[],[f515,f21217]) ).
fof(f21217,plain,
( spl0_1935
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X8,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble2,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f515,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X8,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble2,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).
fof(f21215,plain,
spl0_1934,
inference(avatar_split_clause,[],[f514,f21213]) ).
fof(f21213,plain,
( spl0_1934
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X8,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble1,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f514,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X67,X74,X33,X64] : c_List_Onibble_Onibble__case(X33,X8,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble1,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).
fof(f21211,plain,
spl0_1933,
inference(avatar_split_clause,[],[f513,f21209]) ).
fof(f21209,plain,
( spl0_1933
<=> ! [X64,X32,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X8,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f513,axiom,
! [X75,X65,X72,X70,X73,X71,X8,X68,X69,X76,X63,X66,X5,X32,X67,X64,X74] : c_List_Onibble_Onibble__case(X8,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble0,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).
fof(f21207,plain,
spl0_1932,
inference(avatar_split_clause,[],[f512,f21205]) ).
fof(f21205,plain,
( spl0_1932
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X32] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X8,c_List_Onibble_ONibbleF,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f512,axiom,
! [X74,X65,X72,X70,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X74,X8,c_List_Onibble_ONibbleF,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).
fof(f21203,plain,
spl0_1931,
inference(avatar_split_clause,[],[f511,f21201]) ).
fof(f21201,plain,
( spl0_1931
<=> ! [X64,X33,X65,X72,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X32,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X8,X75,c_List_Onibble_ONibbleE,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f511,axiom,
! [X75,X65,X72,X70,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X73,X8,X75,c_List_Onibble_ONibbleE,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).
fof(f21199,plain,
spl0_1930,
inference(avatar_split_clause,[],[f510,f21197]) ).
fof(f21197,plain,
( spl0_1930
<=> ! [X64,X32,X33,X65,X72,X70,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X8,X74,X75,c_List_Onibble_ONibbleD,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f510,axiom,
! [X74,X75,X65,X72,X70,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X72,X8,X74,X75,c_List_Onibble_ONibbleD,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).
fof(f21195,plain,
spl0_1929,
inference(avatar_split_clause,[],[f509,f21193]) ).
fof(f21193,plain,
( spl0_1929
<=> ! [X64,X32,X33,X65,X70,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X8,X73,X74,X75,c_List_Onibble_ONibbleC,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f509,axiom,
! [X74,X75,X65,X70,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X71,X8,X73,X74,X75,c_List_Onibble_ONibbleC,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).
fof(f21174,plain,
spl0_1928,
inference(avatar_split_clause,[],[f508,f21172]) ).
fof(f21172,plain,
( spl0_1928
<=> ! [X64,X32,X33,X65,X72,X70,X73,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X8,X72,X73,X74,X75,c_List_Onibble_ONibbleB,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f508,axiom,
! [X74,X75,X65,X72,X70,X73,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X70,X8,X72,X73,X74,X75,c_List_Onibble_ONibbleB,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).
fof(f21170,plain,
spl0_1927,
inference(avatar_split_clause,[],[f507,f21168]) ).
fof(f21168,plain,
( spl0_1927
<=> ! [X64,X32,X33,X65,X72,X73,X71,X8,X69,X76,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X8,X71,X72,X73,X74,X75,c_List_Onibble_ONibbleA,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f507,axiom,
! [X74,X75,X65,X72,X73,X71,X68,X8,X69,X76,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X76,X8,X71,X72,X73,X74,X75,c_List_Onibble_ONibbleA,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).
fof(f21166,plain,
spl0_1926,
inference(avatar_split_clause,[],[f506,f21164]) ).
fof(f21164,plain,
( spl0_1926
<=> ! [X64,X32,X33,X65,X72,X70,X73,X71,X8,X69,X68,X63,X5,X67,X74,X66,X75] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X8,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble9,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f506,axiom,
! [X74,X75,X65,X72,X70,X73,X71,X68,X8,X69,X63,X66,X5,X32,X67,X33,X64] : c_List_Onibble_Onibble__case(X33,X32,X63,X64,X65,X66,X67,X68,X69,X8,X70,X71,X72,X73,X74,X75,c_List_Onibble_ONibble9,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).
fof(f21162,plain,
spl0_1925,
inference(avatar_split_clause,[],[f494,f21160]) ).
fof(f21160,plain,
( spl0_1925
<=> ! [X61,X21,X56,X2] :
( ~ c_in(X2,c_List_Oset(X61,X21),X21)
| c_List_Olist__inter(c_List_Olist_OCons(X2,X56,X21),X61,X21) = c_List_Olist_OCons(X2,c_List_Olist__inter(X56,X61,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f494,axiom,
! [X2,X21,X56,X61] :
( ~ c_in(X2,c_List_Oset(X61,X21),X21)
| c_List_Olist__inter(c_List_Olist_OCons(X2,X56,X21),X61,X21) = c_List_Olist_OCons(X2,c_List_Olist__inter(X56,X61,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
fof(f21158,plain,
spl0_1924,
inference(avatar_split_clause,[],[f479,f21156]) ).
fof(f21156,plain,
( spl0_1924
<=> ! [X44,X23,X5,X45] : c_Nat_Osize(c_List_Ozip(X44,X45,X5,X23),tc_List_Olist(tc_prod(X5,X23))) = c_Orderings_Omin(c_Nat_Osize(X44,tc_List_Olist(X5)),c_Nat_Osize(X45,tc_List_Olist(X23)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f479,axiom,
! [X44,X45,X5,X23] : c_Nat_Osize(c_List_Ozip(X44,X45,X5,X23),tc_List_Olist(tc_prod(X5,X23))) = c_Orderings_Omin(c_Nat_Osize(X44,tc_List_Olist(X5)),c_Nat_Osize(X45,tc_List_Olist(X23)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
fof(f21154,plain,
spl0_1923,
inference(avatar_split_clause,[],[f388,f21152]) ).
fof(f21152,plain,
( spl0_1923
<=> ! [X48,X49,X44,X5,X45] :
( X48 = X49
| c_Nat_Osize(X48,tc_List_Olist(X5)) != c_Nat_Osize(X49,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f388,axiom,
! [X48,X49,X44,X45,X5] :
( X48 = X49
| c_Nat_Osize(X48,tc_List_Olist(X5)) != c_Nat_Osize(X49,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
fof(f21150,plain,
spl0_1922,
inference(avatar_split_clause,[],[f387,f21148]) ).
fof(f21148,plain,
( spl0_1922
<=> ! [X44,X49,X5,X48,X45] :
( X44 = X45
| c_Nat_Osize(X48,tc_List_Olist(X5)) != c_Nat_Osize(X49,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f387,axiom,
! [X48,X49,X44,X45,X5] :
( X44 = X45
| c_Nat_Osize(X48,tc_List_Olist(X5)) != c_Nat_Osize(X49,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
fof(f21146,plain,
spl0_1921,
inference(avatar_split_clause,[],[f386,f21144]) ).
fof(f21144,plain,
( spl0_1921
<=> ! [X48,X49,X44,X5,X45] :
( X48 = X49
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f386,axiom,
! [X48,X49,X44,X45,X5] :
( X48 = X49
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
fof(f21142,plain,
spl0_1920,
inference(avatar_split_clause,[],[f385,f21140]) ).
fof(f21140,plain,
( spl0_1920
<=> ! [X44,X49,X5,X48,X45] :
( X44 = X45
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f385,axiom,
! [X48,X49,X44,X45,X5] :
( X44 = X45
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X5))
| c_append(X44,X48,X5) != c_append(X45,X49,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
fof(f21138,plain,
spl0_1919,
inference(avatar_split_clause,[],[f333,f21136]) ).
fof(f21136,plain,
( spl0_1919
<=> ! [X40,X39] : c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f333,axiom,
! [X40,X39] : c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X39,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(f21115,plain,
spl0_1918,
inference(avatar_split_clause,[],[f148,f21113]) ).
fof(f21113,plain,
( spl0_1918
<=> ! [X35,X5,X2,X1] :
( ~ c_in(c_minus(X1,X35,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X1,c_insert(X2,X35,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f148,axiom,
! [X2,X1,X35,X5] :
( ~ c_in(c_minus(X1,X35,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X1,c_insert(X2,X35,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f21111,plain,
spl0_1917,
inference(avatar_split_clause,[],[f147,f21109]) ).
fof(f21109,plain,
( spl0_1917
<=> ! [X35,X5,X2,X1] :
( c_in(c_minus(X1,X35,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_minus(X1,c_insert(X2,X35,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f147,axiom,
! [X2,X1,X35,X5] :
( c_in(c_minus(X1,X35,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_minus(X1,c_insert(X2,X35,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f21018,plain,
( spl0_1916
| ~ spl0_58
| ~ spl0_1452
| ~ spl0_1897 ),
inference(avatar_split_clause,[],[f20583,f20580,f11747,f3460,f21016]) ).
fof(f21016,plain,
( spl0_1916
<=> ! [X80,X40] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f3460,plain,
( spl0_58
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f11747,plain,
( spl0_1452
<=> ! [X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X39),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f20580,plain,
( spl0_1897
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f20583,plain,
( ! [X40,X80] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) )
| ~ spl0_58
| ~ spl0_1452
| ~ spl0_1897 ),
inference(forward_demodulation,[],[f20581,f12825]) ).
fof(f12825,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_58
| ~ spl0_1452 ),
inference(resolution,[],[f11748,f3462]) ).
fof(f3462,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f3460]) ).
fof(f11748,plain,
( ! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X39),X5) )
| ~ spl0_1452 ),
inference(avatar_component_clause,[],[f11747]) ).
fof(f20581,plain,
( ! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) )
| ~ spl0_1897 ),
inference(avatar_component_clause,[],[f20580]) ).
fof(f21014,plain,
( spl0_1915
| ~ spl0_58
| ~ spl0_1452
| ~ spl0_1896 ),
inference(avatar_split_clause,[],[f20578,f20575,f11747,f3460,f21012]) ).
fof(f21012,plain,
( spl0_1915
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f20575,plain,
( spl0_1896
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f20578,plain,
( ! [X40,X80] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) )
| ~ spl0_58
| ~ spl0_1452
| ~ spl0_1896 ),
inference(forward_demodulation,[],[f20576,f12825]) ).
fof(f20576,plain,
( ! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) )
| ~ spl0_1896 ),
inference(avatar_component_clause,[],[f20575]) ).
fof(f21010,plain,
( spl0_1914
| ~ spl0_1432
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f20719,f20519,f11642,f21008]) ).
fof(f11642,plain,
( spl0_1432
<=> ! [X5,X1,X35] : c_union(X1,X35,X5) = c_union(X1,c_minus(X35,X1,tc_set(X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f20519,plain,
( spl0_1882
<=> ! [X0] : c_minus(X0,v_A,tc_set(t_a)) = c_minus(c_insert(v_a,X0,t_a),v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f20719,plain,
( ! [X0] : c_union(v_A,c_insert(v_a,X0,t_a),t_a) = c_union(v_A,X0,t_a)
| ~ spl0_1432
| ~ spl0_1882 ),
inference(forward_demodulation,[],[f20705,f11643]) ).
fof(f11643,plain,
( ! [X1,X35,X5] : c_union(X1,X35,X5) = c_union(X1,c_minus(X35,X1,tc_set(X5)),X5)
| ~ spl0_1432 ),
inference(avatar_component_clause,[],[f11642]) ).
fof(f20705,plain,
( ! [X0] : c_union(v_A,c_insert(v_a,X0,t_a),t_a) = c_union(v_A,c_minus(X0,v_A,tc_set(t_a)),t_a)
| ~ spl0_1432
| ~ spl0_1882 ),
inference(superposition,[],[f11643,f20520]) ).
fof(f20520,plain,
( ! [X0] : c_minus(X0,v_A,tc_set(t_a)) = c_minus(c_insert(v_a,X0,t_a),v_A,tc_set(t_a))
| ~ spl0_1882 ),
inference(avatar_component_clause,[],[f20519]) ).
fof(f20878,plain,
( spl0_1913
| ~ spl0_1431
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f20718,f20519,f11638,f20876]) ).
fof(f11638,plain,
( spl0_1431
<=> ! [X5,X1,X35] : c_union(c_minus(X35,X1,tc_set(X5)),X1,X5) = c_union(X35,X1,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f20718,plain,
( ! [X0] : c_union(c_insert(v_a,X0,t_a),v_A,t_a) = c_union(X0,v_A,t_a)
| ~ spl0_1431
| ~ spl0_1882 ),
inference(forward_demodulation,[],[f20704,f11639]) ).
fof(f11639,plain,
( ! [X1,X35,X5] : c_union(c_minus(X35,X1,tc_set(X5)),X1,X5) = c_union(X35,X1,X5)
| ~ spl0_1431 ),
inference(avatar_component_clause,[],[f11638]) ).
fof(f20704,plain,
( ! [X0] : c_union(c_insert(v_a,X0,t_a),v_A,t_a) = c_union(c_minus(X0,v_A,tc_set(t_a)),v_A,t_a)
| ~ spl0_1431
| ~ spl0_1882 ),
inference(superposition,[],[f11639,f20520]) ).
fof(f20729,plain,
( spl0_1912
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1911 ),
inference(avatar_split_clause,[],[f20725,f20722,f11811,f7579,f7221,f6994,f6890,f6880,f20727]) ).
fof(f20727,plain,
( spl0_1912
<=> ! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f6880,plain,
( spl0_702
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f6890,plain,
( spl0_704
<=> ! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f6994,plain,
( spl0_729
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f7221,plain,
( spl0_782
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f7579,plain,
( spl0_870
<=> ! [X39] : c_Numeral_Obin__add(c_Numeral_OMin,X39) = c_Numeral_Obin__add(X39,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f11811,plain,
( spl0_1457
<=> ! [X39] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X39)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f20722,plain,
( spl0_1911
<=> ! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f20725,plain,
( ! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) )
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1911 ),
inference(forward_demodulation,[],[f20723,f12849]) ).
fof(f12849,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457 ),
inference(forward_demodulation,[],[f12848,f6882]) ).
fof(f6882,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f6880]) ).
fof(f12848,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_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457 ),
inference(forward_demodulation,[],[f12847,f7223]) ).
fof(f7223,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_782 ),
inference(avatar_component_clause,[],[f7221]) ).
fof(f12847,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_704
| ~ spl0_729
| ~ spl0_870
| ~ spl0_1457 ),
inference(forward_demodulation,[],[f12846,f6891]) ).
fof(f6891,plain,
( ! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8
| ~ spl0_704 ),
inference(avatar_component_clause,[],[f6890]) ).
fof(f12846,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_729
| ~ spl0_870
| ~ spl0_1457 ),
inference(forward_demodulation,[],[f12840,f7580]) ).
fof(f7580,plain,
( ! [X39] : c_Numeral_Obin__add(c_Numeral_OMin,X39) = c_Numeral_Obin__add(X39,c_Numeral_OMin)
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f7579]) ).
fof(f12840,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_729
| ~ spl0_1457 ),
inference(superposition,[],[f11812,f6996]) ).
fof(f6996,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_729 ),
inference(avatar_component_clause,[],[f6994]) ).
fof(f11812,plain,
( ! [X39] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X39)),c_Numeral_Obit_OB1)
| ~ spl0_1457 ),
inference(avatar_component_clause,[],[f11811]) ).
fof(f20723,plain,
( ! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) )
| ~ spl0_1911 ),
inference(avatar_component_clause,[],[f20722]) ).
fof(f20724,plain,
spl0_1911,
inference(avatar_split_clause,[],[f3169,f20722]) ).
fof(f3169,plain,
! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2966,f1021]) ).
fof(f2966,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f184,f994]) ).
fof(f184,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
fof(f20697,plain,
spl0_1910,
inference(avatar_split_clause,[],[f3167,f20695]) ).
fof(f20695,plain,
( spl0_1910
<=> ! [X5,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f3167,plain,
! [X8,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2964,f1021]) ).
fof(f2964,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f180,f994]) ).
fof(f180,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
fof(f20693,plain,
spl0_1909,
inference(avatar_split_clause,[],[f3165,f20691]) ).
fof(f20691,plain,
( spl0_1909
<=> ! [X4,X5] :
( 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,X4)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f3165,plain,
! [X4,X5] :
( 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,X4)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2962,f1021]) ).
fof(f2962,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| 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,X4)),X5),X5) ),
inference(definition_unfolding,[],[f192,f994]) ).
fof(f192,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| 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(X4)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
fof(f20673,plain,
( spl0_1908
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1907 ),
inference(avatar_split_clause,[],[f20669,f20666,f11811,f7579,f7221,f6994,f6890,f6880,f20671]) ).
fof(f20671,plain,
( spl0_1908
<=> ! [X5,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f20666,plain,
( spl0_1907
<=> ! [X5,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f20669,plain,
( ! [X8,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) )
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1907 ),
inference(forward_demodulation,[],[f20667,f12849]) ).
fof(f20667,plain,
( ! [X8,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) )
| ~ spl0_1907 ),
inference(avatar_component_clause,[],[f20666]) ).
fof(f20668,plain,
spl0_1907,
inference(avatar_split_clause,[],[f3162,f20666]) ).
fof(f3162,plain,
! [X8,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2960,f1021]) ).
fof(f2960,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f188,f994]) ).
fof(f188,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
fof(f20648,plain,
( spl0_1906
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1905 ),
inference(avatar_split_clause,[],[f20644,f20641,f11811,f7579,f7221,f6994,f6890,f6880,f20646]) ).
fof(f20646,plain,
( spl0_1906
<=> ! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f20641,plain,
( spl0_1905
<=> ! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f20644,plain,
( ! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) )
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1905 ),
inference(forward_demodulation,[],[f20642,f12849]) ).
fof(f20642,plain,
( ! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) )
| ~ spl0_1905 ),
inference(avatar_component_clause,[],[f20641]) ).
fof(f20643,plain,
spl0_1905,
inference(avatar_split_clause,[],[f3159,f20641]) ).
fof(f3159,plain,
! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2958,f1021]) ).
fof(f2958,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f183,f994]) ).
fof(f183,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
fof(f20639,plain,
spl0_1904,
inference(avatar_split_clause,[],[f3157,f20637]) ).
fof(f20637,plain,
( spl0_1904
<=> ! [X5,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f3157,plain,
! [X8,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2956,f1021]) ).
fof(f2956,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f179,f994]) ).
fof(f179,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
fof(f20635,plain,
spl0_1903,
inference(avatar_split_clause,[],[f3155,f20633]) ).
fof(f20633,plain,
( spl0_1903
<=> ! [X4,X5] :
( ~ 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,X4)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f3155,plain,
! [X4,X5] :
( ~ 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,X4)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2954,f1021]) ).
fof(f2954,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| ~ 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,X4)),X5),X5) ),
inference(definition_unfolding,[],[f191,f994]) ).
fof(f191,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_1,X5)
| ~ 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(X4)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
fof(f20631,plain,
( spl0_1902
| ~ spl0_4
| ~ spl0_1855 ),
inference(avatar_split_clause,[],[f19995,f19912,f3190,f20629]) ).
fof(f20629,plain,
( spl0_1902
<=> ! [X0] :
( ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f3190,plain,
( spl0_4
<=> c_Tarski_OisLub(v_S,v_cl,v_L,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f19912,plain,
( spl0_1855
<=> ! [X0,X8,X3] :
( ~ c_in(X8,X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X3,t_a)
| c_in(c_Pair(X8,X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f19995,plain,
( ! [X0] :
( ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| ~ spl0_4
| ~ spl0_1855 ),
inference(resolution,[],[f19913,f3192]) ).
fof(f3192,plain,
( c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3190]) ).
fof(f19913,plain,
( ! [X3,X0,X8] :
( ~ c_Tarski_OisLub(X0,v_cl,X3,t_a)
| ~ c_in(X8,X0,t_a)
| c_in(c_Pair(X8,X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| ~ spl0_1855 ),
inference(avatar_component_clause,[],[f19912]) ).
fof(f20619,plain,
( spl0_1901
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1900 ),
inference(avatar_split_clause,[],[f20615,f20612,f11811,f7579,f7221,f6994,f6890,f6880,f20617]) ).
fof(f20617,plain,
( spl0_1901
<=> ! [X5,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f20612,plain,
( spl0_1900
<=> ! [X5,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f20615,plain,
( ! [X8,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) )
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1900 ),
inference(forward_demodulation,[],[f20613,f12849]) ).
fof(f20613,plain,
( ! [X8,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) )
| ~ spl0_1900 ),
inference(avatar_component_clause,[],[f20612]) ).
fof(f20614,plain,
spl0_1900,
inference(avatar_split_clause,[],[f3152,f20612]) ).
fof(f3152,plain,
! [X8,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2952,f1021]) ).
fof(f2952,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f187,f994]) ).
fof(f187,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
fof(f20593,plain,
( spl0_1899
| ~ spl0_58
| ~ spl0_1347
| ~ spl0_1898 ),
inference(avatar_split_clause,[],[f20589,f20585,f10464,f3460,f20591]) ).
fof(f20591,plain,
( spl0_1899
<=> ! [X4] :
( c_1 = c_Divides_Oop_Amod(X4,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X4,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f10464,plain,
( spl0_1347
<=> ! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f20585,plain,
( spl0_1898
<=> ! [X4] :
( c_0 = c_Divides_Oop_Amod(X4,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(X4,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_1898])]) ).
fof(f20589,plain,
( ! [X4] :
( c_1 = c_Divides_Oop_Amod(X4,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X4,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1347
| ~ spl0_1898 ),
inference(forward_demodulation,[],[f20588,f11327]) ).
fof(f11327,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_58
| ~ spl0_1347 ),
inference(resolution,[],[f10465,f3462]) ).
fof(f10465,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X5) )
| ~ spl0_1347 ),
inference(avatar_component_clause,[],[f10464]) ).
fof(f20588,plain,
( ! [X4] :
( c_0 = c_Divides_Oop_Amod(X4,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X4,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1347
| ~ spl0_1898 ),
inference(forward_demodulation,[],[f20586,f11327]) ).
fof(f20586,plain,
( ! [X4] :
( c_0 = c_Divides_Oop_Amod(X4,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(X4,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1898 ),
inference(avatar_component_clause,[],[f20585]) ).
fof(f20587,plain,
spl0_1898,
inference(avatar_split_clause,[],[f3110,f20585]) ).
fof(f3110,plain,
! [X4] :
( c_0 = c_Divides_Oop_Amod(X4,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(X4,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3109,f1021]) ).
fof(f3109,plain,
! [X4] :
( c_0 = c_Divides_Oop_Amod(X4,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(X4,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3108,f1019]) ).
fof(f3108,plain,
! [X4] :
( c_0 = c_Divides_Oop_Amod(X4,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(X4,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3107,f1021]) ).
fof(f3107,plain,
! [X4] :
( c_1 = c_Divides_Oop_Amod(X4,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(X4,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,[],[f3106,f1021]) ).
fof(f3106,plain,
! [X4] :
( c_1 = c_Divides_Oop_Amod(X4,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(X4,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,[],[f3105,f1019]) ).
fof(f3105,plain,
! [X4] :
( c_1 = c_Divides_Oop_Amod(X4,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(X4,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,[],[f1173,f1021]) ).
fof(f1173,axiom,
! [X4] :
( c_1 = c_Divides_Oop_Amod(X4,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(X4,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(f20582,plain,
spl0_1897,
inference(avatar_split_clause,[],[f2947,f20580]) ).
fof(f2947,plain,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f720,f994]) ).
fof(f720,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X80),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
fof(f20577,plain,
spl0_1896,
inference(avatar_split_clause,[],[f2946,f20575]) ).
fof(f2946,plain,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f723,f994]) ).
fof(f723,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X80),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
fof(f20573,plain,
spl0_1895,
inference(avatar_split_clause,[],[f1625,f20571]) ).
fof(f20571,plain,
( spl0_1895
<=> ! [X5,X1] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| ~ c_in(c_Main_Ofinite__Union__1(X1,X5),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Union(X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f1625,axiom,
! [X1,X5] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| ~ c_in(c_Main_Ofinite__Union__1(X1,X5),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Union(X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f20569,plain,
spl0_1894,
inference(avatar_split_clause,[],[f1624,f20567]) ).
fof(f20567,plain,
( spl0_1894
<=> ! [X5,X1] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| c_in(c_Main_Ofinite__Union__1(X1,X5),X1,tc_set(X5))
| c_in(c_Union(X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f1624,axiom,
! [X1,X5] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| c_in(c_Main_Ofinite__Union__1(X1,X5),X1,tc_set(X5))
| c_in(c_Union(X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f20565,plain,
( spl0_1893
| ~ spl0_3
| ~ spl0_1844 ),
inference(avatar_split_clause,[],[f19734,f18887,f3185,f20563]) ).
fof(f20563,plain,
( spl0_1893
<=> ! [X0] : c_minus(X0,v_A,tc_set(t_a)) = c_minus(c_insert(v_b,X0,t_a),v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f18887,plain,
( spl0_1844
<=> ! [X35,X4,X5,X1] :
( ~ c_in(X4,X35,X5)
| c_minus(X1,X35,tc_set(X5)) = c_minus(c_insert(X4,X1,X5),X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f19734,plain,
( ! [X0] : c_minus(X0,v_A,tc_set(t_a)) = c_minus(c_insert(v_b,X0,t_a),v_A,tc_set(t_a))
| ~ spl0_3
| ~ spl0_1844 ),
inference(resolution,[],[f18888,f3187]) ).
fof(f3187,plain,
( c_in(v_b,v_A,t_a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f3185]) ).
fof(f18888,plain,
( ! [X1,X4,X35,X5] :
( ~ c_in(X4,X35,X5)
| c_minus(X1,X35,tc_set(X5)) = c_minus(c_insert(X4,X1,X5),X35,tc_set(X5)) )
| ~ spl0_1844 ),
inference(avatar_component_clause,[],[f18887]) ).
fof(f20561,plain,
spl0_1892,
inference(avatar_split_clause,[],[f1217,f20559]) ).
fof(f20559,plain,
( spl0_1892
<=> ! [X19,X5,X2,X30] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| X19 = X30
| ~ c_less(c_1,X2,X5)
| c_Nat_Opower(X2,X19,X5) != c_Nat_Opower(X2,X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f1217,axiom,
! [X2,X19,X5,X30] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| X19 = X30
| ~ c_less(c_1,X2,X5)
| c_Nat_Opower(X2,X19,X5) != c_Nat_Opower(X2,X30,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
fof(f20557,plain,
spl0_1891,
inference(avatar_split_clause,[],[f1192,f20555]) ).
fof(f20555,plain,
( spl0_1891
<=> ! [X4,X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X19,tc_nat)
| c_Nat_Opower(c_uminus(X4,X5),X19,X5) = c_uminus(c_Nat_Opower(X4,X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f1192,axiom,
! [X19,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X19,tc_nat)
| c_Nat_Opower(c_uminus(X4,X5),X19,X5) = c_uminus(c_Nat_Opower(X4,X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
fof(f20553,plain,
spl0_1890,
inference(avatar_split_clause,[],[f1185,f20551]) ).
fof(f20551,plain,
( spl0_1890
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X4
| c_lessequals(X4,c_0,X5)
| ~ c_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f1185,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X4
| c_lessequals(X4,c_0,X5)
| ~ c_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f20549,plain,
spl0_1889,
inference(avatar_split_clause,[],[f838,f20547]) ).
fof(f20547,plain,
( spl0_1889
<=> ! [X2,X40,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23)
| c_less(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f838,axiom,
! [X40,X2,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23)
| c_less(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f20545,plain,
spl0_1888,
inference(avatar_split_clause,[],[f837,f20543]) ).
fof(f20543,plain,
( spl0_1888
<=> ! [X2,X40,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f837,axiom,
! [X2,X40,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f20541,plain,
spl0_1887,
inference(avatar_split_clause,[],[f834,f20539]) ).
fof(f20539,plain,
( spl0_1887
<=> ! [X2,X40,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23)
| c_lessequals(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f834,axiom,
! [X40,X2,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23)
| c_lessequals(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f20537,plain,
spl0_1886,
inference(avatar_split_clause,[],[f833,f20535]) ).
fof(f20535,plain,
( spl0_1886
<=> ! [X2,X40,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f833,axiom,
! [X2,X40,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(c_uminus(X2,X23),c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X2,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f20533,plain,
spl0_1885,
inference(avatar_split_clause,[],[f827,f20531]) ).
fof(f20531,plain,
( spl0_1885
<=> ! [X40,X23,X7] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f827,axiom,
! [X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f20529,plain,
spl0_1884,
inference(avatar_split_clause,[],[f826,f20527]) ).
fof(f20527,plain,
( spl0_1884
<=> ! [X40,X23,X7] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23)
| c_less(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f826,axiom,
! [X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_less(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23)
| c_less(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f20525,plain,
spl0_1883,
inference(avatar_split_clause,[],[f811,f20523]) ).
fof(f20523,plain,
( spl0_1883
<=> ! [X40,X23,X7] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f811,axiom,
! [X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f20521,plain,
( spl0_1882
| ~ spl0_2
| ~ spl0_1844 ),
inference(avatar_split_clause,[],[f19733,f18887,f3180,f20519]) ).
fof(f19733,plain,
( ! [X0] : c_minus(X0,v_A,tc_set(t_a)) = c_minus(c_insert(v_a,X0,t_a),v_A,tc_set(t_a))
| ~ spl0_2
| ~ spl0_1844 ),
inference(resolution,[],[f18888,f3182]) ).
fof(f3182,plain,
( c_in(v_a,v_A,t_a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f20517,plain,
spl0_1881,
inference(avatar_split_clause,[],[f810,f20515]) ).
fof(f20515,plain,
( spl0_1881
<=> ! [X40,X23,X7] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23)
| c_lessequals(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f810,axiom,
! [X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ c_lessequals(c_Numeral_Onumber__of(X40,X23),c_uminus(X7,X23),X23)
| c_lessequals(X7,c_uminus(c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f20513,plain,
spl0_1880,
inference(avatar_split_clause,[],[f741,f20511]) ).
fof(f20511,plain,
( spl0_1880
<=> ! [X39,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X39,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X39,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f741,axiom,
! [X40,X39] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X39,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X39,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f20509,plain,
spl0_1879,
inference(avatar_split_clause,[],[f620,f20507]) ).
fof(f20507,plain,
( spl0_1879
<=> ! [X4,X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Oset(c_List_Oremove1(X4,X44,X5),X5) = c_minus(c_List_Oset(X44,X5),c_insert(X4,c_emptyset,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f620,axiom,
! [X44,X4,X5] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Oset(c_List_Oremove1(X4,X44,X5),X5) = c_minus(c_List_Oset(X44,X5),c_insert(X4,c_emptyset,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).
fof(f20505,plain,
spl0_1878,
inference(avatar_split_clause,[],[f139,f20503]) ).
fof(f20503,plain,
( spl0_1878
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMin(X1,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f139,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMin(X1,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
fof(f20501,plain,
spl0_1877,
inference(avatar_split_clause,[],[f121,f20499]) ).
fof(f20499,plain,
( spl0_1877
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X4,c_Finite__Set_OMax(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f121,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X4,c_Finite__Set_OMax(X1,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
fof(f20087,plain,
( spl0_1876
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1862 ),
inference(avatar_split_clause,[],[f19944,f19941,f16039,f7177,f7153,f20085]) ).
fof(f20085,plain,
( spl0_1876
<=> ! [X44,X8,X5,X45] :
( c_append(c_List_Orev(X45,X5),c_List_Oreplicate(c_1,X8,X5),X5) = X44
| c_List_Olist_OCons(X8,X45,X5) != c_List_Orev(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f19941,plain,
( spl0_1862
<=> ! [X44,X8,X5,X45] :
( c_List_Olist_OCons(X8,X45,X5) != c_List_Orev(X44,X5)
| c_append(c_List_Orev(X45,X5),c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) = X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f19944,plain,
( ! [X8,X44,X45,X5] :
( c_append(c_List_Orev(X45,X5),c_List_Oreplicate(c_1,X8,X5),X5) = X44
| c_List_Olist_OCons(X8,X45,X5) != c_List_Orev(X44,X5) )
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1862 ),
inference(forward_demodulation,[],[f19942,f16065]) ).
fof(f19942,plain,
( ! [X8,X44,X45,X5] :
( c_List_Olist_OCons(X8,X45,X5) != c_List_Orev(X44,X5)
| c_append(c_List_Orev(X45,X5),c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) = X44 )
| ~ spl0_1862 ),
inference(avatar_component_clause,[],[f19941]) ).
fof(f20055,plain,
( spl0_1875
| ~ spl0_58
| ~ spl0_1009
| ~ spl0_1858 ),
inference(avatar_split_clause,[],[f19927,f19924,f8331,f3460,f20053]) ).
fof(f20053,plain,
( spl0_1875
<=> ! [X7] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X7,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X7,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f8331,plain,
( spl0_1009
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_uminus(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f19924,plain,
( spl0_1858
<=> ! [X7] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X7,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X7,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f19927,plain,
( ! [X7] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X7,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X7,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1009
| ~ spl0_1858 ),
inference(forward_demodulation,[],[f19925,f8621]) ).
fof(f8621,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1009 ),
inference(resolution,[],[f8332,f3462]) ).
fof(f8332,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_uminus(c_1,X5) )
| ~ spl0_1009 ),
inference(avatar_component_clause,[],[f8331]) ).
fof(f19925,plain,
( ! [X7] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X7,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X7,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1858 ),
inference(avatar_component_clause,[],[f19924]) ).
fof(f19994,plain,
spl0_1874,
inference(avatar_split_clause,[],[f3085,f19992]) ).
fof(f19992,plain,
( spl0_1874
<=> ! [X80] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f3085,plain,
! [X80] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2910,f2763]) ).
fof(f2763,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f881,f1409]) ).
fof(f881,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2910,plain,
! [X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,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(X80,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f737,f1409]) ).
fof(f737,axiom,
! [X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f19990,plain,
spl0_1873,
inference(avatar_split_clause,[],[f2916,f19988]) ).
fof(f19988,plain,
( spl0_1873
<=> ! [X6,X5,X43] :
( ~ c_in(X43,X6,tc_prod(X5,X5))
| c_in(X43,c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f2916,plain,
! [X6,X5,X43] :
( ~ c_in(X43,X6,tc_prod(X5,X5))
| c_in(X43,c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1711,f1581]) ).
fof(f1711,axiom,
! [X6,X5,X43] :
( ~ c_in(X43,X6,tc_prod(X5,X5))
| c_in(X43,c_Transitive__Closure_Ortrancl(X6,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f19986,plain,
spl0_1872,
inference(avatar_split_clause,[],[f2914,f19984]) ).
fof(f19984,plain,
( spl0_1872
<=> ! [X45,X5,X44] :
( ~ c_List_Odistinct(c_append(X44,X45,X5),X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X44,X5),X5),c_List_Oset(X45,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f2914,plain,
! [X44,X45,X5] :
( ~ c_List_Odistinct(c_append(X44,X45,X5),X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X44,X5),X5),c_List_Oset(X45,X5),X5,X5) ),
inference(definition_unfolding,[],[f422,f1238]) ).
fof(f422,axiom,
! [X44,X45,X5] :
( ~ c_List_Odistinct(c_append(X44,X45,X5),X5)
| c_emptyset = c_inter(c_List_Oset(X44,X5),c_List_Oset(X45,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f19982,plain,
spl0_1871,
inference(avatar_split_clause,[],[f2865,f19980]) ).
fof(f19980,plain,
( spl0_1871
<=> ! [X9,X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_uminus(c_Numeral_Onumber__of(X39,X5),X5),X9,X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X39),X5),X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f2865,plain,
! [X39,X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_uminus(c_Numeral_Onumber__of(X39,X5),X5),X9,X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X39),X5),X9,X5) ),
inference(definition_unfolding,[],[f1030,f994]) ).
fof(f1030,axiom,
! [X39,X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_uminus(c_Numeral_Onumber__of(X39,X5),X5),X9,X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X39),X5),X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f19976,plain,
spl0_1870,
inference(avatar_split_clause,[],[f2839,f19974]) ).
fof(f19974,plain,
( spl0_1870
<=> ! [X44,X4,X21,X45] : c_append(c_List_Orev(c_List_Olist_OCons(X4,X44,X21),X21),X45,X21) = c_append(c_List_Orev(X44,X21),c_List_Olist_OCons(X4,X45,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f2839,plain,
! [X21,X44,X45,X4] : c_append(c_List_Orev(c_List_Olist_OCons(X4,X44,X21),X21),X45,X21) = c_append(c_List_Orev(X44,X21),c_List_Olist_OCons(X4,X45,X21),X21),
inference(definition_unfolding,[],[f452,f450,f450]) ).
fof(f450,axiom,
! [X44,X4,X5] : c_List_Oitrev(X44,X4,X5) = c_append(c_List_Orev(X44,X5),X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f452,axiom,
! [X21,X44,X45,X4] : c_List_Oitrev(c_List_Olist_OCons(X4,X44,X21),X45,X21) = c_List_Oitrev(X44,c_List_Olist_OCons(X4,X45,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f19972,plain,
spl0_1869,
inference(avatar_split_clause,[],[f1649,f19970]) ).
fof(f19970,plain,
( spl0_1869
<=> ! [X6,X5,X44] :
( c_List_Olist_ONil = X44
| ~ c_in(c_Pair(X44,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f1649,axiom,
! [X44,X6,X5] :
( c_List_Olist_ONil = X44
| ~ c_in(c_Pair(X44,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f19968,plain,
spl0_1868,
inference(avatar_split_clause,[],[f1648,f19966]) ).
fof(f19966,plain,
( spl0_1868
<=> ! [X6,X5,X44] :
( c_List_Olist_ONil = X44
| ~ c_in(c_Pair(c_List_Olist_ONil,X44,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f1648,axiom,
! [X44,X6,X5] :
( c_List_Olist_ONil = X44
| ~ c_in(c_Pair(c_List_Olist_ONil,X44,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f19964,plain,
spl0_1867,
inference(avatar_split_clause,[],[f987,f19962]) ).
fof(f19962,plain,
( spl0_1867
<=> ! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_Numeral_Onumber__of(X4,X5) = c_HOL_Oabs(c_Numeral_Onumber__of(X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f987,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_Numeral_Onumber__of(X4,X5) = c_HOL_Oabs(c_Numeral_Onumber__of(X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f19960,plain,
spl0_1866,
inference(avatar_split_clause,[],[f729,f19958]) ).
fof(f19958,plain,
( spl0_1866
<=> ! [X80,X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X40,X80),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f729,axiom,
! [X40,X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X40,X80),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f19956,plain,
spl0_1865,
inference(avatar_split_clause,[],[f665,f19954]) ).
fof(f19954,plain,
( spl0_1865
<=> ! [X29,X18,X55] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_minus(X29,c_minus(X55,X18,tc_nat),tc_nat) = c_minus(c_plus(X29,X18,tc_nat),X55,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f665,axiom,
! [X29,X18,X55] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_minus(X29,c_minus(X55,X18,tc_nat),tc_nat) = c_minus(c_plus(X29,X18,tc_nat),X55,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f19952,plain,
spl0_1864,
inference(avatar_split_clause,[],[f661,f19950]) ).
fof(f19950,plain,
( spl0_1864
<=> ! [X29,X18,X55] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_plus(X29,c_minus(X55,X18,tc_nat),tc_nat) = c_minus(c_plus(X29,X55,tc_nat),X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f661,axiom,
! [X29,X18,X55] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_plus(X29,c_minus(X55,X18,tc_nat),tc_nat) = c_minus(c_plus(X29,X55,tc_nat),X18,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f19948,plain,
spl0_1863,
inference(avatar_split_clause,[],[f660,f19946]) ).
fof(f19946,plain,
( spl0_1863
<=> ! [X29,X18,X55] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_plus(c_minus(X55,X18,tc_nat),X29,tc_nat) = c_minus(c_plus(X55,X29,tc_nat),X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f660,axiom,
! [X29,X18,X55] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_plus(c_minus(X55,X18,tc_nat),X29,tc_nat) = c_minus(c_plus(X55,X29,tc_nat),X18,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f19943,plain,
spl0_1862,
inference(avatar_split_clause,[],[f591,f19941]) ).
fof(f591,axiom,
! [X8,X44,X45,X5] :
( c_List_Olist_OCons(X8,X45,X5) != c_List_Orev(X44,X5)
| c_append(c_List_Orev(X45,X5),c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) = X44 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f19939,plain,
spl0_1861,
inference(avatar_split_clause,[],[f579,f19937]) ).
fof(f19937,plain,
( spl0_1861
<=> ! [X4,X21,X44] :
( c_in(X4,c_List_Oset(X44,X21),X21)
| c_List_Oremdups(c_List_Olist_OCons(X4,X44,X21),X21) = c_List_Olist_OCons(X4,c_List_Oremdups(X44,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f579,axiom,
! [X21,X44,X4] :
( c_in(X4,c_List_Oset(X44,X21),X21)
| c_List_Oremdups(c_List_Olist_OCons(X4,X44,X21),X21) = c_List_Olist_OCons(X4,c_List_Oremdups(X44,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f19935,plain,
( spl0_1860
| ~ spl0_1066
| ~ spl0_1817 ),
inference(avatar_split_clause,[],[f19853,f18481,f8759,f19933]) ).
fof(f19933,plain,
( spl0_1860
<=> ! [X0] : c_0 = c_Finite__Set_Ocard(c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f8759,plain,
( spl0_1066
<=> ! [X5,X1] :
( c_0 = c_Finite__Set_Ocard(X1,X5)
| c_in(X1,c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f18481,plain,
( spl0_1817
<=> ! [X0] : ~ c_in(c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),c_Finite__Set_OFinites,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f19853,plain,
( ! [X0] : c_0 = c_Finite__Set_Ocard(c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a)
| ~ spl0_1066
| ~ spl0_1817 ),
inference(resolution,[],[f18482,f8760]) ).
fof(f8760,plain,
( ! [X1,X5] :
( c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_0 = c_Finite__Set_Ocard(X1,X5) )
| ~ spl0_1066 ),
inference(avatar_component_clause,[],[f8759]) ).
fof(f18482,plain,
( ! [X0] : ~ c_in(c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1817 ),
inference(avatar_component_clause,[],[f18481]) ).
fof(f19931,plain,
spl0_1859,
inference(avatar_split_clause,[],[f482,f19929]) ).
fof(f19929,plain,
( spl0_1859
<=> ! [X6,X57,X5,X34] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X34,X57,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f482,axiom,
! [X57,X6,X34,X5] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X34,X57,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f19926,plain,
spl0_1858,
inference(avatar_split_clause,[],[f318,f19924]) ).
fof(f318,axiom,
! [X7] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X7,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X7,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f19922,plain,
spl0_1857,
inference(avatar_split_clause,[],[f84,f19920]) ).
fof(f19920,plain,
( spl0_1857
<=> ! [X2,X7,X31] :
( ~ c_less(c_0,X31,tc_nat)
| c_div(X2,X7,tc_nat) = c_div(c_times(X2,X31,tc_nat),c_times(X7,X31,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f84,axiom,
! [X31,X2,X7] :
( ~ c_less(c_0,X31,tc_nat)
| c_div(X2,X7,tc_nat) = c_div(c_times(X2,X31,tc_nat),c_times(X7,X31,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f19918,plain,
spl0_1856,
inference(avatar_split_clause,[],[f83,f19916]) ).
fof(f19916,plain,
( spl0_1856
<=> ! [X2,X7,X31] :
( ~ c_less(c_0,X31,tc_nat)
| c_div(c_times(X31,X2,tc_nat),c_times(X31,X7,tc_nat),tc_nat) = c_div(X2,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f83,axiom,
! [X31,X2,X7] :
( ~ c_less(c_0,X31,tc_nat)
| c_div(c_times(X31,X2,tc_nat),c_times(X31,X7,tc_nat),tc_nat) = c_div(X2,X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f19914,plain,
spl0_1855,
inference(avatar_split_clause,[],[f9,f19912]) ).
fof(f9,axiom,
! [X3,X0,X8] :
( ~ c_in(X8,X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X3,t_a)
| c_in(c_Pair(X8,X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
fof(f19248,plain,
( spl0_1854
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1825 ),
inference(avatar_split_clause,[],[f18811,f18807,f16039,f7177,f7153,f19246]) ).
fof(f19246,plain,
( spl0_1854
<=> ! [X44,X4,X45,X5,X8] :
( c_append(X45,c_List_Oreplicate(c_1,X8,X5),X5) != c_append(X44,c_List_Oreplicate(c_1,X4,X5),X5)
| X4 = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f18807,plain,
( spl0_1825
<=> ! [X44,X4,X8,X5,X45] :
( X4 = X8
| c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f18811,plain,
( ! [X8,X44,X45,X4,X5] :
( c_append(X45,c_List_Oreplicate(c_1,X8,X5),X5) != c_append(X44,c_List_Oreplicate(c_1,X4,X5),X5)
| X4 = X8 )
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1825 ),
inference(forward_demodulation,[],[f18810,f16065]) ).
fof(f18810,plain,
( ! [X8,X44,X45,X4,X5] :
( c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Oreplicate(c_1,X8,X5),X5)
| X4 = X8 )
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1825 ),
inference(forward_demodulation,[],[f18808,f16065]) ).
fof(f18808,plain,
( ! [X8,X44,X45,X4,X5] :
( X4 = X8
| c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) )
| ~ spl0_1825 ),
inference(avatar_component_clause,[],[f18807]) ).
fof(f19244,plain,
( spl0_1853
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1824 ),
inference(avatar_split_clause,[],[f18805,f18801,f16039,f7177,f7153,f19242]) ).
fof(f19242,plain,
( spl0_1853
<=> ! [X44,X4,X45,X5,X8] :
( c_append(X45,c_List_Oreplicate(c_1,X8,X5),X5) != c_append(X44,c_List_Oreplicate(c_1,X4,X5),X5)
| X44 = X45 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f18801,plain,
( spl0_1824
<=> ! [X44,X4,X8,X5,X45] :
( X44 = X45
| c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f18805,plain,
( ! [X8,X44,X45,X4,X5] :
( c_append(X45,c_List_Oreplicate(c_1,X8,X5),X5) != c_append(X44,c_List_Oreplicate(c_1,X4,X5),X5)
| X44 = X45 )
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1824 ),
inference(forward_demodulation,[],[f18804,f16065]) ).
fof(f18804,plain,
( ! [X8,X44,X45,X4,X5] :
( c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Oreplicate(c_1,X8,X5),X5)
| X44 = X45 )
| ~ spl0_765
| ~ spl0_771
| ~ spl0_1696
| ~ spl0_1824 ),
inference(forward_demodulation,[],[f18802,f16065]) ).
fof(f18802,plain,
( ! [X8,X44,X45,X4,X5] :
( X44 = X45
| c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) )
| ~ spl0_1824 ),
inference(avatar_component_clause,[],[f18801]) ).
fof(f18923,plain,
( spl0_1852
| ~ spl0_1340
| ~ spl0_1631 ),
inference(avatar_split_clause,[],[f18877,f15496,f10433,f18921]) ).
fof(f18921,plain,
( spl0_1852
<=> ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(c_Finite__Set_OFinites,t_a),t_a),v_S,t_a)
| c_lessequals(X0,c_Union(c_Finite__Set_OFinites,t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f10433,plain,
( spl0_1340
<=> ! [X5,X1,X35] :
( c_lessequals(X1,X35,tc_set(X5))
| ~ c_in(c_Main_OsubsetI__1(X1,X35,X5),X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f15496,plain,
( spl0_1631
<=> ! [X0] :
( ~ c_in(X0,v_S,t_a)
| c_in(X0,c_Union(c_Finite__Set_OFinites,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f18877,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(c_Finite__Set_OFinites,t_a),t_a),v_S,t_a)
| c_lessequals(X0,c_Union(c_Finite__Set_OFinites,t_a),tc_set(t_a)) )
| ~ spl0_1340
| ~ spl0_1631 ),
inference(resolution,[],[f15497,f10434]) ).
fof(f10434,plain,
( ! [X1,X35,X5] :
( ~ c_in(c_Main_OsubsetI__1(X1,X35,X5),X35,X5)
| c_lessequals(X1,X35,tc_set(X5)) )
| ~ spl0_1340 ),
inference(avatar_component_clause,[],[f10433]) ).
fof(f15497,plain,
( ! [X0] :
( c_in(X0,c_Union(c_Finite__Set_OFinites,t_a),t_a)
| ~ c_in(X0,v_S,t_a) )
| ~ spl0_1631 ),
inference(avatar_component_clause,[],[f15496]) ).
fof(f18919,plain,
( spl0_1851
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1850 ),
inference(avatar_split_clause,[],[f18915,f18911,f10445,f10140,f6747,f3739,f18917]) ).
fof(f18911,plain,
( spl0_1850
<=> ! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X19,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_1850])]) ).
fof(f18915,plain,
( ! [X19] : c_plus(X19,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,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1850 ),
inference(forward_demodulation,[],[f18914,f11255]) ).
fof(f18914,plain,
( ! [X19] : c_plus(X19,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,X19,tc_nat),tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1850 ),
inference(forward_demodulation,[],[f18912,f11255]) ).
fof(f18912,plain,
( ! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_1850 ),
inference(avatar_component_clause,[],[f18911]) ).
fof(f18913,plain,
spl0_1850,
inference(avatar_split_clause,[],[f3010,f18911]) ).
fof(f3010,plain,
! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3009,f1021]) ).
fof(f3009,plain,
! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X19,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,[],[f3008,f1019]) ).
fof(f3008,plain,
! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X19,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,[],[f2829,f1021]) ).
fof(f2829,plain,
! [X19] : c_plus(X19,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(X19,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f747,f1409,f1409]) ).
fof(f747,axiom,
! [X19] : c_Suc(c_Suc(X19)) = c_plus(X19,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(f18909,plain,
spl0_1849,
inference(avatar_split_clause,[],[f2940,f18907]) ).
fof(f18907,plain,
( spl0_1849
<=> ! [X35,X31,X5,X1] :
( ~ c_in(X31,X35,X5)
| ~ c_in(X31,X1,X5)
| c_in(X31,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f2940,plain,
! [X31,X1,X35,X5] :
( ~ c_in(X31,X35,X5)
| ~ c_in(X31,X1,X5)
| c_in(X31,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) ),
inference(definition_unfolding,[],[f1473,f1238]) ).
fof(f1473,axiom,
! [X31,X1,X35,X5] :
( ~ c_in(X31,X35,X5)
| ~ c_in(X31,X1,X5)
| c_in(X31,c_inter(X1,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f18905,plain,
spl0_1848,
inference(avatar_split_clause,[],[f2935,f18903]) ).
fof(f18903,plain,
( spl0_1848
<=> ! [X4,X5,X8] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X8,X5) = c_Numeral_Onumber__of(X4,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f2935,plain,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X8,X5) = c_Numeral_Onumber__of(X4,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f1007,f994]) ).
fof(f1007,axiom,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X8,X5) = c_Numeral_Onumber__of(X4,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f18901,plain,
spl0_1847,
inference(avatar_split_clause,[],[f2934,f18899]) ).
fof(f18899,plain,
( spl0_1847
<=> ! [X4,X5,X8] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X8,X5) != c_Numeral_Onumber__of(X4,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f2934,plain,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X8,X5) != c_Numeral_Onumber__of(X4,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f1006,f994]) ).
fof(f1006,axiom,
! [X8,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X8,X5) != c_Numeral_Onumber__of(X4,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f18897,plain,
spl0_1846,
inference(avatar_split_clause,[],[f2882,f18895]) ).
fof(f18895,plain,
( spl0_1846
<=> ! [X5,X44,X29,X19] :
( ~ c_less(X29,X19,tc_nat)
| c_List_Onth(X44,X29,X5) = c_List_Onth(c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),X29,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f2882,plain,
! [X29,X19,X44,X5] :
( ~ c_less(X29,X19,tc_nat)
| c_List_Onth(X44,X29,X5) = c_List_Onth(c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),X29,X5) ),
inference(definition_unfolding,[],[f568,f631]) ).
fof(f568,axiom,
! [X29,X19,X44,X5] :
( ~ c_less(X29,X19,tc_nat)
| c_List_Onth(c_List_Otake(X19,X44,X5),X29,X5) = c_List_Onth(X44,X29,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f18893,plain,
spl0_1845,
inference(avatar_split_clause,[],[f2862,f18891]) ).
fof(f18891,plain,
( spl0_1845
<=> ! [X40,X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X40,X5),c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X39)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f2862,plain,
! [X40,X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X40,X5),c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X39)),X5) ),
inference(definition_unfolding,[],[f985,f994]) ).
fof(f985,axiom,
! [X40,X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__minus(X39)),X5) = c_minus(c_Numeral_Onumber__of(X40,X5),c_Numeral_Onumber__of(X39,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f18889,plain,
spl0_1844,
inference(avatar_split_clause,[],[f1539,f18887]) ).
fof(f1539,axiom,
! [X1,X4,X35,X5] :
( ~ c_in(X4,X35,X5)
| c_minus(X1,X35,tc_set(X5)) = c_minus(c_insert(X4,X1,X5),X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f18885,plain,
spl0_1843,
inference(avatar_split_clause,[],[f1512,f18883]) ).
fof(f18883,plain,
( spl0_1843
<=> ! [X35,X5,X1,X83] :
( ~ c_lessequals(X35,X83,tc_set(X5))
| ~ c_lessequals(X1,X83,tc_set(X5))
| c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f1512,axiom,
! [X83,X1,X35,X5] :
( ~ c_lessequals(X35,X83,tc_set(X5))
| ~ c_lessequals(X1,X83,tc_set(X5))
| c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f18881,plain,
spl0_1842,
inference(avatar_split_clause,[],[f1462,f18879]) ).
fof(f18879,plain,
( spl0_1842
<=> ! [X35,X4,X5,X1] :
( c_in(X4,X1,X5)
| c_minus(X1,X35,tc_set(X5)) = c_minus(X1,c_insert(X4,X35,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f1462,axiom,
! [X1,X4,X5,X35] :
( c_in(X4,X1,X5)
| c_minus(X1,X35,tc_set(X5)) = c_minus(X1,c_insert(X4,X35,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f18875,plain,
spl0_1841,
inference(avatar_split_clause,[],[f1202,f18873]) ).
fof(f18873,plain,
( spl0_1841
<=> ! [X4,X39] :
( c_less(c_0,X4,tc_nat)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f1202,axiom,
! [X39,X4] :
( c_less(c_0,X4,tc_nat)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f18871,plain,
spl0_1840,
inference(avatar_split_clause,[],[f1194,f18869]) ).
fof(f18869,plain,
( spl0_1840
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f1194,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f18867,plain,
spl0_1839,
inference(avatar_split_clause,[],[f1191,f18865]) ).
fof(f18865,plain,
( spl0_1839
<=> ! [X4,X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X19,tc_nat)
| c_Nat_Opower(c_uminus(X4,X5),X19,X5) = c_Nat_Opower(X4,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f1191,axiom,
! [X19,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X19,tc_nat)
| c_Nat_Opower(c_uminus(X4,X5),X19,X5) = c_Nat_Opower(X4,X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f18863,plain,
spl0_1838,
inference(avatar_split_clause,[],[f1188,f18861]) ).
fof(f18861,plain,
( spl0_1838
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f1188,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X39,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f18859,plain,
spl0_1837,
inference(avatar_split_clause,[],[f942,f18857]) ).
fof(f18857,plain,
( spl0_1837
<=> ! [X30,X18,X19] :
( ~ c_less(X30,X19,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f942,axiom,
! [X18,X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f18855,plain,
spl0_1836,
inference(avatar_split_clause,[],[f939,f18853]) ).
fof(f18853,plain,
( spl0_1836
<=> ! [X30,X18,X19] :
( ~ c_less(X30,X19,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f939,axiom,
! [X18,X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f18851,plain,
spl0_1835,
inference(avatar_split_clause,[],[f934,f18849]) ).
fof(f18849,plain,
( spl0_1835
<=> ! [X30,X18,X19] :
( ~ c_less(c_0,X18,tc_nat)
| c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f934,axiom,
! [X18,X19,X30] :
( ~ c_less(c_0,X18,tc_nat)
| c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f18847,plain,
spl0_1834,
inference(avatar_split_clause,[],[f931,f18845]) ).
fof(f18845,plain,
( spl0_1834
<=> ! [X30,X18,X19] :
( ~ c_less(c_0,X18,tc_nat)
| c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f931,axiom,
! [X18,X19,X30] :
( ~ c_less(c_0,X18,tc_nat)
| c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f18843,plain,
spl0_1833,
inference(avatar_split_clause,[],[f794,f18841]) ).
fof(f18841,plain,
( spl0_1833
<=> ! [X40,X23,X7] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Oab__group__add(X23)
| c_uminus(X7,X23) != c_Numeral_Onumber__of(X40,X23)
| c_uminus(c_Numeral_Onumber__of(X40,X23),X23) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f794,axiom,
! [X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_OrderedGroup_Oab__group__add(X23)
| c_uminus(X7,X23) != c_Numeral_Onumber__of(X40,X23)
| c_uminus(c_Numeral_Onumber__of(X40,X23),X23) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f18839,plain,
spl0_1832,
inference(avatar_split_clause,[],[f695,f18837]) ).
fof(f18837,plain,
( spl0_1832
<=> ! [X4,X8] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f695,axiom,
! [X8,X4] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f18835,plain,
spl0_1831,
inference(avatar_split_clause,[],[f694,f18833]) ).
fof(f18833,plain,
( spl0_1831
<=> ! [X4,X8] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f694,axiom,
! [X8,X4] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_nat),c_Numeral_Onumber__of(X8,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_nat),c_Numeral_Onumber__of(X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f18831,plain,
spl0_1830,
inference(avatar_split_clause,[],[f586,f18829]) ).
fof(f18829,plain,
( spl0_1830
<=> ! [X44,X4,X8,X21] :
( X4 = X8
| c_List_Oremove1(X4,c_List_Olist_OCons(X8,X44,X21),X21) = c_List_Olist_OCons(X8,c_List_Oremove1(X4,X44,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f586,axiom,
! [X21,X8,X44,X4] :
( X4 = X8
| c_List_Oremove1(X4,c_List_Olist_OCons(X8,X44,X21),X21) = c_List_Olist_OCons(X8,c_List_Oremove1(X4,X44,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f18827,plain,
spl0_1829,
inference(avatar_split_clause,[],[f569,f18825]) ).
fof(f18825,plain,
( spl0_1829
<=> ! [X29,X18,X55] :
( ~ c_less(c_plus(X29,X18,tc_nat),X55,tc_nat)
| c_plus(X29,X18,tc_nat) = c_List_Onth(c_List_Oupt(X29,X55),X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f569,axiom,
! [X29,X18,X55] :
( ~ c_less(c_plus(X29,X18,tc_nat),X55,tc_nat)
| c_plus(X29,X18,tc_nat) = c_List_Onth(c_List_Oupt(X29,X55),X18,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f18823,plain,
spl0_1828,
inference(avatar_split_clause,[],[f562,f18821]) ).
fof(f18821,plain,
( spl0_1828
<=> ! [X44,X19,X5,X45] : c_List_Onth(c_append(X44,X45,X5),c_plus(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat),X5) = c_List_Onth(X45,X19,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f562,axiom,
! [X44,X19,X45,X5] : c_List_Onth(c_append(X44,X45,X5),c_plus(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat),X5) = c_List_Onth(X45,X19,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f18819,plain,
spl0_1827,
inference(avatar_split_clause,[],[f495,f18817]) ).
fof(f18817,plain,
( spl0_1827
<=> ! [X61,X21,X56,X2] :
( c_in(X2,c_List_Oset(X61,X21),X21)
| c_List_Olist__inter(c_List_Olist_OCons(X2,X56,X21),X61,X21) = c_List_Olist__inter(X56,X61,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f495,axiom,
! [X2,X21,X56,X61] :
( c_in(X2,c_List_Oset(X61,X21),X21)
| c_List_Olist__inter(c_List_Olist_OCons(X2,X56,X21),X61,X21) = c_List_Olist__inter(X56,X61,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f18815,plain,
spl0_1826,
inference(avatar_split_clause,[],[f464,f18813]) ).
fof(f18813,plain,
( spl0_1826
<=> ! [X45,X5,X44] : c_Nat_Osize(c_append(X44,X45,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X44,tc_List_Olist(X5)),c_Nat_Osize(X45,tc_List_Olist(X5)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f464,axiom,
! [X44,X45,X5] : c_Nat_Osize(c_append(X44,X45,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X44,tc_List_Olist(X5)),c_Nat_Osize(X45,tc_List_Olist(X5)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f18809,plain,
spl0_1825,
inference(avatar_split_clause,[],[f382,f18807]) ).
fof(f382,axiom,
! [X8,X44,X45,X4,X5] :
( X4 = X8
| c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f18803,plain,
spl0_1824,
inference(avatar_split_clause,[],[f381,f18801]) ).
fof(f381,axiom,
! [X8,X44,X45,X4,X5] :
( X44 = X45
| c_append(X44,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) != c_append(X45,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f18799,plain,
spl0_1823,
inference(avatar_split_clause,[],[f346,f18797]) ).
fof(f18797,plain,
( spl0_1823
<=> ! [X4,X8] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X4,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f346,axiom,
! [X8,X4] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X4,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f18795,plain,
spl0_1822,
inference(avatar_split_clause,[],[f345,f18793]) ).
fof(f18793,plain,
( spl0_1822
<=> ! [X4,X8] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X4,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f345,axiom,
! [X8,X4] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X4,tc_IntDef_Oint),c_Numeral_Onumber__of(X8,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X8,tc_IntDef_Oint),c_Numeral_Onumber__of(X4,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f18791,plain,
( ~ spl0_1546
| spl0_1
| ~ spl0_1358
| ~ spl0_1548 ),
inference(avatar_split_clause,[],[f15582,f13636,f11344,f3175,f13345]) ).
fof(f13345,plain,
( spl0_1546
<=> c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f3175,plain,
( spl0_1
<=> c_emptyset = v_S ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f11344,plain,
( spl0_1358
<=> ! [X5,X1] :
( c_emptyset = X1
| c_0 != c_Finite__Set_Ocard(X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f13636,plain,
( spl0_1548
<=> c_0 = c_Finite__Set_Ocard(v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f15582,plain,
( c_emptyset = v_S
| ~ c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1358
| ~ spl0_1548 ),
inference(trivial_inequality_removal,[],[f15581]) ).
fof(f15581,plain,
( c_0 != c_0
| c_emptyset = v_S
| ~ c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1358
| ~ spl0_1548 ),
inference(superposition,[],[f11345,f13638]) ).
fof(f13638,plain,
( c_0 = c_Finite__Set_Ocard(v_S,t_a)
| ~ spl0_1548 ),
inference(avatar_component_clause,[],[f13636]) ).
fof(f11345,plain,
( ! [X1,X5] :
( c_0 != c_Finite__Set_Ocard(X1,X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5)) )
| ~ spl0_1358 ),
inference(avatar_component_clause,[],[f11344]) ).
fof(f18790,plain,
spl0_1821,
inference(avatar_split_clause,[],[f338,f18788]) ).
fof(f18788,plain,
( spl0_1821
<=> ! [X2,X7] :
( c_0 = X2
| c_plus(c_div(X7,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X7,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f338,axiom,
! [X2,X7] :
( c_0 = X2
| c_plus(c_div(X7,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X7,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f18786,plain,
spl0_1820,
inference(avatar_split_clause,[],[f337,f18784]) ).
fof(f18784,plain,
( spl0_1820
<=> ! [X2,X7] :
( c_0 = X2
| c_div(c_plus(X2,X7,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_plus(c_div(X7,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f337,axiom,
! [X2,X7] :
( c_0 = X2
| c_div(c_plus(X2,X7,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_plus(c_div(X7,X2,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f18782,plain,
spl0_1819,
inference(avatar_split_clause,[],[f157,f18780]) ).
fof(f18780,plain,
( spl0_1819
<=> ! [X1,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_lessequals(c_Finite__Set_OMin(X1,X23),c_Finite__Set_OMax(X1,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f157,axiom,
! [X1,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_lessequals(c_Finite__Set_OMin(X1,X23),c_Finite__Set_OMax(X1,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f18778,plain,
spl0_1818,
inference(avatar_split_clause,[],[f153,f18776]) ).
fof(f18776,plain,
( spl0_1818
<=> ! [X38,X5,X37] :
( ~ c_in(X38,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(X37,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_union(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f153,axiom,
! [X38,X37,X5] :
( ~ c_in(X38,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(X37,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_union(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f18483,plain,
( spl0_1546
| spl0_1817
| ~ spl0_1361
| ~ spl0_1813 ),
inference(avatar_split_clause,[],[f18105,f17911,f11356,f18481,f13345]) ).
fof(f11356,plain,
( spl0_1361
<=> ! [X38,X5,X37] :
( c_in(X37,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f17911,plain,
( spl0_1813
<=> ! [X0] : c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) = c_union(v_S,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f18105,plain,
( ! [X0] :
( ~ c_in(c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),c_Finite__Set_OFinites,tc_set(t_a))
| c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a)) )
| ~ spl0_1361
| ~ spl0_1813 ),
inference(superposition,[],[f11357,f17912]) ).
fof(f17912,plain,
( ! [X0] : c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) = c_union(v_S,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a)
| ~ spl0_1813 ),
inference(avatar_component_clause,[],[f17911]) ).
fof(f11357,plain,
( ! [X38,X37,X5] :
( ~ c_in(c_union(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5))
| c_in(X37,c_Finite__Set_OFinites,tc_set(X5)) )
| ~ spl0_1361 ),
inference(avatar_component_clause,[],[f11356]) ).
fof(f18199,plain,
( spl0_1816
| ~ spl0_1203
| ~ spl0_1813 ),
inference(avatar_split_clause,[],[f18103,f17911,f9510,f18197]) ).
fof(f18197,plain,
( spl0_1816
<=> ! [X0,X1] :
( c_in(X1,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a)
| ~ c_in(X1,v_S,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f9510,plain,
( spl0_1203
<=> ! [X35,X31,X5,X1] :
( ~ c_in(X31,X1,X5)
| c_in(X31,c_union(X1,X35,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f18103,plain,
( ! [X0,X1] :
( c_in(X1,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a)
| ~ c_in(X1,v_S,t_a) )
| ~ spl0_1203
| ~ spl0_1813 ),
inference(superposition,[],[f9511,f17912]) ).
fof(f9511,plain,
( ! [X31,X1,X35,X5] :
( c_in(X31,c_union(X1,X35,X5),X5)
| ~ c_in(X31,X1,X5) )
| ~ spl0_1203 ),
inference(avatar_component_clause,[],[f9510]) ).
fof(f17995,plain,
( spl0_1815
| ~ spl0_1527
| ~ spl0_1600 ),
inference(avatar_split_clause,[],[f15213,f14374,f13133,f17993]) ).
fof(f17993,plain,
( spl0_1815
<=> ! [X0] : c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) = c_union(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),c_insert(X0,v_S,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f13133,plain,
( spl0_1527
<=> c_Tarski_Ointerval(v_r,v_a,v_b,t_a) = c_union(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f14374,plain,
( spl0_1600
<=> ! [X35,X5,X2,X1] : c_union(X1,c_insert(X2,X35,X5),X5) = c_insert(X2,c_union(X1,X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f15213,plain,
( ! [X0] : c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) = c_union(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),c_insert(X0,v_S,t_a),t_a)
| ~ spl0_1527
| ~ spl0_1600 ),
inference(superposition,[],[f14375,f13135]) ).
fof(f13135,plain,
( c_Tarski_Ointerval(v_r,v_a,v_b,t_a) = c_union(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,t_a)
| ~ spl0_1527 ),
inference(avatar_component_clause,[],[f13133]) ).
fof(f14375,plain,
( ! [X2,X1,X35,X5] : c_union(X1,c_insert(X2,X35,X5),X5) = c_insert(X2,c_union(X1,X35,X5),X5)
| ~ spl0_1600 ),
inference(avatar_component_clause,[],[f14374]) ).
fof(f17917,plain,
spl0_1814,
inference(avatar_split_clause,[],[f3168,f17915]) ).
fof(f17915,plain,
( spl0_1814
<=> ! [X5,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f3168,plain,
! [X8,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2965,f979]) ).
fof(f979,axiom,
! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f2965,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f178,f994]) ).
fof(f178,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f17913,plain,
( spl0_1813
| ~ spl0_1516
| ~ spl0_1600 ),
inference(avatar_split_clause,[],[f15212,f14374,f13088,f17911]) ).
fof(f13088,plain,
( spl0_1516
<=> c_Tarski_Ointerval(v_r,v_a,v_b,t_a) = c_union(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f15212,plain,
( ! [X0] : c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) = c_union(v_S,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a)
| ~ spl0_1516
| ~ spl0_1600 ),
inference(superposition,[],[f14375,f13090]) ).
fof(f13090,plain,
( c_Tarski_Ointerval(v_r,v_a,v_b,t_a) = c_union(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_1516 ),
inference(avatar_component_clause,[],[f13088]) ).
fof(f17909,plain,
spl0_1812,
inference(avatar_split_clause,[],[f3166,f17907]) ).
fof(f17907,plain,
( spl0_1812
<=> ! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X4),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f3166,plain,
! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X4),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2963,f979]) ).
fof(f2963,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X4)),X5),X5) ),
inference(definition_unfolding,[],[f190,f994]) ).
fof(f190,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X4)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f17905,plain,
spl0_1811,
inference(avatar_split_clause,[],[f3158,f17903]) ).
fof(f17903,plain,
( spl0_1811
<=> ! [X5,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f3158,plain,
! [X8,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2957,f979]) ).
fof(f2957,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f177,f994]) ).
fof(f177,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f17901,plain,
spl0_1810,
inference(avatar_split_clause,[],[f3156,f17899]) ).
fof(f17899,plain,
( spl0_1810
<=> ! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X4),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f3156,plain,
! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X4),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2955,f979]) ).
fof(f2955,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X4)),X5),X5) ),
inference(definition_unfolding,[],[f189,f994]) ).
fof(f189,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X4)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f17897,plain,
spl0_1809,
inference(avatar_split_clause,[],[f3124,f17895]) ).
fof(f17895,plain,
( spl0_1809
<=> ! [X5,X8] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f3124,plain,
! [X8,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X8,X5) ),
inference(forward_demodulation,[],[f2931,f1021]) ).
fof(f2931,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X8,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f201,f994]) ).
fof(f201,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X8,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f17889,plain,
( spl0_1808
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1807 ),
inference(avatar_split_clause,[],[f17885,f17882,f11811,f7579,f7221,f6994,f6890,f6880,f17887]) ).
fof(f17887,plain,
( spl0_1808
<=> ! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f17882,plain,
( spl0_1807
<=> ! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f17885,plain,
( ! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X4,X5) )
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1807 ),
inference(forward_demodulation,[],[f17883,f12849]) ).
fof(f17883,plain,
( ! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X4,X5) )
| ~ spl0_1807 ),
inference(avatar_component_clause,[],[f17882]) ).
fof(f17884,plain,
spl0_1807,
inference(avatar_split_clause,[],[f3123,f17882]) ).
fof(f3123,plain,
! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X4,X5) ),
inference(forward_demodulation,[],[f2930,f1021]) ).
fof(f2930,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X4,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f205,f994]) ).
fof(f205,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X4,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f17880,plain,
spl0_1806,
inference(avatar_split_clause,[],[f3118,f17878]) ).
fof(f17878,plain,
( spl0_1806
<=> ! [X5,X8] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f3118,plain,
! [X8,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X8,X5) ),
inference(forward_demodulation,[],[f2927,f1021]) ).
fof(f2927,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X8,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f200,f994]) ).
fof(f200,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X8,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f17872,plain,
( spl0_1805
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1804 ),
inference(avatar_split_clause,[],[f17866,f17863,f11811,f7579,f7221,f6994,f6890,f6880,f17870]) ).
fof(f17870,plain,
( spl0_1805
<=> ! [X4,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f17863,plain,
( spl0_1804
<=> ! [X4,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f17866,plain,
( ! [X4,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X4,X5) )
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1804 ),
inference(forward_demodulation,[],[f17864,f12849]) ).
fof(f17864,plain,
( ! [X4,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X4,X5) )
| ~ spl0_1804 ),
inference(avatar_component_clause,[],[f17863]) ).
fof(f17865,plain,
spl0_1804,
inference(avatar_split_clause,[],[f3117,f17863]) ).
fof(f3117,plain,
! [X4,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X4,X5) ),
inference(forward_demodulation,[],[f2926,f1021]) ).
fof(f2926,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X4,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f204,f994]) ).
fof(f204,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X4,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f17860,plain,
( spl0_1803
| ~ spl0_58
| ~ spl0_1347
| ~ spl0_1802 ),
inference(avatar_split_clause,[],[f17856,f17853,f10464,f3460,f17858]) ).
fof(f17858,plain,
( spl0_1803
<=> ! [X40] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f17853,plain,
( spl0_1802
<=> ! [X40] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f17856,plain,
( ! [X40] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1347
| ~ spl0_1802 ),
inference(forward_demodulation,[],[f17854,f11327]) ).
fof(f17854,plain,
( ! [X40] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1802 ),
inference(avatar_component_clause,[],[f17853]) ).
fof(f17855,plain,
spl0_1802,
inference(avatar_split_clause,[],[f3088,f17853]) ).
fof(f3088,plain,
! [X40] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3087,f1021]) ).
fof(f3087,plain,
! [X40] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3086,f1019]) ).
fof(f3086,plain,
! [X40] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1138,f1021]) ).
fof(f1138,axiom,
! [X40] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(f17850,plain,
( spl0_1801
| ~ spl0_58
| ~ spl0_1347
| ~ spl0_1800 ),
inference(avatar_split_clause,[],[f17846,f17843,f10464,f3460,f17848]) ).
fof(f17848,plain,
( spl0_1801
<=> ! [X40] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f17843,plain,
( spl0_1800
<=> ! [X40] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f17846,plain,
( ! [X40] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1347
| ~ spl0_1800 ),
inference(forward_demodulation,[],[f17844,f11327]) ).
fof(f17844,plain,
( ! [X40] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1800 ),
inference(avatar_component_clause,[],[f17843]) ).
fof(f17845,plain,
spl0_1800,
inference(avatar_split_clause,[],[f3084,f17843]) ).
fof(f3084,plain,
! [X40] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3083,f1021]) ).
fof(f3083,plain,
! [X40] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3082,f1019]) ).
fof(f3082,plain,
! [X40] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1137,f1021]) ).
fof(f1137,axiom,
! [X40] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,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(f17840,plain,
( spl0_1799
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1798 ),
inference(avatar_split_clause,[],[f17836,f17833,f11811,f7579,f7221,f6994,f6890,f6880,f17838]) ).
fof(f17838,plain,
( spl0_1799
<=> ! [X5,X40] :
( c_minus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_OMin),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f17833,plain,
( spl0_1798
<=> ! [X5,X40] :
( c_minus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f17836,plain,
( ! [X40,X5] :
( c_minus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_OMin),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_702
| ~ spl0_704
| ~ spl0_729
| ~ spl0_782
| ~ spl0_870
| ~ spl0_1457
| ~ spl0_1798 ),
inference(forward_demodulation,[],[f17834,f12849]) ).
fof(f17834,plain,
( ! [X40,X5] :
( c_minus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_1798 ),
inference(avatar_component_clause,[],[f17833]) ).
fof(f17835,plain,
spl0_1798,
inference(avatar_split_clause,[],[f3053,f17833]) ).
fof(f3053,plain,
! [X40,X5] :
( c_minus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f2864,f1021]) ).
fof(f2864,plain,
! [X40,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5) ),
inference(definition_unfolding,[],[f197,f994]) ).
fof(f197,axiom,
! [X40,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f17831,plain,
( spl0_1797
| ~ spl0_1340
| ~ spl0_1465 ),
inference(avatar_split_clause,[],[f12873,f12774,f10433,f17829]) ).
fof(f17829,plain,
( spl0_1797
<=> ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),v_S,t_a)
| c_lessequals(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f12774,plain,
( spl0_1465
<=> ! [X0] :
( c_in(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ c_in(X0,v_S,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f12873,plain,
( ! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),v_S,t_a)
| c_lessequals(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )
| ~ spl0_1340
| ~ spl0_1465 ),
inference(resolution,[],[f12775,f10434]) ).
fof(f12775,plain,
( ! [X0] :
( c_in(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ c_in(X0,v_S,t_a) )
| ~ spl0_1465 ),
inference(avatar_component_clause,[],[f12774]) ).
fof(f17827,plain,
spl0_1796,
inference(avatar_split_clause,[],[f3052,f17825]) ).
fof(f17825,plain,
( spl0_1796
<=> ! [X5,X39] :
( c_minus(c_1,c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X39)),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f3052,plain,
! [X39,X5] :
( c_minus(c_1,c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X39)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f2863,f1021]) ).
fof(f2863,plain,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_1,c_Numeral_Onumber__of(X39,X5),X5) = 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,X39)),X5) ),
inference(definition_unfolding,[],[f196,f994]) ).
fof(f196,axiom,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_1,c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X39)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f17823,plain,
spl0_1795,
inference(avatar_split_clause,[],[f3014,f17821]) ).
fof(f17821,plain,
( spl0_1795
<=> ! [X19] : c_plus(X19,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),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f3014,plain,
! [X19] : c_plus(X19,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),X19,tc_nat),
inference(forward_demodulation,[],[f3013,f1021]) ).
fof(f3013,plain,
! [X19] : c_plus(X19,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),X19,tc_nat),
inference(forward_demodulation,[],[f3012,f1019]) ).
fof(f3012,plain,
! [X19] : c_plus(X19,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),X19,tc_nat),
inference(forward_demodulation,[],[f3011,f1021]) ).
fof(f3011,plain,
! [X19] : 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),X19,tc_nat) = c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2835,f3010]) ).
fof(f2835,plain,
! [X19] : 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),X19,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f746,f1409,f1409]) ).
fof(f746,axiom,
! [X19] : 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),X19,tc_nat) = c_Suc(c_Suc(X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f17803,plain,
( spl0_1794
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1793 ),
inference(avatar_split_clause,[],[f17799,f17796,f10445,f10140,f6747,f3739,f17801]) ).
fof(f17801,plain,
( spl0_1794
<=> ! [X40] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X40),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f17796,plain,
( spl0_1793
<=> ! [X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X40),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f17799,plain,
( ! [X40] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X40),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1793 ),
inference(forward_demodulation,[],[f17797,f11255]) ).
fof(f17797,plain,
( ! [X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X40),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1793 ),
inference(avatar_component_clause,[],[f17796]) ).
fof(f17798,plain,
spl0_1793,
inference(avatar_split_clause,[],[f2909,f17796]) ).
fof(f2909,plain,
! [X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X40),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f688,f1409]) ).
fof(f688,axiom,
! [X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X40,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X40),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f17794,plain,
spl0_1792,
inference(avatar_split_clause,[],[f2840,f17792]) ).
fof(f17792,plain,
( spl0_1792
<=> ! [X5,X18,X4,X29] : c_List_Oreplicate(c_Orderings_Omin(X29,X18,tc_nat),X4,X5) = c_List_Osublist(c_List_Oreplicate(X18,X4,X5),c_SetInterval_OlessThan(X29,tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f2840,plain,
! [X29,X18,X4,X5] : c_List_Oreplicate(c_Orderings_Omin(X29,X18,tc_nat),X4,X5) = c_List_Osublist(c_List_Oreplicate(X18,X4,X5),c_SetInterval_OlessThan(X29,tc_nat),X5),
inference(definition_unfolding,[],[f640,f631]) ).
fof(f640,axiom,
! [X29,X18,X4,X5] : c_List_Otake(X29,c_List_Oreplicate(X18,X4,X5),X5) = c_List_Oreplicate(c_Orderings_Omin(X29,X18,tc_nat),X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f17790,plain,
spl0_1791,
inference(avatar_split_clause,[],[f2838,f17788]) ).
fof(f17788,plain,
( spl0_1791
<=> ! [X5,X44,X19] : c_Orderings_Omin(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat) = c_Nat_Osize(c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f2838,plain,
! [X44,X19,X5] : c_Orderings_Omin(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat) = c_Nat_Osize(c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),tc_List_Olist(X5)),
inference(definition_unfolding,[],[f476,f631]) ).
fof(f476,axiom,
! [X19,X44,X5] : c_Nat_Osize(c_List_Otake(X19,X44,X5),tc_List_Olist(X5)) = c_Orderings_Omin(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f17786,plain,
spl0_1790,
inference(avatar_split_clause,[],[f2834,f17784]) ).
fof(f17784,plain,
( spl0_1790
<=> ! [X2,X5,X35] : c_Inter(c_insert(X2,X35,tc_set(X5)),X5) = c_Relation_OImage(c_Relation_Odiag(X2,X5),c_Inter(X35,X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f2834,plain,
! [X2,X35,X5] : c_Inter(c_insert(X2,X35,tc_set(X5)),X5) = c_Relation_OImage(c_Relation_Odiag(X2,X5),c_Inter(X35,X5),X5,X5),
inference(definition_unfolding,[],[f1488,f1238]) ).
fof(f1488,axiom,
! [X2,X35,X5] : c_Inter(c_insert(X2,X35,tc_set(X5)),X5) = c_inter(X2,c_Inter(X35,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f17781,plain,
( spl0_1789
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1788 ),
inference(avatar_split_clause,[],[f17765,f17762,f10445,f10140,f6747,f3739,f17779]) ).
fof(f17779,plain,
( spl0_1789
<=> ! [X5,X18,X23,X29] : c_Datatype__Universe_ONumb(X29,X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_ONumb(X29,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f17762,plain,
( spl0_1788
<=> ! [X5,X18,X23,X29] : c_Datatype__Universe_ONumb(X29,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X29,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f17765,plain,
( ! [X29,X18,X5,X23] : c_Datatype__Universe_ONumb(X29,X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_ONumb(X29,X5,X23),X5,X23)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1788 ),
inference(forward_demodulation,[],[f17763,f11255]) ).
fof(f17763,plain,
( ! [X29,X18,X5,X23] : c_Datatype__Universe_ONumb(X29,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X29,X5,X23),X5,X23)
| ~ spl0_1788 ),
inference(avatar_component_clause,[],[f17762]) ).
fof(f17764,plain,
spl0_1788,
inference(avatar_split_clause,[],[f2833,f17762]) ).
fof(f2833,plain,
! [X29,X18,X5,X23] : c_Datatype__Universe_ONumb(X29,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X29,X5,X23),X5,X23),
inference(definition_unfolding,[],[f72,f1409]) ).
fof(f72,axiom,
! [X29,X18,X5,X23] : c_Datatype__Universe_ONumb(X29,X5,X23) = c_Datatype__Universe_Ontrunc(c_Suc(X18),c_Datatype__Universe_ONumb(X29,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f17759,plain,
( spl0_1787
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1786 ),
inference(avatar_split_clause,[],[f17755,f17752,f10445,f10140,f6747,f3739,f17757]) ).
fof(f17757,plain,
( spl0_1787
<=> ! [X18,X23,X5,X2] : c_Datatype__Universe_OLeaf(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_OLeaf(X2,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f17752,plain,
( spl0_1786
<=> ! [X18,X23,X5,X2] : c_Datatype__Universe_OLeaf(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X2,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f17755,plain,
( ! [X2,X18,X5,X23] : c_Datatype__Universe_OLeaf(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_OLeaf(X2,X5,X23),X5,X23)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1786 ),
inference(forward_demodulation,[],[f17753,f11255]) ).
fof(f17753,plain,
( ! [X2,X18,X5,X23] : c_Datatype__Universe_OLeaf(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X2,X5,X23),X5,X23)
| ~ spl0_1786 ),
inference(avatar_component_clause,[],[f17752]) ).
fof(f17754,plain,
spl0_1786,
inference(avatar_split_clause,[],[f2832,f17752]) ).
fof(f2832,plain,
! [X2,X18,X5,X23] : c_Datatype__Universe_OLeaf(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X2,X5,X23),X5,X23),
inference(definition_unfolding,[],[f71,f1409]) ).
fof(f71,axiom,
! [X2,X18,X5,X23] : c_Datatype__Universe_OLeaf(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Suc(X18),c_Datatype__Universe_OLeaf(X2,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f17749,plain,
( spl0_1785
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1784 ),
inference(avatar_split_clause,[],[f17745,f17742,f10445,f10140,f6747,f3739,f17747]) ).
fof(f17747,plain,
( spl0_1785
<=> ! [X18,X23,X5,X2] : c_Datatype__Universe_OAtom(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_OAtom(X2,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f17742,plain,
( spl0_1784
<=> ! [X18,X23,X5,X2] : c_Datatype__Universe_OAtom(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X2,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f17745,plain,
( ! [X2,X18,X5,X23] : c_Datatype__Universe_OAtom(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_OAtom(X2,X5,X23),X5,X23)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1784 ),
inference(forward_demodulation,[],[f17743,f11255]) ).
fof(f17743,plain,
( ! [X2,X18,X5,X23] : c_Datatype__Universe_OAtom(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X2,X5,X23),X5,X23)
| ~ spl0_1784 ),
inference(avatar_component_clause,[],[f17742]) ).
fof(f17744,plain,
spl0_1784,
inference(avatar_split_clause,[],[f2831,f17742]) ).
fof(f2831,plain,
! [X2,X18,X5,X23] : c_Datatype__Universe_OAtom(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X2,X5,X23),X5,X23),
inference(definition_unfolding,[],[f68,f1409]) ).
fof(f68,axiom,
! [X2,X18,X5,X23] : c_Datatype__Universe_OAtom(X2,X5,X23) = c_Datatype__Universe_Ontrunc(c_Suc(X18),c_Datatype__Universe_OAtom(X2,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f17740,plain,
spl0_1783,
inference(avatar_split_clause,[],[f2820,f17738]) ).
fof(f17738,plain,
( spl0_1783
<=> ! [X6,X2,X5] : c_in(c_Pair(X2,X2,X5,X5),c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f2820,plain,
! [X2,X6,X5] : c_in(c_Pair(X2,X2,X5,X5),c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)),
inference(definition_unfolding,[],[f1712,f1581]) ).
fof(f1712,axiom,
! [X2,X6,X5] : c_in(c_Pair(X2,X2,X5,X5),c_Transitive__Closure_Ortrancl(X6,X5),tc_prod(X5,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f17736,plain,
spl0_1782,
inference(avatar_split_clause,[],[f2818,f17734]) ).
fof(f17734,plain,
( spl0_1782
<=> ! [X6,X5] : c_union(c_Transitive__Closure_Otrancl(X6,X5),c_Relation_OId,tc_prod(X5,X5)) = c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f2818,plain,
! [X6,X5] : c_union(c_Transitive__Closure_Otrancl(X6,X5),c_Relation_OId,tc_prod(X5,X5)) = c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1573,f1581]) ).
fof(f1573,axiom,
! [X6,X5] : c_union(c_Transitive__Closure_Otrancl(X6,X5),c_Relation_OId,tc_prod(X5,X5)) = c_Transitive__Closure_Ortrancl(X6,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f17713,plain,
( spl0_1781
| ~ spl0_796
| ~ spl0_1600
| ~ spl0_1741 ),
inference(avatar_split_clause,[],[f17483,f17430,f14374,f7278,f17711]) ).
fof(f17711,plain,
( spl0_1781
<=> ! [X0,X1] : c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_insert(X1,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f7278,plain,
( spl0_796
<=> ! [X5,X35] : c_UNIV = c_union(c_UNIV,X35,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f17430,plain,
( spl0_1741
<=> ! [X0] : c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f17483,plain,
( ! [X0,X1] : c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_insert(X1,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a),t_a)
| ~ spl0_796
| ~ spl0_1600
| ~ spl0_1741 ),
inference(forward_demodulation,[],[f17482,f15225]) ).
fof(f15225,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_796
| ~ spl0_1600 ),
inference(forward_demodulation,[],[f15208,f7279]) ).
fof(f7279,plain,
( ! [X35,X5] : c_UNIV = c_union(c_UNIV,X35,X5)
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f7278]) ).
fof(f15208,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_796
| ~ spl0_1600 ),
inference(superposition,[],[f14375,f7279]) ).
fof(f17482,plain,
( ! [X0,X1] : c_union(c_uminus(v_S,tc_set(t_a)),c_insert(X1,c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a),t_a) = c_insert(X1,c_UNIV,t_a)
| ~ spl0_1600
| ~ spl0_1741 ),
inference(superposition,[],[f14375,f17431]) ).
fof(f17431,plain,
( ! [X0] : c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a)
| ~ spl0_1741 ),
inference(avatar_component_clause,[],[f17430]) ).
fof(f17709,plain,
( spl0_1780
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1779 ),
inference(avatar_split_clause,[],[f17705,f17702,f10445,f10140,f6747,f3739,f17707]) ).
fof(f17707,plain,
( spl0_1780
<=> ! [X30,X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(X30,c_plus(c_1,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f17702,plain,
( spl0_1779
<=> ! [X30,X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f17705,plain,
( ! [X19,X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(X30,c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1779 ),
inference(forward_demodulation,[],[f17703,f11255]) ).
fof(f17703,plain,
( ! [X19,X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat)
| ~ spl0_1779 ),
inference(avatar_component_clause,[],[f17702]) ).
fof(f17704,plain,
spl0_1779,
inference(avatar_split_clause,[],[f2811,f17702]) ).
fof(f2811,plain,
! [X19,X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f892,f1409,f1409]) ).
fof(f892,axiom,
! [X19,X30] : c_plus(X30,c_Suc(X19),tc_nat) = c_Suc(c_plus(X30,X19,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f17619,plain,
( spl0_1778
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1777 ),
inference(avatar_split_clause,[],[f17615,f17611,f10445,f10140,f6747,f3739,f17617]) ).
fof(f17617,plain,
( spl0_1778
<=> ! [X30,X19] : c_plus(c_plus(c_1,X30,tc_nat),X19,tc_nat) = c_plus(c_1,c_plus(X30,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f17611,plain,
( spl0_1777
<=> ! [X30,X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f17615,plain,
( ! [X19,X30] : c_plus(c_plus(c_1,X30,tc_nat),X19,tc_nat) = c_plus(c_1,c_plus(X30,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1777 ),
inference(forward_demodulation,[],[f17614,f11255]) ).
fof(f17614,plain,
( ! [X19,X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X30,tc_nat),X19,tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1777 ),
inference(forward_demodulation,[],[f17612,f11255]) ).
fof(f17612,plain,
( ! [X19,X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X19,tc_nat)
| ~ spl0_1777 ),
inference(avatar_component_clause,[],[f17611]) ).
fof(f17613,plain,
spl0_1777,
inference(avatar_split_clause,[],[f2810,f17611]) ).
fof(f2810,plain,
! [X19,X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,X19,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X19,tc_nat),
inference(definition_unfolding,[],[f966,f1409,f1409]) ).
fof(f966,axiom,
! [X19,X30] : c_Suc(c_plus(X30,X19,tc_nat)) = c_plus(c_Suc(X30),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f17587,plain,
( spl0_1776
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1775 ),
inference(avatar_split_clause,[],[f17583,f17579,f10445,f10140,f6747,f3739,f17585]) ).
fof(f17585,plain,
( spl0_1776
<=> ! [X30,X19] : c_minus(X30,X19,tc_nat) = c_minus(c_plus(c_1,X30,tc_nat),c_plus(c_1,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f17579,plain,
( spl0_1775
<=> ! [X30,X19] : c_minus(X30,X19,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f17583,plain,
( ! [X19,X30] : c_minus(X30,X19,tc_nat) = c_minus(c_plus(c_1,X30,tc_nat),c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1775 ),
inference(forward_demodulation,[],[f17582,f11255]) ).
fof(f17582,plain,
( ! [X19,X30] : c_minus(X30,X19,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1775 ),
inference(forward_demodulation,[],[f17580,f11255]) ).
fof(f17580,plain,
( ! [X19,X30] : c_minus(X30,X19,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat)
| ~ spl0_1775 ),
inference(avatar_component_clause,[],[f17579]) ).
fof(f17581,plain,
spl0_1775,
inference(avatar_split_clause,[],[f2809,f17579]) ).
fof(f2809,plain,
! [X19,X30] : c_minus(X30,X19,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f900,f1409,f1409]) ).
fof(f900,axiom,
! [X19,X30] : c_minus(X30,X19,tc_nat) = c_minus(c_Suc(X30),c_Suc(X19),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f17577,plain,
spl0_1774,
inference(avatar_split_clause,[],[f1706,f17575]) ).
fof(f17575,plain,
( spl0_1774
<=> ! [X35,X23,X7,X5,X1] :
( ~ c_in(X7,X35,X5)
| c_in(c_Sum__Type_OInr(X7,X5,X23),c_Sum__Type_OPlus(X1,X35,X23,X5),tc_sum(X23,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f1706,axiom,
! [X1,X7,X35,X5,X23] :
( ~ c_in(X7,X35,X5)
| c_in(c_Sum__Type_OInr(X7,X5,X23),c_Sum__Type_OPlus(X1,X35,X23,X5),tc_sum(X23,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f17573,plain,
spl0_1773,
inference(avatar_split_clause,[],[f1705,f17571]) ).
fof(f17571,plain,
( spl0_1773
<=> ! [X35,X23,X5,X2,X1] :
( ~ c_in(X2,X1,X5)
| c_in(c_Sum__Type_OInl(X2,X5,X23),c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f1705,axiom,
! [X2,X1,X5,X35,X23] :
( ~ c_in(X2,X1,X5)
| c_in(c_Sum__Type_OInl(X2,X5,X23),c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f17567,plain,
spl0_1772,
inference(avatar_split_clause,[],[f1668,f17565]) ).
fof(f17565,plain,
( spl0_1772
<=> ! [X5,X23,X6,X2,X7] :
( c_in(X7,c_Relation_ORange(X6,X5,X23),X23)
| ~ c_in(c_Pair(X2,X7,X5,X23),X6,tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f1668,axiom,
! [X2,X6,X7,X5,X23] :
( c_in(X7,c_Relation_ORange(X6,X5,X23),X23)
| ~ c_in(c_Pair(X2,X7,X5,X23),X6,tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f17563,plain,
spl0_1771,
inference(avatar_split_clause,[],[f1664,f17561]) ).
fof(f17561,plain,
( spl0_1771
<=> ! [X5,X23,X6,X1,X7] :
( ~ c_in(X7,c_Relation_OImage(X6,X1,X23,X5),X5)
| c_in(c_Main_OImageE__1(X1,X7,X6,X23,X5),X1,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f1664,axiom,
! [X1,X6,X7,X5,X23] :
( ~ c_in(X7,c_Relation_OImage(X6,X1,X23,X5),X5)
| c_in(c_Main_OImageE__1(X1,X7,X6,X23,X5),X1,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f17559,plain,
spl0_1770,
inference(avatar_split_clause,[],[f1663,f17557]) ).
fof(f17557,plain,
( spl0_1770
<=> ! [X5,X43] :
( ~ c_in(X43,c_Relation_OId,tc_prod(X5,X5))
| c_Pair(c_Main_OIdE__1(X43,X5),c_Main_OIdE__1(X43,X5),X5,X5) = X43 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f1663,axiom,
! [X5,X43] :
( ~ c_in(X43,c_Relation_OId,tc_prod(X5,X5))
| c_Pair(c_Main_OIdE__1(X43,X5),c_Main_OIdE__1(X43,X5),X5,X5) = X43 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f17555,plain,
spl0_1769,
inference(avatar_split_clause,[],[f1662,f17553]) ).
fof(f17553,plain,
( spl0_1769
<=> ! [X5,X23,X6,X2,X7] :
( c_in(X2,c_Relation_ODomain(X6,X5,X23),X5)
| ~ c_in(c_Pair(X2,X7,X5,X23),X6,tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f1662,axiom,
! [X2,X6,X7,X5,X23] :
( c_in(X2,c_Relation_ODomain(X6,X5,X23),X5)
| ~ c_in(c_Pair(X2,X7,X5,X23),X6,tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f17551,plain,
spl0_1768,
inference(avatar_split_clause,[],[f1650,f17549]) ).
fof(f17549,plain,
( spl0_1768
<=> ! [X77,X4,X5,X1] :
( c_in(X77,c_List_Olists(X1,X5),tc_List_Olist(X5))
| ~ c_in(c_List_Olist_OCons(X4,X77,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f1650,axiom,
! [X1,X77,X4,X5] :
( c_in(X77,c_List_Olists(X1,X5),tc_List_Olist(X5))
| ~ c_in(c_List_Olist_OCons(X4,X77,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f17547,plain,
spl0_1767,
inference(avatar_split_clause,[],[f1638,f17545]) ).
fof(f17545,plain,
( spl0_1767
<=> ! [X44,X34,X5,X1] :
( c_in(X34,X1,X5)
| ~ c_in(X34,c_List_Oset(X44,X5),X5)
| ~ c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f1638,axiom,
! [X1,X44,X34,X5] :
( c_in(X34,X1,X5)
| ~ c_in(X34,c_List_Oset(X44,X5),X5)
| ~ c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f17543,plain,
spl0_1766,
inference(avatar_split_clause,[],[f1559,f17541]) ).
fof(f17541,plain,
( spl0_1766
<=> ! [X4,X5,X1] :
( ~ c_lessequals(X1,c_insert(X4,c_emptyset,X5),tc_set(X5))
| c_insert(X4,X1,X5) = c_insert(X4,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f1559,axiom,
! [X1,X4,X5] :
( ~ c_lessequals(X1,c_insert(X4,c_emptyset,X5),tc_set(X5))
| c_insert(X4,X1,X5) = c_insert(X4,c_emptyset,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
fof(f17539,plain,
spl0_1765,
inference(avatar_split_clause,[],[f1558,f17537]) ).
fof(f17537,plain,
( spl0_1765
<=> ! [X2,X5,X1,X7] :
( c_lessequals(X1,c_insert(X7,c_emptyset,X5),tc_set(X5))
| c_insert(X2,X1,X5) != c_insert(X7,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f1558,axiom,
! [X2,X1,X7,X5] :
( c_lessequals(X1,c_insert(X7,c_emptyset,X5),tc_set(X5))
| c_insert(X2,X1,X5) != c_insert(X7,c_emptyset,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
fof(f17535,plain,
spl0_1764,
inference(avatar_split_clause,[],[f1555,f17533]) ).
fof(f17533,plain,
( spl0_1764
<=> ! [X35,X4,X5,X1] :
( ~ c_in(X4,X35,X5)
| ~ c_lessequals(X1,X35,tc_set(X5))
| c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f1555,axiom,
! [X1,X4,X35,X5] :
( ~ c_in(X4,X35,X5)
| ~ c_lessequals(X1,X35,tc_set(X5))
| c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f17531,plain,
spl0_1763,
inference(avatar_split_clause,[],[f1438,f17529]) ).
fof(f17529,plain,
( spl0_1763
<=> ! [X18,X5] :
( ~ class_Orderings_Oorder(X5)
| c_insert(X18,c_emptyset,X5) = c_minus(c_insert(X18,c_emptyset,X5),c_SetInterval_OlessThan(X18,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f1438,axiom,
! [X18,X5] :
( ~ class_Orderings_Oorder(X5)
| c_insert(X18,c_emptyset,X5) = c_minus(c_insert(X18,c_emptyset,X5),c_SetInterval_OlessThan(X18,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f17527,plain,
( spl0_1762
| ~ spl0_1599
| ~ spl0_1720 ),
inference(avatar_split_clause,[],[f17386,f17334,f14370,f17525]) ).
fof(f17525,plain,
( spl0_1762
<=> ! [X0] :
( ~ c_in(X0,c_UNIV,t_a)
| c_in(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(X0,c_uminus(v_S,tc_set(t_a)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f14370,plain,
( spl0_1599
<=> ! [X35,X31,X5,X1] :
( c_in(X31,X1,X5)
| c_in(X31,X35,X5)
| ~ c_in(X31,c_union(X1,X35,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f17334,plain,
( spl0_1720
<=> c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f17386,plain,
( ! [X0] :
( ~ c_in(X0,c_UNIV,t_a)
| c_in(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(X0,c_uminus(v_S,tc_set(t_a)),t_a) )
| ~ spl0_1599
| ~ spl0_1720 ),
inference(superposition,[],[f14371,f17336]) ).
fof(f17336,plain,
( c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_1720 ),
inference(avatar_component_clause,[],[f17334]) ).
fof(f14371,plain,
( ! [X31,X1,X35,X5] :
( ~ c_in(X31,c_union(X1,X35,X5),X5)
| c_in(X31,X35,X5)
| c_in(X31,X1,X5) )
| ~ spl0_1599 ),
inference(avatar_component_clause,[],[f14370]) ).
fof(f17523,plain,
spl0_1761,
inference(avatar_split_clause,[],[f1430,f17521]) ).
fof(f17521,plain,
( spl0_1761
<=> ! [X5,X55,X29,X19,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X55,X29,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f1430,axiom,
! [X29,X19,X55,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X55,X29,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X29,X55,X5),c_SetInterval_OatLeastLessThan(X30,X19,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f17519,plain,
spl0_1760,
inference(avatar_split_clause,[],[f1421,f17517]) ).
fof(f17517,plain,
( spl0_1760
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X77,X29,X5)
| ~ c_less(X29,X41,X5)
| c_in(X29,c_SetInterval_OgreaterThanLessThan(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f1421,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X77,X29,X5)
| ~ c_less(X29,X41,X5)
| c_in(X29,c_SetInterval_OgreaterThanLessThan(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f17515,plain,
spl0_1759,
inference(avatar_split_clause,[],[f1418,f17513]) ).
fof(f17513,plain,
( spl0_1759
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X29,X41,X5)
| ~ c_less(X77,X29,X5)
| c_in(X29,c_SetInterval_OgreaterThanAtMost(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f1418,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X29,X41,X5)
| ~ c_less(X77,X29,X5)
| c_in(X29,c_SetInterval_OgreaterThanAtMost(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f17511,plain,
spl0_1758,
inference(avatar_split_clause,[],[f1391,f17509]) ).
fof(f17509,plain,
( spl0_1758
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X77,X29,X5)
| ~ c_less(X29,X41,X5)
| c_in(X29,c_SetInterval_OatLeastLessThan(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f1391,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X77,X29,X5)
| ~ c_less(X29,X41,X5)
| c_in(X29,c_SetInterval_OatLeastLessThan(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f17507,plain,
spl0_1757,
inference(avatar_split_clause,[],[f1386,f17505]) ).
fof(f17505,plain,
( spl0_1757
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X77,X29,X5)
| ~ c_lessequals(X29,X41,X5)
| c_in(X29,c_SetInterval_OatLeastAtMost(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f1386,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X77,X29,X5)
| ~ c_lessequals(X29,X41,X5)
| c_in(X29,c_SetInterval_OatLeastAtMost(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f17503,plain,
spl0_1756,
inference(avatar_split_clause,[],[f1189,f17501]) ).
fof(f17501,plain,
( spl0_1756
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X4,c_0,X5)
| ~ c_less(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f1189,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X4,c_0,X5)
| ~ c_less(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f17499,plain,
spl0_1755,
inference(avatar_split_clause,[],[f1172,f17497]) ).
fof(f17497,plain,
( spl0_1755
<=> ! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| c_Parity_Oeven(X4,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f1172,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| c_Parity_Oeven(X4,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f17495,plain,
spl0_1754,
inference(avatar_split_clause,[],[f1170,f17493]) ).
fof(f17493,plain,
( spl0_1754
<=> ! [X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X4,tc_nat)
| c_uminus(c_1,X5) = c_Nat_Opower(c_uminus(c_1,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f1170,axiom,
! [X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X4,tc_nat)
| c_uminus(c_1,X5) = c_Nat_Opower(c_uminus(c_1,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f17491,plain,
spl0_1753,
inference(avatar_split_clause,[],[f1131,f17489]) ).
fof(f17489,plain,
( spl0_1753
<=> ! [X4,X23,X9,X8] :
( ~ class_Orderings_Olinorder(X23)
| ~ c_lessequals(X4,X9,X23)
| ~ c_lessequals(X8,X9,X23)
| c_lessequals(c_Orderings_Omax(X4,X8,X23),X9,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f1131,axiom,
! [X8,X9,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| ~ c_lessequals(X4,X9,X23)
| ~ c_lessequals(X8,X9,X23)
| c_lessequals(c_Orderings_Omax(X4,X8,X23),X9,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f17487,plain,
spl0_1752,
inference(avatar_split_clause,[],[f1126,f17485]) ).
fof(f17485,plain,
( spl0_1752
<=> ! [X4,X23,X9,X8] :
( ~ class_Orderings_Olinorder(X23)
| ~ c_lessequals(X4,X8,X23)
| ~ c_lessequals(X4,X9,X23)
| c_lessequals(X4,c_Orderings_Omin(X8,X9,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f1126,axiom,
! [X8,X9,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| ~ c_lessequals(X4,X8,X23)
| ~ c_lessequals(X4,X9,X23)
| c_lessequals(X4,c_Orderings_Omin(X8,X9,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f17472,plain,
spl0_1751,
inference(avatar_split_clause,[],[f1123,f17470]) ).
fof(f17470,plain,
( spl0_1751
<=> ! [X4,X9,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X9,X4,X5)
| ~ c_less(X9,X8,X5)
| c_less(X9,c_Orderings_Omin(X4,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f1123,axiom,
! [X8,X9,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X9,X4,X5)
| ~ c_less(X9,X8,X5)
| c_less(X9,c_Orderings_Omin(X4,X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f17468,plain,
spl0_1750,
inference(avatar_split_clause,[],[f1120,f17466]) ).
fof(f17466,plain,
( spl0_1750
<=> ! [X5,X4,X9,X8] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X4,X9,X5)
| ~ c_less(X8,X9,X5)
| c_less(c_Orderings_Omax(X4,X8,X5),X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f1120,axiom,
! [X8,X9,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X4,X9,X5)
| ~ c_less(X8,X9,X5)
| c_less(c_Orderings_Omax(X4,X8,X5),X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f17464,plain,
spl0_1749,
inference(avatar_split_clause,[],[f1102,f17462]) ).
fof(f17462,plain,
( spl0_1749
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Omeet(X2,X7,X5),X5) = c_LOrder_Ojoin(c_uminus(X2,X5),c_uminus(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f1102,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Omeet(X2,X7,X5),X5) = c_LOrder_Ojoin(c_uminus(X2,X5),c_uminus(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f17460,plain,
spl0_1748,
inference(avatar_split_clause,[],[f1093,f17458]) ).
fof(f17458,plain,
( spl0_1748
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Ojoin(X2,X7,X5),X5) = c_LOrder_Omeet(c_uminus(X2,X5),c_uminus(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f1093,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Ojoin(X2,X7,X5),X5) = c_LOrder_Omeet(c_uminus(X2,X5),c_uminus(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f17456,plain,
spl0_1747,
inference(avatar_split_clause,[],[f1079,f17454]) ).
fof(f17454,plain,
( spl0_1747
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_plus(X2,X7,X5),X5) = c_plus(c_uminus(X2,X5),c_uminus(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f1079,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_plus(X2,X7,X5),X5) = c_plus(c_uminus(X2,X5),c_uminus(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f17452,plain,
spl0_1746,
inference(avatar_split_clause,[],[f708,f17450]) ).
fof(f17450,plain,
( spl0_1746
<=> ! [X80,X40] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_Numeral_Onumber__of(X80,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f708,axiom,
! [X40,X80] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_Numeral_Onumber__of(X80,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f17448,plain,
spl0_1745,
inference(avatar_split_clause,[],[f701,f17446]) ).
fof(f17446,plain,
( spl0_1745
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_Numeral_Onumber__of(X80,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f701,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_nat) = c_Numeral_Onumber__of(X80,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f17444,plain,
spl0_1744,
inference(avatar_split_clause,[],[f689,f17442]) ).
fof(f17442,plain,
( spl0_1744
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X80,tc_nat) = c_plus(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f689,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X80,tc_nat) = c_plus(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f17440,plain,
spl0_1743,
inference(avatar_split_clause,[],[f686,f17438]) ).
fof(f17438,plain,
( spl0_1743
<=> ! [X30,X5,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_times(X30,X19,tc_nat),X5) = c_times(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f686,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_times(X30,X19,tc_nat),X5) = c_times(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f17436,plain,
spl0_1742,
inference(avatar_split_clause,[],[f674,f17434]) ).
fof(f17434,plain,
( spl0_1742
<=> ! [X30,X5,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_plus(X30,X19,tc_nat),X5) = c_plus(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f674,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_plus(X30,X19,tc_nat),X5) = c_plus(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f17432,plain,
( spl0_1741
| ~ spl0_796
| ~ spl0_1600
| ~ spl0_1720 ),
inference(avatar_split_clause,[],[f17388,f17334,f14374,f7278,f17430]) ).
fof(f17388,plain,
( ! [X0] : c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a)
| ~ spl0_796
| ~ spl0_1600
| ~ spl0_1720 ),
inference(forward_demodulation,[],[f17387,f15225]) ).
fof(f17387,plain,
( ! [X0] : c_union(c_uminus(v_S,tc_set(t_a)),c_insert(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),t_a) = c_insert(X0,c_UNIV,t_a)
| ~ spl0_1600
| ~ spl0_1720 ),
inference(superposition,[],[f14375,f17336]) ).
fof(f17428,plain,
spl0_1740,
inference(avatar_split_clause,[],[f646,f17426]) ).
fof(f17426,plain,
( spl0_1740
<=> ! [X4,X5,X19] :
( c_0 = X19
| c_List_Otl(c_List_Oreplicate(X19,X4,X5),X5) = c_List_Oreplicate(c_minus(X19,c_1,tc_nat),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f646,axiom,
! [X19,X4,X5] :
( c_0 = X19
| c_List_Otl(c_List_Oreplicate(X19,X4,X5),X5) = c_List_Oreplicate(c_minus(X19,c_1,tc_nat),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f17424,plain,
spl0_1739,
inference(avatar_split_clause,[],[f564,f17422]) ).
fof(f17422,plain,
( spl0_1739
<=> ! [X5,X44,X29,X8] :
( ~ c_less(X29,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Olist__update(X44,X29,X8,X5),X29,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f564,axiom,
! [X29,X8,X44,X5] :
( ~ c_less(X29,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Olist__update(X44,X29,X8,X5),X29,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f17420,plain,
spl0_1738,
inference(avatar_split_clause,[],[f498,f17418]) ).
fof(f17418,plain,
( spl0_1738
<=> ! [X29,X5,X8] :
( ~ c_less(X29,c_Nat_Osize(X8,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(X8,X29,c_List_Onth(X8,X29,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f498,axiom,
! [X29,X8,X5] :
( ~ c_less(X29,c_Nat_Osize(X8,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(X8,X29,c_List_Onth(X8,X29,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f17416,plain,
spl0_1737,
inference(avatar_split_clause,[],[f457,f17414]) ).
fof(f17414,plain,
( spl0_1737
<=> ! [X5,X44,X19] :
( ~ c_less(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Olast(X44,X5) = c_List_Olast(c_List_Odrop(X19,X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f457,axiom,
! [X19,X44,X5] :
( ~ c_less(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Olast(X44,X5) = c_List_Olast(c_List_Odrop(X19,X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f17412,plain,
spl0_1736,
inference(avatar_split_clause,[],[f390,f17410]) ).
fof(f17410,plain,
( spl0_1736
<=> ! [X45,X5,X1,X44] :
( c_in(X45,c_List_Olists(X1,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X44,X45,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f390,axiom,
! [X1,X44,X45,X5] :
( c_in(X45,c_List_Olists(X1,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X44,X45,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f17408,plain,
spl0_1735,
inference(avatar_split_clause,[],[f389,f17406]) ).
fof(f17406,plain,
( spl0_1735
<=> ! [X44,X5,X45,X1] :
( c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X44,X45,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f389,axiom,
! [X1,X44,X45,X5] :
( c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X44,X45,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f17404,plain,
spl0_1734,
inference(avatar_split_clause,[],[f282,f17402]) ).
fof(f17402,plain,
( spl0_1734
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_times(X39,X9,tc_IntDef_Oint),X5) = c_times(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f282,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_times(X39,X9,tc_IntDef_Oint),X5) = c_times(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f17400,plain,
spl0_1733,
inference(avatar_split_clause,[],[f268,f17398]) ).
fof(f17398,plain,
( spl0_1733
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_minus(X39,X9,tc_IntDef_Oint),X5) = c_minus(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f268,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_minus(X39,X9,tc_IntDef_Oint),X5) = c_minus(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f17396,plain,
spl0_1732,
inference(avatar_split_clause,[],[f267,f17394]) ).
fof(f17394,plain,
( spl0_1732
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_plus(X39,X9,tc_IntDef_Oint),X5) = c_plus(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f267,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_plus(X39,X9,tc_IntDef_Oint),X5) = c_plus(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f17392,plain,
spl0_1731,
inference(avatar_split_clause,[],[f231,f17390]) ).
fof(f17390,plain,
( spl0_1731
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X2,c_IntDef_ONats,X5)
| ~ c_in(X7,c_IntDef_ONats,X5)
| c_in(c_times(X2,X7,X5),c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f231,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X2,c_IntDef_ONats,X5)
| ~ c_in(X7,c_IntDef_ONats,X5)
| c_in(c_times(X2,X7,X5),c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f17377,plain,
spl0_1730,
inference(avatar_split_clause,[],[f230,f17375]) ).
fof(f17375,plain,
( spl0_1730
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X2,c_IntDef_ONats,X5)
| ~ c_in(X7,c_IntDef_ONats,X5)
| c_in(c_plus(X2,X7,X5),c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f230,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X2,c_IntDef_ONats,X5)
| ~ c_in(X7,c_IntDef_ONats,X5)
| c_in(c_plus(X2,X7,X5),c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f17373,plain,
spl0_1729,
inference(avatar_split_clause,[],[f227,f17371]) ).
fof(f17371,plain,
( spl0_1729
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| ~ c_in(X7,c_IntDef_OInts,X5)
| c_in(c_times(X2,X7,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f227,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| ~ c_in(X7,c_IntDef_OInts,X5)
| c_in(c_times(X2,X7,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f17369,plain,
spl0_1728,
inference(avatar_split_clause,[],[f225,f17367]) ).
fof(f17367,plain,
( spl0_1728
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| ~ c_in(X7,c_IntDef_OInts,X5)
| c_in(c_minus(X2,X7,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f225,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| ~ c_in(X7,c_IntDef_OInts,X5)
| c_in(c_minus(X2,X7,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f17365,plain,
spl0_1727,
inference(avatar_split_clause,[],[f224,f17363]) ).
fof(f17363,plain,
( spl0_1727
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| ~ c_in(X7,c_IntDef_OInts,X5)
| c_in(c_plus(X2,X7,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f224,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| ~ c_in(X7,c_IntDef_OInts,X5)
| c_in(c_plus(X2,X7,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f17361,plain,
spl0_1726,
inference(avatar_split_clause,[],[f171,f17359]) ).
fof(f17359,plain,
( spl0_1726
<=> ! [X30,X18,X19] :
( ~ c_Divides_Oop_Advd(X18,X19,tc_nat)
| ~ c_Divides_Oop_Advd(X18,X30,tc_nat)
| c_Divides_Oop_Advd(X18,c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f171,axiom,
! [X18,X19,X30] :
( ~ c_Divides_Oop_Advd(X18,X19,tc_nat)
| ~ c_Divides_Oop_Advd(X18,X30,tc_nat)
| c_Divides_Oop_Advd(X18,c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f17357,plain,
spl0_1725,
inference(avatar_split_clause,[],[f155,f17355]) ).
fof(f17355,plain,
( spl0_1725
<=> ! [X6,X5,X23] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X23,X5)))
| c_in(c_Relation_Oconverse(X6,X23,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f155,axiom,
! [X6,X5,X23] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X23,X5)))
| c_in(c_Relation_Oconverse(X6,X23,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f17353,plain,
spl0_1724,
inference(avatar_split_clause,[],[f154,f17351]) ).
fof(f17351,plain,
( spl0_1724
<=> ! [X6,X5,X23] :
( c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X23,X5)))
| ~ c_in(c_Relation_Oconverse(X6,X23,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f154,axiom,
! [X6,X5,X23] :
( c_in(X6,c_Finite__Set_OFinites,tc_set(tc_prod(X23,X5)))
| ~ c_in(c_Relation_Oconverse(X6,X23,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f17349,plain,
spl0_1723,
inference(avatar_split_clause,[],[f24,f17347]) ).
fof(f17347,plain,
( spl0_1723
<=> ! [X5,X17,X11,X14,X13,X12] : c_Tarski_Opotype_Omore__update(X17,c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14),X14,X5) = c_Tarski_Opotype_Opotype__ext(X11,X12,X17,X5,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f24,axiom,
! [X11,X14,X17,X5,X12,X13] : c_Tarski_Opotype_Omore__update(X17,c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14),X14,X5) = c_Tarski_Opotype_Opotype__ext(X11,X12,X17,X5,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oupdate__convs__3_0) ).
fof(f17345,plain,
spl0_1722,
inference(avatar_split_clause,[],[f23,f17343]) ).
fof(f17343,plain,
( spl0_1722
<=> ! [X11,X13,X14,X12,X5,X16] : c_Tarski_Opotype_Oorder__update(X16,c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14),X5,X14) = c_Tarski_Opotype_Opotype__ext(X11,X16,X13,X5,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f23,axiom,
! [X11,X16,X14,X5,X12,X13] : c_Tarski_Opotype_Oorder__update(X16,c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14),X5,X14) = c_Tarski_Opotype_Opotype__ext(X11,X16,X13,X5,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oupdate__convs__2_0) ).
fof(f17341,plain,
spl0_1721,
inference(avatar_split_clause,[],[f22,f17339]) ).
fof(f17339,plain,
( spl0_1721
<=> ! [X11,X13,X14,X12,X5,X15] : c_Tarski_Opotype_Opset__update(X15,c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14),X5,X14) = c_Tarski_Opotype_Opotype__ext(X15,X12,X13,X5,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f22,axiom,
! [X11,X14,X15,X5,X12,X13] : c_Tarski_Opotype_Opset__update(X15,c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14),X5,X14) = c_Tarski_Opotype_Opotype__ext(X15,X12,X13,X5,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oupdate__convs__1_0) ).
fof(f17337,plain,
( spl0_1720
| ~ spl0_795
| ~ spl0_1355
| ~ spl0_1677 ),
inference(avatar_split_clause,[],[f17089,f15687,f11157,f7274,f17334]) ).
fof(f7274,plain,
( spl0_795
<=> ! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f11157,plain,
( spl0_1355
<=> c_emptyset = c_minus(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f15687,plain,
( spl0_1677
<=> ! [X5,X1,X35] : c_uminus(c_minus(X1,X35,tc_set(X5)),tc_set(X5)) = c_union(c_uminus(X1,tc_set(X5)),X35,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f17089,plain,
( c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_795
| ~ spl0_1355
| ~ spl0_1677 ),
inference(forward_demodulation,[],[f17050,f7275]) ).
fof(f7275,plain,
( ! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5))
| ~ spl0_795 ),
inference(avatar_component_clause,[],[f7274]) ).
fof(f17050,plain,
( c_union(c_uminus(v_S,tc_set(t_a)),c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) = c_uminus(c_emptyset,tc_set(t_a))
| ~ spl0_1355
| ~ spl0_1677 ),
inference(superposition,[],[f15688,f11159]) ).
fof(f11159,plain,
( c_emptyset = c_minus(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ spl0_1355 ),
inference(avatar_component_clause,[],[f11157]) ).
fof(f15688,plain,
( ! [X1,X35,X5] : c_uminus(c_minus(X1,X35,tc_set(X5)),tc_set(X5)) = c_union(c_uminus(X1,tc_set(X5)),X35,X5)
| ~ spl0_1677 ),
inference(avatar_component_clause,[],[f15687]) ).
fof(f16240,plain,
( spl0_1717
| spl0_1719 ),
inference(avatar_split_clause,[],[f3173,f16238,f16217]) ).
fof(f16217,plain,
( spl0_1717
<=> ! [X39] : c_0 != c_Numeral_Onumber__of(X39,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f16238,plain,
( spl0_1719
<=> ! [X4,X5] :
( ~ class_Power_Orecpower(X5)
| c_less(c_0,c_Nat_Opower(X4,c_0,X5),X5)
| ~ class_Ring__and__Field_Oordered__idom(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f3173,plain,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X39,tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_0,X5),X5) ),
inference(inner_rewriting,[],[f1199]) ).
fof(f1199,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X39,tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f16226,plain,
( ~ spl0_701
| ~ spl0_1717 ),
inference(avatar_contradiction_clause,[],[f16225]) ).
fof(f16225,plain,
( $false
| ~ spl0_701
| ~ spl0_1717 ),
inference(trivial_inequality_removal,[],[f16223]) ).
fof(f16223,plain,
( c_0 != c_0
| ~ spl0_701
| ~ spl0_1717 ),
inference(superposition,[],[f16218,f6877]) ).
fof(f6877,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f6875]) ).
fof(f6875,plain,
( spl0_701
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f16218,plain,
( ! [X39] : c_0 != c_Numeral_Onumber__of(X39,tc_nat)
| ~ spl0_1717 ),
inference(avatar_component_clause,[],[f16217]) ).
fof(f16222,plain,
( spl0_1717
| spl0_1718 ),
inference(avatar_split_clause,[],[f3172,f16220,f16217]) ).
fof(f16220,plain,
( spl0_1718
<=> ! [X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ c_lessequals(c_Nat_Opower(X4,c_0,X5),c_0,X5)
| ~ class_Ring__and__Field_Oordered__idom(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f3172,plain,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X39,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X4,c_0,X5),c_0,X5) ),
inference(inner_rewriting,[],[f1182]) ).
fof(f1182,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X39,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f16187,plain,
( spl0_1716
| ~ spl0_1364
| ~ spl0_1406 ),
inference(avatar_split_clause,[],[f14410,f11537,f11368,f16184]) ).
fof(f16184,plain,
( spl0_1716
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f11368,plain,
( spl0_1364
<=> v_S = c_Tarski_Ointerval(v_r,v_a,v_b,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f11537,plain,
( spl0_1406
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f14410,plain,
( c_emptyset = c_SetInterval_OgreaterThanAtMost(v_S,v_S,tc_set(t_a))
| ~ spl0_1364
| ~ spl0_1406 ),
inference(superposition,[],[f11539,f11370]) ).
fof(f11370,plain,
( v_S = c_Tarski_Ointerval(v_r,v_a,v_b,t_a)
| ~ spl0_1364 ),
inference(avatar_component_clause,[],[f11368]) ).
fof(f11539,plain,
( c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_1406 ),
inference(avatar_component_clause,[],[f11537]) ).
fof(f16182,plain,
( spl0_1715
| ~ spl0_115
| ~ spl0_673
| ~ spl0_771
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1610
| ~ spl0_1714 ),
inference(avatar_split_clause,[],[f16178,f16174,f14448,f10445,f10140,f7177,f6747,f3739,f16180]) ).
fof(f16180,plain,
( spl0_1715
<=> ! [X8] :
( c_plus(c_1,c_minus(X8,c_1,tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f14448,plain,
( spl0_1610
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,c_plus(c_1,X77,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f16174,plain,
( spl0_1714
<=> ! [X8] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f16178,plain,
( ! [X8] :
( c_plus(c_1,c_minus(X8,c_1,tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_771
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1610
| ~ spl0_1714 ),
inference(forward_demodulation,[],[f16177,f14451]) ).
fof(f14451,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_771
| ~ spl0_1610 ),
inference(superposition,[],[f14449,f7178]) ).
fof(f14449,plain,
( ! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,c_plus(c_1,X77,tc_nat),tc_nat)
| ~ spl0_1610 ),
inference(avatar_component_clause,[],[f14448]) ).
fof(f16177,plain,
( ! [X8] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1714 ),
inference(forward_demodulation,[],[f16175,f11255]) ).
fof(f16175,plain,
( ! [X8] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) )
| ~ spl0_1714 ),
inference(avatar_component_clause,[],[f16174]) ).
fof(f16176,plain,
spl0_1714,
inference(avatar_split_clause,[],[f3064,f16174]) ).
fof(f3064,plain,
! [X8] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X8,tc_nat),tc_nat),tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) ),
inference(forward_demodulation,[],[f2884,f2814]) ).
fof(f2814,plain,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,c_Finite__Set_Ocard(c_SetInterval_OatMost(X77,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1412,f1409]) ).
fof(f1412,axiom,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,c_Suc(X77),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f2884,plain,
! [X8] :
( ~ c_less(c_0,X8,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X8 ),
inference(definition_unfolding,[],[f889,f1409,f1409]) ).
fof(f889,axiom,
! [X8] :
( ~ c_less(c_0,X8,tc_nat)
| c_Suc(c_minus(X8,c_Suc(c_0),tc_nat)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f16172,plain,
spl0_1713,
inference(avatar_split_clause,[],[f2912,f16170]) ).
fof(f16170,plain,
( spl0_1713
<=> ! [X35,X5,X1,X83] :
( c_lessequals(X83,X1,tc_set(X5))
| ~ c_lessequals(X83,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f2912,plain,
! [X83,X1,X5,X35] :
( c_lessequals(X83,X1,tc_set(X5))
| ~ c_lessequals(X83,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)) ),
inference(definition_unfolding,[],[f1474,f1238]) ).
fof(f1474,axiom,
! [X83,X1,X5,X35] :
( c_lessequals(X83,X1,tc_set(X5))
| ~ c_lessequals(X83,c_inter(X1,X35,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f16168,plain,
spl0_1712,
inference(avatar_split_clause,[],[f2911,f16166]) ).
fof(f16166,plain,
( spl0_1712
<=> ! [X35,X5,X1,X83] :
( c_lessequals(X83,X35,tc_set(X5))
| ~ c_lessequals(X83,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f2911,plain,
! [X83,X1,X35,X5] :
( c_lessequals(X83,X35,tc_set(X5))
| ~ c_lessequals(X83,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),tc_set(X5)) ),
inference(definition_unfolding,[],[f1475,f1238]) ).
fof(f1475,axiom,
! [X83,X1,X35,X5] :
( c_lessequals(X83,X35,tc_set(X5))
| ~ c_lessequals(X83,c_inter(X1,X35,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f16164,plain,
spl0_1711,
inference(avatar_split_clause,[],[f2907,f16162]) ).
fof(f16162,plain,
( spl0_1711
<=> ! [X38,X5,X37] :
( ~ c_in(X37,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X37,X5),X38,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f2907,plain,
! [X38,X37,X5] :
( ~ c_in(X37,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X37,X5),X38,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
inference(definition_unfolding,[],[f1622,f1238]) ).
fof(f1622,axiom,
! [X38,X37,X5] :
( ~ c_in(X37,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_inter(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f16160,plain,
spl0_1710,
inference(avatar_split_clause,[],[f2906,f16158]) ).
fof(f16158,plain,
( spl0_1710
<=> ! [X38,X5,X37] :
( ~ c_in(X38,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X37,X5),X38,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f2906,plain,
! [X38,X37,X5] :
( ~ c_in(X38,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X37,X5),X38,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
inference(definition_unfolding,[],[f1623,f1238]) ).
fof(f1623,axiom,
! [X38,X37,X5] :
( ~ c_in(X38,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_inter(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f16154,plain,
spl0_1709,
inference(avatar_split_clause,[],[f2899,f16152]) ).
fof(f16152,plain,
( spl0_1709
<=> ! [X30,X19] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f2899,plain,
! [X19,X30] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f886,f1409,f1409]) ).
fof(f886,axiom,
! [X19,X30] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_Suc(X30),c_Suc(X19),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f16148,plain,
spl0_1708,
inference(avatar_split_clause,[],[f2895,f16146]) ).
fof(f16146,plain,
( spl0_1708
<=> ! [X19,X30] :
( c_lessequals(X19,X30,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f2895,plain,
! [X19,X30] :
( c_lessequals(X19,X30,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f884,f1409,f1409]) ).
fof(f884,axiom,
! [X19,X30] :
( c_lessequals(X19,X30,tc_nat)
| ~ c_lessequals(c_Suc(X19),c_Suc(X30),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f16144,plain,
spl0_1707,
inference(avatar_split_clause,[],[f2892,f16142]) ).
fof(f2892,plain,
! [X2,X1,X35,X5] :
( ~ c_in(X2,X35,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X2,X1,X5),X5),X35,X5,X5) ),
inference(definition_unfolding,[],[f1542,f1238]) ).
fof(f1542,axiom,
! [X2,X1,X35,X5] :
( ~ c_in(X2,X35,X5)
| c_emptyset != c_inter(c_insert(X2,X1,X5),X35,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
fof(f16140,plain,
spl0_1706,
inference(avatar_split_clause,[],[f2890,f16138]) ).
fof(f2890,plain,
! [X1,X7,X5,X35] :
( ~ c_in(X7,X1,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X1,X5),c_insert(X7,X35,X5),X5,X5) ),
inference(definition_unfolding,[],[f1529,f1238]) ).
fof(f1529,axiom,
! [X1,X7,X5,X35] :
( ~ c_in(X7,X1,X5)
| c_emptyset != c_inter(X1,c_insert(X7,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
fof(f16135,plain,
( ~ spl0_726
| spl0_1698 ),
inference(avatar_contradiction_clause,[],[f16133]) ).
fof(f16133,plain,
( $false
| ~ spl0_726
| spl0_1698 ),
inference(resolution,[],[f16076,f6983]) ).
fof(f6983,plain,
( ! [X1,X5] : c_lessequals(X1,X1,tc_set(X5))
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f6982]) ).
fof(f6982,plain,
( spl0_726
<=> ! [X5,X1] : c_lessequals(X1,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f16076,plain,
( ~ c_lessequals(v_S,v_S,tc_set(t_a))
| spl0_1698 ),
inference(avatar_component_clause,[],[f16074]) ).
fof(f16074,plain,
( spl0_1698
<=> c_lessequals(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f16130,plain,
spl0_1705,
inference(avatar_split_clause,[],[f2886,f16128]) ).
fof(f16128,plain,
( spl0_1705
<=> ! [X19,X30] :
( ~ c_lessequals(X19,X30,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f2886,plain,
! [X19,X30] :
( ~ c_lessequals(X19,X30,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f885,f1409,f1409]) ).
fof(f885,axiom,
! [X19,X30] :
( ~ c_lessequals(X19,X30,tc_nat)
| c_lessequals(c_Suc(X19),c_Suc(X30),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f16124,plain,
spl0_1704,
inference(avatar_split_clause,[],[f2881,f16122]) ).
fof(f16122,plain,
( spl0_1704
<=> ! [X30,X19] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f2881,plain,
! [X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f887,f1409,f1409]) ).
fof(f887,axiom,
! [X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_Suc(X30),c_Suc(X19),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f16116,plain,
( spl0_1703
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1702 ),
inference(avatar_split_clause,[],[f16112,f16109,f10445,f10140,f6747,f3739,f16114]) ).
fof(f16114,plain,
( spl0_1703
<=> ! [X21,X30] :
( c_plus(c_NatArith_Oof__nat(X30,X21),c_1,X21) = c_NatArith_Oof__nat(c_plus(c_1,X30,tc_nat),X21)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f16109,plain,
( spl0_1702
<=> ! [X21,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X21)
| c_plus(c_NatArith_Oof__nat(X30,X21),c_1,X21) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f16112,plain,
( ! [X21,X30] :
( c_plus(c_NatArith_Oof__nat(X30,X21),c_1,X21) = c_NatArith_Oof__nat(c_plus(c_1,X30,tc_nat),X21)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X21) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1702 ),
inference(forward_demodulation,[],[f16110,f11255]) ).
fof(f16110,plain,
( ! [X21,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X21)
| c_plus(c_NatArith_Oof__nat(X30,X21),c_1,X21) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X21) )
| ~ spl0_1702 ),
inference(avatar_component_clause,[],[f16109]) ).
fof(f16111,plain,
spl0_1702,
inference(avatar_split_clause,[],[f2868,f16109]) ).
fof(f2868,plain,
! [X21,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X21)
| c_plus(c_NatArith_Oof__nat(X30,X21),c_1,X21) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X21) ),
inference(definition_unfolding,[],[f667,f1409]) ).
fof(f667,axiom,
! [X21,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X21)
| c_NatArith_Oof__nat(c_Suc(X30),X21) = c_plus(c_NatArith_Oof__nat(X30,X21),c_1,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f16103,plain,
( spl0_1701
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1700 ),
inference(avatar_split_clause,[],[f16099,f16096,f10445,f10140,f6747,f3739,f16101]) ).
fof(f16101,plain,
( spl0_1701
<=> ! [X44,X4,X5,X19] : c_List_Onth(X44,X19,X5) = c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_plus(c_1,X19,tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f16096,plain,
( spl0_1700
<=> ! [X44,X4,X5,X19] : c_List_Onth(X44,X19,X5) = c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f16099,plain,
( ! [X44,X19,X4,X5] : c_List_Onth(X44,X19,X5) = c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_plus(c_1,X19,tc_nat),X5)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1700 ),
inference(forward_demodulation,[],[f16097,f11255]) ).
fof(f16097,plain,
( ! [X44,X19,X4,X5] : c_List_Onth(X44,X19,X5) = c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X5)
| ~ spl0_1700 ),
inference(avatar_component_clause,[],[f16096]) ).
fof(f16098,plain,
spl0_1700,
inference(avatar_split_clause,[],[f2828,f16096]) ).
fof(f2828,plain,
! [X44,X19,X4,X5] : c_List_Onth(X44,X19,X5) = c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X5),
inference(definition_unfolding,[],[f558,f1409]) ).
fof(f558,axiom,
! [X44,X19,X4,X5] : c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_Suc(X19),X5) = c_List_Onth(X44,X19,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f16081,plain,
( spl0_1699
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1697 ),
inference(avatar_split_clause,[],[f16072,f16069,f10445,f10140,f6747,f3739,f16079]) ).
fof(f16079,plain,
( spl0_1699
<=> ! [X44,X4,X5,X19] : c_List_Odrop(X19,X44,X5) = c_List_Odrop(c_plus(c_1,X19,tc_nat),c_List_Olist_OCons(X4,X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f16069,plain,
( spl0_1697
<=> ! [X44,X4,X5,X19] : c_List_Odrop(X19,X44,X5) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_List_Olist_OCons(X4,X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f16072,plain,
( ! [X19,X44,X4,X5] : c_List_Odrop(X19,X44,X5) = c_List_Odrop(c_plus(c_1,X19,tc_nat),c_List_Olist_OCons(X4,X44,X5),X5)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1697 ),
inference(forward_demodulation,[],[f16070,f11255]) ).
fof(f16070,plain,
( ! [X19,X44,X4,X5] : c_List_Odrop(X19,X44,X5) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_List_Olist_OCons(X4,X44,X5),X5)
| ~ spl0_1697 ),
inference(avatar_component_clause,[],[f16069]) ).
fof(f16077,plain,
( ~ spl0_1698
| ~ spl0_1364
| spl0_1626 ),
inference(avatar_split_clause,[],[f15828,f15287,f11368,f16074]) ).
fof(f15287,plain,
( spl0_1626
<=> c_lessequals(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f15828,plain,
( ~ c_lessequals(v_S,v_S,tc_set(t_a))
| ~ spl0_1364
| spl0_1626 ),
inference(superposition,[],[f15289,f11370]) ).
fof(f15289,plain,
( ~ c_lessequals(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| spl0_1626 ),
inference(avatar_component_clause,[],[f15287]) ).
fof(f16071,plain,
spl0_1697,
inference(avatar_split_clause,[],[f2827,f16069]) ).
fof(f2827,plain,
! [X19,X44,X4,X5] : c_List_Odrop(X19,X44,X5) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_List_Olist_OCons(X4,X44,X5),X5),
inference(definition_unfolding,[],[f437,f1409]) ).
fof(f437,axiom,
! [X19,X44,X4,X5] : c_List_Odrop(c_Suc(X19),c_List_Olist_OCons(X4,X44,X5),X5) = c_List_Odrop(X19,X44,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f16041,plain,
( spl0_1696
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1695 ),
inference(avatar_split_clause,[],[f16037,f16034,f10445,f10140,f6747,f3739,f16039]) ).
fof(f16034,plain,
( spl0_1695
<=> ! [X4,X21,X19] : c_List_Olist_OCons(X4,c_List_Oreplicate(X19,X4,X21),X21) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X4,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f16037,plain,
( ! [X21,X19,X4] : c_List_Olist_OCons(X4,c_List_Oreplicate(X19,X4,X21),X21) = c_List_Oreplicate(c_plus(c_1,X19,tc_nat),X4,X21)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1695 ),
inference(forward_demodulation,[],[f16035,f11255]) ).
fof(f16035,plain,
( ! [X21,X19,X4] : c_List_Olist_OCons(X4,c_List_Oreplicate(X19,X4,X21),X21) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X4,X21)
| ~ spl0_1695 ),
inference(avatar_component_clause,[],[f16034]) ).
fof(f16036,plain,
spl0_1695,
inference(avatar_split_clause,[],[f2826,f16034]) ).
fof(f2826,plain,
! [X21,X19,X4] : c_List_Olist_OCons(X4,c_List_Oreplicate(X19,X4,X21),X21) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X4,X21),
inference(definition_unfolding,[],[f588,f1409]) ).
fof(f588,axiom,
! [X21,X19,X4] : c_List_Oreplicate(c_Suc(X19),X4,X21) = c_List_Olist_OCons(X4,c_List_Oreplicate(X19,X4,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f15937,plain,
( spl0_1694
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1693 ),
inference(avatar_split_clause,[],[f15933,f15930,f10445,f10140,f6747,f3739,f15935]) ).
fof(f15935,plain,
( spl0_1694
<=> ! [X30,X19] : c_plus(X19,c_times(X30,X19,tc_nat),tc_nat) = c_times(c_plus(c_1,X30,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f15930,plain,
( spl0_1693
<=> ! [X30,X19] : c_plus(X19,c_times(X30,X19,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f15933,plain,
( ! [X19,X30] : c_plus(X19,c_times(X30,X19,tc_nat),tc_nat) = c_times(c_plus(c_1,X30,tc_nat),X19,tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1693 ),
inference(forward_demodulation,[],[f15931,f11255]) ).
fof(f15931,plain,
( ! [X19,X30] : c_plus(X19,c_times(X30,X19,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X19,tc_nat)
| ~ spl0_1693 ),
inference(avatar_component_clause,[],[f15930]) ).
fof(f15932,plain,
spl0_1693,
inference(avatar_split_clause,[],[f2825,f15930]) ).
fof(f2825,plain,
! [X19,X30] : c_plus(X19,c_times(X30,X19,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),X19,tc_nat),
inference(definition_unfolding,[],[f964,f1409]) ).
fof(f964,axiom,
! [X19,X30] : c_times(c_Suc(X30),X19,tc_nat) = c_plus(X19,c_times(X30,X19,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f15837,plain,
( spl0_1692
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1691 ),
inference(avatar_split_clause,[],[f15833,f15830,f10445,f10140,f6747,f3739,f15835]) ).
fof(f15835,plain,
( spl0_1692
<=> ! [X30,X19] : c_plus(X30,c_times(X30,X19,tc_nat),tc_nat) = c_times(X30,c_plus(c_1,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f15830,plain,
( spl0_1691
<=> ! [X30,X19] : c_plus(X30,c_times(X30,X19,tc_nat),tc_nat) = c_times(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f15833,plain,
( ! [X19,X30] : c_plus(X30,c_times(X30,X19,tc_nat),tc_nat) = c_times(X30,c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1691 ),
inference(forward_demodulation,[],[f15831,f11255]) ).
fof(f15831,plain,
( ! [X19,X30] : c_plus(X30,c_times(X30,X19,tc_nat),tc_nat) = c_times(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat)
| ~ spl0_1691 ),
inference(avatar_component_clause,[],[f15830]) ).
fof(f15832,plain,
spl0_1691,
inference(avatar_split_clause,[],[f2824,f15830]) ).
fof(f2824,plain,
! [X19,X30] : c_plus(X30,c_times(X30,X19,tc_nat),tc_nat) = c_times(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f922,f1409]) ).
fof(f922,axiom,
! [X19,X30] : c_times(X30,c_Suc(X19),tc_nat) = c_plus(X30,c_times(X30,X19,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f15765,plain,
( spl0_1690
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1689 ),
inference(avatar_split_clause,[],[f15761,f15758,f10445,f10140,f6747,f3739,f15763]) ).
fof(f15763,plain,
( spl0_1690
<=> ! [X43,X19] : c_times(X43,c_Nat_Opower(X43,X19,tc_nat),tc_nat) = c_Nat_Opower(X43,c_plus(c_1,X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f15758,plain,
( spl0_1689
<=> ! [X43,X19] : c_times(X43,c_Nat_Opower(X43,X19,tc_nat),tc_nat) = c_Nat_Opower(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f15761,plain,
( ! [X19,X43] : c_times(X43,c_Nat_Opower(X43,X19,tc_nat),tc_nat) = c_Nat_Opower(X43,c_plus(c_1,X19,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1689 ),
inference(forward_demodulation,[],[f15759,f11255]) ).
fof(f15759,plain,
( ! [X19,X43] : c_times(X43,c_Nat_Opower(X43,X19,tc_nat),tc_nat) = c_Nat_Opower(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat)
| ~ spl0_1689 ),
inference(avatar_component_clause,[],[f15758]) ).
fof(f15760,plain,
spl0_1689,
inference(avatar_split_clause,[],[f2823,f15758]) ).
fof(f2823,plain,
! [X19,X43] : c_times(X43,c_Nat_Opower(X43,X19,tc_nat),tc_nat) = c_Nat_Opower(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1210,f1409]) ).
fof(f1210,axiom,
! [X19,X43] : c_Nat_Opower(X43,c_Suc(X19),tc_nat) = c_times(X43,c_Nat_Opower(X43,X19,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f15735,plain,
( spl0_1688
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1687 ),
inference(avatar_split_clause,[],[f15731,f15728,f10445,f10140,f6747,f3739,f15733]) ).
fof(f15733,plain,
( spl0_1688
<=> ! [X43,X19] : c_times(X43,c_Nat_Opower(X43,X19,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X43,c_plus(c_1,X19,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f15728,plain,
( spl0_1687
<=> ! [X43,X19] : c_times(X43,c_Nat_Opower(X43,X19,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f15731,plain,
( ! [X19,X43] : c_times(X43,c_Nat_Opower(X43,X19,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X43,c_plus(c_1,X19,tc_nat),tc_IntDef_Oint)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1687 ),
inference(forward_demodulation,[],[f15729,f11255]) ).
fof(f15729,plain,
( ! [X19,X43] : c_times(X43,c_Nat_Opower(X43,X19,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_1687 ),
inference(avatar_component_clause,[],[f15728]) ).
fof(f15730,plain,
spl0_1687,
inference(avatar_split_clause,[],[f2822,f15728]) ).
fof(f2822,plain,
! [X19,X43] : c_times(X43,c_Nat_Opower(X43,X19,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f330,f1409]) ).
fof(f330,axiom,
! [X19,X43] : c_Nat_Opower(X43,c_Suc(X19),tc_IntDef_Oint) = c_times(X43,c_Nat_Opower(X43,X19,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f15726,plain,
spl0_1686,
inference(avatar_split_clause,[],[f2821,f15724]) ).
fof(f15724,plain,
( spl0_1686
<=> ! [X5,X1,X35] : c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5) = c_minus(X1,c_uminus(X35,tc_set(X5)),tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f2821,plain,
! [X1,X5,X35] : c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5) = c_minus(X1,c_uminus(X35,tc_set(X5)),tc_set(X5)),
inference(definition_unfolding,[],[f1451,f1238]) ).
fof(f1451,axiom,
! [X1,X35,X5] : c_inter(X1,X35,X5) = c_minus(X1,c_uminus(X35,tc_set(X5)),tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f15722,plain,
spl0_1685,
inference(avatar_split_clause,[],[f1673,f15720]) ).
fof(f15720,plain,
( spl0_1685
<=> ! [X2,X5,X1] :
( ~ c_in(X2,X1,X5)
| c_in(c_Pair(X2,X2,X5,X5),c_Relation_Odiag(X1,X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f1673,axiom,
! [X2,X1,X5] :
( ~ c_in(X2,X1,X5)
| c_in(c_Pair(X2,X2,X5,X5),c_Relation_Odiag(X1,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f15718,plain,
spl0_1684,
inference(avatar_split_clause,[],[f1639,f15716]) ).
fof(f15716,plain,
( spl0_1684
<=> ! [X5,X1,X44] :
( c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5))
| c_in(c_Main_Oin__listsI__1(X1,X44,X5),c_List_Oset(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f1639,axiom,
! [X1,X44,X5] :
( c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5))
| c_in(c_Main_Oin__listsI__1(X1,X44,X5),c_List_Oset(X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f15714,plain,
spl0_1683,
inference(avatar_split_clause,[],[f1540,f15712]) ).
fof(f15712,plain,
( spl0_1683
<=> ! [X2,X5,X1] : c_insert(X2,X1,X5) = c_insert(X2,c_minus(X1,c_insert(X2,c_emptyset,X5),tc_set(X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f1540,axiom,
! [X2,X1,X5] : c_insert(X2,X1,X5) = c_insert(X2,c_minus(X1,c_insert(X2,c_emptyset,X5),tc_set(X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f15710,plain,
( spl0_1682
| ~ spl0_1354
| ~ spl0_1302
| ~ spl0_1463 ),
inference(avatar_split_clause,[],[f15112,f12403,f10280,f10979,f15707]) ).
fof(f15707,plain,
( spl0_1682
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f10979,plain,
( spl0_1354
<=> class_Orderings_Oorder(tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f10280,plain,
( spl0_1302
<=> ! [X5,X19,X30] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X19,X30,X5)
| c_emptyset = c_SetInterval_OatLeastAtMost(X30,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f12403,plain,
( spl0_1463
<=> c_less(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f15112,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| c_emptyset = c_SetInterval_OatLeastAtMost(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_1302
| ~ spl0_1463 ),
inference(resolution,[],[f12405,f10281]) ).
fof(f10281,plain,
( ! [X19,X5,X30] :
( ~ c_less(X19,X30,X5)
| ~ class_Orderings_Oorder(X5)
| c_emptyset = c_SetInterval_OatLeastAtMost(X30,X19,X5) )
| ~ spl0_1302 ),
inference(avatar_component_clause,[],[f10280]) ).
fof(f12405,plain,
( c_less(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ spl0_1463 ),
inference(avatar_component_clause,[],[f12403]) ).
fof(f15705,plain,
spl0_1681,
inference(avatar_split_clause,[],[f1515,f15703]) ).
fof(f15703,plain,
( spl0_1681
<=> ! [X5,X1,X35] : c_Union(c_union(X1,X35,tc_set(X5)),X5) = c_union(c_Union(X1,X5),c_Union(X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f1515,axiom,
! [X1,X35,X5] : c_Union(c_union(X1,X35,tc_set(X5)),X5) = c_union(c_Union(X1,X5),c_Union(X35,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f15701,plain,
spl0_1680,
inference(avatar_split_clause,[],[f1461,f15699]) ).
fof(f15699,plain,
( spl0_1680
<=> ! [X35,X31,X5,X1] :
( ~ c_in(X31,X1,X5)
| c_in(X31,X35,X5)
| c_in(X31,c_minus(X1,X35,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f1461,axiom,
! [X31,X1,X5,X35] :
( ~ c_in(X31,X1,X5)
| c_in(X31,X35,X5)
| c_in(X31,c_minus(X1,X35,tc_set(X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f15697,plain,
spl0_1679,
inference(avatar_split_clause,[],[f1450,f15695]) ).
fof(f15695,plain,
( spl0_1679
<=> ! [X5,X1,X35] :
( ~ c_lessequals(X35,X1,tc_set(X5))
| c_lessequals(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f1450,axiom,
! [X1,X35,X5] :
( ~ c_lessequals(X35,X1,tc_set(X5))
| c_lessequals(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f15693,plain,
spl0_1678,
inference(avatar_split_clause,[],[f1449,f15691]) ).
fof(f15691,plain,
( spl0_1678
<=> ! [X5,X1,X35] :
( c_lessequals(X35,X1,tc_set(X5))
| ~ c_lessequals(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f1449,axiom,
! [X1,X35,X5] :
( c_lessequals(X35,X1,tc_set(X5))
| ~ c_lessequals(c_uminus(X1,tc_set(X5)),c_uminus(X35,tc_set(X5)),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f15689,plain,
spl0_1677,
inference(avatar_split_clause,[],[f1439,f15687]) ).
fof(f1439,axiom,
! [X1,X35,X5] : c_uminus(c_minus(X1,X35,tc_set(X5)),tc_set(X5)) = c_union(c_uminus(X1,tc_set(X5)),X35,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f15685,plain,
spl0_1676,
inference(avatar_split_clause,[],[f1225,f15683]) ).
fof(f15683,plain,
( spl0_1676
<=> ! [X2,X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X2
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,X5),X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f1225,axiom,
! [X2,X19,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X2
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,X5),X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f15681,plain,
spl0_1675,
inference(avatar_split_clause,[],[f1224,f15679]) ).
fof(f15679,plain,
( spl0_1675
<=> ! [X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X19
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X5),X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f1224,axiom,
! [X19,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X19
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X5),X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f15677,plain,
spl0_1674,
inference(avatar_split_clause,[],[f1059,f15675]) ).
fof(f15675,plain,
( spl0_1674
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f1059,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f15673,plain,
spl0_1673,
inference(avatar_split_clause,[],[f1058,f15671]) ).
fof(f15671,plain,
( spl0_1673
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f1058,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f15669,plain,
spl0_1672,
inference(avatar_split_clause,[],[f1057,f15667]) ).
fof(f15667,plain,
( spl0_1672
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f1057,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f15663,plain,
spl0_1671,
inference(avatar_split_clause,[],[f1056,f15661]) ).
fof(f15661,plain,
( spl0_1671
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f1056,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f15659,plain,
spl0_1670,
inference(avatar_split_clause,[],[f1054,f15657]) ).
fof(f15657,plain,
( spl0_1670
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f1054,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f15655,plain,
spl0_1669,
inference(avatar_split_clause,[],[f1053,f15653]) ).
fof(f15653,plain,
( spl0_1669
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f1053,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_plus(X2,X31,X5),c_plus(X7,X31,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f15651,plain,
spl0_1668,
inference(avatar_split_clause,[],[f1052,f15649]) ).
fof(f15649,plain,
( spl0_1668
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f1052,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f15647,plain,
spl0_1667,
inference(avatar_split_clause,[],[f1051,f15645]) ).
fof(f15645,plain,
( spl0_1667
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f1051,axiom,
! [X2,X31,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_plus(X31,X2,X5),c_plus(X31,X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f15643,plain,
spl0_1666,
inference(avatar_split_clause,[],[f1011,f15641]) ).
fof(f15641,plain,
( spl0_1666
<=> ! [X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X39,X5),X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f1011,axiom,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X39,X5),X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f15639,plain,
spl0_1665,
inference(avatar_split_clause,[],[f1010,f15637]) ).
fof(f15637,plain,
( spl0_1665
<=> ! [X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X39,X5),X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f1010,axiom,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X39,X5),X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f15635,plain,
spl0_1664,
inference(avatar_split_clause,[],[f1003,f15633]) ).
fof(f15633,plain,
( spl0_1664
<=> ! [X4,X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X39,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X39,X4),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f1003,axiom,
! [X39,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X39,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X39,X4),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f15631,plain,
spl0_1663,
inference(avatar_split_clause,[],[f1002,f15629]) ).
fof(f15629,plain,
( spl0_1663
<=> ! [X4,X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X39,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X39,X4),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f1002,axiom,
! [X39,X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X39,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X39,X4),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f15627,plain,
spl0_1662,
inference(avatar_split_clause,[],[f984,f15625]) ).
fof(f15625,plain,
( spl0_1662
<=> ! [X40,X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X40,X5),c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X40,X39),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f984,axiom,
! [X40,X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X40,X5),c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X40,X39),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f15622,plain,
spl0_1661,
inference(avatar_split_clause,[],[f981,f15620]) ).
fof(f15620,plain,
( spl0_1661
<=> ! [X40,X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,X39),X5) = c_plus(c_Numeral_Onumber__of(X40,X5),c_Numeral_Onumber__of(X39,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f981,axiom,
! [X40,X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,X39),X5) = c_plus(c_Numeral_Onumber__of(X40,X5),c_Numeral_Onumber__of(X39,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f15618,plain,
spl0_1660,
inference(avatar_split_clause,[],[f836,f15616]) ).
fof(f15616,plain,
( spl0_1660
<=> ! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(c_uminus(c_1,X23),X2,X23)
| c_less(c_uminus(X2,X23),c_1,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f836,axiom,
! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(c_uminus(c_1,X23),X2,X23)
| c_less(c_uminus(X2,X23),c_1,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f15614,plain,
spl0_1659,
inference(avatar_split_clause,[],[f835,f15612]) ).
fof(f15612,plain,
( spl0_1659
<=> ! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(c_uminus(X2,X23),c_1,X23)
| c_less(c_uminus(c_1,X23),X2,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f835,axiom,
! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(c_uminus(X2,X23),c_1,X23)
| c_less(c_uminus(c_1,X23),X2,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f15610,plain,
spl0_1658,
inference(avatar_split_clause,[],[f832,f15608]) ).
fof(f15608,plain,
( spl0_1658
<=> ! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(c_uminus(c_1,X23),X2,X23)
| c_lessequals(c_uminus(X2,X23),c_1,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f832,axiom,
! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(c_uminus(c_1,X23),X2,X23)
| c_lessequals(c_uminus(X2,X23),c_1,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f15606,plain,
spl0_1657,
inference(avatar_split_clause,[],[f831,f15604]) ).
fof(f15604,plain,
( spl0_1657
<=> ! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(c_uminus(X2,X23),c_1,X23)
| c_lessequals(c_uminus(c_1,X23),X2,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f831,axiom,
! [X2,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(c_uminus(X2,X23),c_1,X23)
| c_lessequals(c_uminus(c_1,X23),X2,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f15602,plain,
spl0_1656,
inference(avatar_split_clause,[],[f825,f15600]) ).
fof(f15600,plain,
( spl0_1656
<=> ! [X23,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(X7,c_uminus(c_1,X23),X23)
| c_less(c_1,c_uminus(X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f825,axiom,
! [X7,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(X7,c_uminus(c_1,X23),X23)
| c_less(c_1,c_uminus(X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f15598,plain,
spl0_1655,
inference(avatar_split_clause,[],[f824,f15596]) ).
fof(f15596,plain,
( spl0_1655
<=> ! [X23,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(c_1,c_uminus(X7,X23),X23)
| c_less(X7,c_uminus(c_1,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f824,axiom,
! [X7,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_less(c_1,c_uminus(X7,X23),X23)
| c_less(X7,c_uminus(c_1,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f15594,plain,
spl0_1654,
inference(avatar_split_clause,[],[f809,f15592]) ).
fof(f15592,plain,
( spl0_1654
<=> ! [X23,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(X7,c_uminus(c_1,X23),X23)
| c_lessequals(c_1,c_uminus(X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f809,axiom,
! [X7,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(X7,c_uminus(c_1,X23),X23)
| c_lessequals(c_1,c_uminus(X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f15590,plain,
spl0_1653,
inference(avatar_split_clause,[],[f808,f15588]) ).
fof(f15588,plain,
( spl0_1653
<=> ! [X23,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(c_1,c_uminus(X7,X23),X23)
| c_lessequals(X7,c_uminus(c_1,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f808,axiom,
! [X7,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
| ~ class_HOL_Oone(X23)
| ~ c_lessequals(c_1,c_uminus(X7,X23),X23)
| c_lessequals(X7,c_uminus(c_1,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f15586,plain,
spl0_1652,
inference(avatar_split_clause,[],[f734,f15584]) ).
fof(f15584,plain,
( spl0_1652
<=> ! [X5,X40] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,X5) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X40,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f734,axiom,
! [X40,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,X5) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X40,tc_nat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f15580,plain,
spl0_1651,
inference(avatar_split_clause,[],[f645,f15578]) ).
fof(f15578,plain,
( spl0_1651
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X44
| c_List_Otl(c_append(X44,X45,X5),X5) = c_append(c_List_Otl(X44,X5),X45,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f645,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X44
| c_List_Otl(c_append(X44,X45,X5),X5) = c_append(c_List_Otl(X44,X5),X45,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f15576,plain,
spl0_1650,
inference(avatar_split_clause,[],[f629,f15574]) ).
fof(f15574,plain,
( spl0_1650
<=> ! [X4,X5,X1] :
( ~ c_in(c_0,X1,tc_nat)
| c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) = c_List_Osublist(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f629,axiom,
! [X1,X4,X5] :
( ~ c_in(c_0,X1,tc_nat)
| c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) = c_List_Osublist(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f15571,plain,
spl0_1649,
inference(avatar_split_clause,[],[f592,f15569]) ).
fof(f15569,plain,
( spl0_1649
<=> ! [X45,X5,X8] : c_List_Olist_OCons(X8,X45,X5) = c_List_Orev(c_append(c_List_Orev(X45,X5),c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f592,axiom,
! [X8,X45,X5] : c_List_Olist_OCons(X8,X45,X5) = c_List_Orev(c_append(c_List_Orev(X45,X5),c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f15567,plain,
spl0_1648,
inference(avatar_split_clause,[],[f589,f15565]) ).
fof(f15565,plain,
( spl0_1648
<=> ! [X4,X21,X44] : c_List_Orev(c_List_Olist_OCons(X4,X44,X21),X21) = c_append(c_List_Orev(X44,X21),c_List_Olist_OCons(X4,c_List_Olist_ONil,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f589,axiom,
! [X21,X44,X4] : c_List_Orev(c_List_Olist_OCons(X4,X44,X21),X21) = c_append(c_List_Orev(X44,X21),c_List_Olist_OCons(X4,c_List_Olist_ONil,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f15563,plain,
spl0_1647,
inference(avatar_split_clause,[],[f578,f15561]) ).
fof(f15561,plain,
( spl0_1647
<=> ! [X4,X21,X44] :
( ~ c_in(X4,c_List_Oset(X44,X21),X21)
| c_List_Oremdups(c_List_Olist_OCons(X4,X44,X21),X21) = c_List_Oremdups(X44,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f578,axiom,
! [X21,X44,X4] :
( ~ c_in(X4,c_List_Oset(X44,X21),X21)
| c_List_Oremdups(c_List_Olist_OCons(X4,X44,X21),X21) = c_List_Oremdups(X44,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f15559,plain,
spl0_1646,
inference(avatar_split_clause,[],[f566,f15557]) ).
fof(f15557,plain,
( spl0_1646
<=> ! [X5,X44,X19] :
( ~ c_less(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_in(c_List_Onth(X44,X19,X5),c_List_Oset(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f566,axiom,
! [X19,X44,X5] :
( ~ c_less(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_in(c_List_Onth(X44,X19,X5),c_List_Oset(X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f15555,plain,
spl0_1645,
inference(avatar_split_clause,[],[f565,f15553]) ).
fof(f15553,plain,
( spl0_1645
<=> ! [X5,X44,X4,X55,X29] :
( X29 = X55
| c_List_Onth(c_List_Olist__update(X44,X29,X4,X5),X55,X5) = c_List_Onth(X44,X55,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f565,axiom,
! [X29,X44,X55,X4,X5] :
( X29 = X55
| c_List_Onth(c_List_Olist__update(X44,X29,X4,X5),X55,X5) = c_List_Onth(X44,X55,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f15551,plain,
spl0_1644,
inference(avatar_split_clause,[],[f483,f15549]) ).
fof(f15549,plain,
( spl0_1644
<=> ! [X6,X4,X5] : ~ c_in(c_Pair(X4,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f483,axiom,
! [X6,X4,X5] : ~ c_in(c_Pair(X4,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f15547,plain,
spl0_1643,
inference(avatar_split_clause,[],[f470,f15545]) ).
fof(f15545,plain,
( spl0_1643
<=> ! [X5,X44] :
( c_List_Oremdups(X44,X5) = X44
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(c_List_Oremdups(X44,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f470,axiom,
! [X44,X5] :
( c_List_Oremdups(X44,X5) = X44
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(c_List_Oremdups(X44,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f15543,plain,
spl0_1642,
inference(avatar_split_clause,[],[f410,f15541]) ).
fof(f15541,plain,
( spl0_1642
<=> ! [X45,X5,X44] : c_List_Oconcat(c_append(X44,X45,tc_List_Olist(X5)),X5) = c_append(c_List_Oconcat(X44,X5),c_List_Oconcat(X45,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f410,axiom,
! [X44,X45,X5] : c_List_Oconcat(c_append(X44,X45,tc_List_Olist(X5)),X5) = c_append(c_List_Oconcat(X44,X5),c_List_Oconcat(X45,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f15538,plain,
spl0_1641,
inference(avatar_split_clause,[],[f403,f15536]) ).
fof(f15536,plain,
( spl0_1641
<=> ! [X4,X21,X44] :
( c_List_Olist_ONil = X44
| c_List_Obutlast(c_List_Olist_OCons(X4,X44,X21),X21) = c_List_Olist_OCons(X4,c_List_Obutlast(X44,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f403,axiom,
! [X21,X44,X4] :
( c_List_Olist_ONil = X44
| c_List_Obutlast(c_List_Olist_OCons(X4,X44,X21),X21) = c_List_Olist_OCons(X4,c_List_Obutlast(X44,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f15534,plain,
spl0_1640,
inference(avatar_split_clause,[],[f384,f15532]) ).
fof(f15532,plain,
( spl0_1640
<=> ! [X5,X8] :
( c_List_Olist_ONil = X8
| c_append(c_List_Obutlast(X8,X5),c_List_Olist_OCons(c_List_Olast(X8,X5),c_List_Olist_ONil,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f384,axiom,
! [X8,X5] :
( c_List_Olist_ONil = X8
| c_append(c_List_Obutlast(X8,X5),c_List_Olist_OCons(c_List_Olast(X8,X5),c_List_Olist_ONil,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f15530,plain,
spl0_1639,
inference(avatar_split_clause,[],[f380,f15528]) ).
fof(f15528,plain,
( spl0_1639
<=> ! [X6,X5,X45] : ~ c_in(c_Pair(c_List_Olist_ONil,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f380,axiom,
! [X6,X45,X5] : ~ c_in(c_Pair(c_List_Olist_ONil,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f15526,plain,
spl0_1638,
inference(avatar_split_clause,[],[f372,f15524]) ).
fof(f15524,plain,
( spl0_1638
<=> ! [X34,X5,X46] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Oconcat(X46,X5)
| ~ c_in(X34,c_List_Oset(X46,tc_List_Olist(X5)),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f372,axiom,
! [X46,X34,X5] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Oconcat(X46,X5)
| ~ c_in(X34,c_List_Oset(X46,tc_List_Olist(X5)),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
fof(f15522,plain,
spl0_1637,
inference(avatar_split_clause,[],[f371,f15520]) ).
fof(f15520,plain,
( spl0_1637
<=> ! [X6,X5,X44] : ~ c_in(c_Pair(X44,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f371,axiom,
! [X44,X6,X5] : ~ c_in(c_Pair(X44,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f15518,plain,
spl0_1636,
inference(avatar_split_clause,[],[f176,f15516]) ).
fof(f15516,plain,
( spl0_1636
<=> ! [X5,X19] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f176,axiom,
! [X19,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f15514,plain,
spl0_1635,
inference(avatar_split_clause,[],[f168,f15512]) ).
fof(f15512,plain,
( spl0_1635
<=> ! [X19,X30] : c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X30,c_plus(X19,X30,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f168,axiom,
! [X19,X30] : c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X30,c_plus(X19,X30,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f15510,plain,
spl0_1634,
inference(avatar_split_clause,[],[f167,f15508]) ).
fof(f15508,plain,
( spl0_1634
<=> ! [X30,X19] : c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X30,c_plus(X30,X19,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f167,axiom,
! [X19,X30] : c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X30,c_plus(X30,X19,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f15506,plain,
spl0_1633,
inference(avatar_split_clause,[],[f166,f15504]) ).
fof(f15504,plain,
( spl0_1633
<=> ! [X30,X19] : c_GCD_Ogcd(c_Pair(c_plus(X30,X19,tc_nat),X19,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f166,axiom,
! [X19,X30] : c_GCD_Ogcd(c_Pair(c_plus(X30,X19,tc_nat),X19,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f15502,plain,
spl0_1632,
inference(avatar_split_clause,[],[f137,f15500]) ).
fof(f15500,plain,
( spl0_1632
<=> ! [X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMin(X1,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f137,axiom,
! [X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMin(X1,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f15498,plain,
( spl0_1631
| ~ spl0_1546
| ~ spl0_1601 ),
inference(avatar_split_clause,[],[f15261,f14378,f13345,f15496]) ).
fof(f14378,plain,
( spl0_1601
<=> ! [X34,X5,X1,X83] :
( ~ c_in(X1,X34,X5)
| ~ c_in(X34,X83,tc_set(X5))
| c_in(X1,c_Union(X83,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f15261,plain,
( ! [X0] :
( ~ c_in(X0,v_S,t_a)
| c_in(X0,c_Union(c_Finite__Set_OFinites,t_a),t_a) )
| ~ spl0_1546
| ~ spl0_1601 ),
inference(resolution,[],[f14379,f13347]) ).
fof(f13347,plain,
( c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1546 ),
inference(avatar_component_clause,[],[f13345]) ).
fof(f14379,plain,
( ! [X83,X1,X34,X5] :
( ~ c_in(X34,X83,tc_set(X5))
| ~ c_in(X1,X34,X5)
| c_in(X1,c_Union(X83,X5),X5) )
| ~ spl0_1601 ),
inference(avatar_component_clause,[],[f14378]) ).
fof(f15494,plain,
spl0_1630,
inference(avatar_split_clause,[],[f122,f15492]) ).
fof(f15492,plain,
( spl0_1630
<=> ! [X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMax(X1,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f122,axiom,
! [X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMax(X1,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f15490,plain,
spl0_1629,
inference(avatar_split_clause,[],[f18,f15488]) ).
fof(f15488,plain,
( spl0_1629
<=> ! [X15,X17,X11,X13,X14,X12,X5,X16] :
( X13 = X17
| c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14) != c_Tarski_Opotype_Opotype__ext(X15,X16,X17,X5,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f18,axiom,
! [X11,X16,X14,X17,X15,X5,X12,X13] :
( X13 = X17
| c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14) != c_Tarski_Opotype_Opotype__ext(X15,X16,X17,X5,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_2) ).
fof(f15486,plain,
spl0_1628,
inference(avatar_split_clause,[],[f17,f15484]) ).
fof(f15484,plain,
( spl0_1628
<=> ! [X15,X17,X11,X14,X13,X12,X5,X16] :
( X12 = X16
| c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14) != c_Tarski_Opotype_Opotype__ext(X15,X16,X17,X5,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f17,axiom,
! [X11,X16,X14,X17,X15,X5,X12,X13] :
( X12 = X16
| c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14) != c_Tarski_Opotype_Opotype__ext(X15,X16,X17,X5,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_1) ).
fof(f15482,plain,
spl0_1627,
inference(avatar_split_clause,[],[f16,f15480]) ).
fof(f15480,plain,
( spl0_1627
<=> ! [X17,X12,X16,X11,X14,X13,X5,X15] :
( X11 = X15
| c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14) != c_Tarski_Opotype_Opotype__ext(X15,X16,X17,X5,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f16,axiom,
! [X11,X16,X14,X17,X15,X5,X12,X13] :
( X11 = X15
| c_Tarski_Opotype_Opotype__ext(X11,X12,X13,X5,X14) != c_Tarski_Opotype_Opotype__ext(X15,X16,X17,X5,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_0) ).
fof(f15290,plain,
( ~ spl0_1626
| ~ spl0_1118
| ~ spl0_1463 ),
inference(avatar_split_clause,[],[f15111,f12403,f8969,f15287]) ).
fof(f8969,plain,
( spl0_1118
<=> ! [X5,X1,X35] :
( ~ c_lessequals(X35,X1,tc_set(X5))
| ~ c_less(X1,X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f15111,plain,
( ~ c_lessequals(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_1118
| ~ spl0_1463 ),
inference(resolution,[],[f12405,f8970]) ).
fof(f8970,plain,
( ! [X1,X35,X5] :
( ~ c_less(X1,X35,tc_set(X5))
| ~ c_lessequals(X35,X1,tc_set(X5)) )
| ~ spl0_1118 ),
inference(avatar_component_clause,[],[f8969]) ).
fof(f14761,plain,
( spl0_1625
| ~ spl0_1353
| ~ spl0_1364 ),
inference(avatar_split_clause,[],[f14408,f11368,f10975,f14758]) ).
fof(f14758,plain,
( spl0_1625
<=> c_emptyset = c_SetInterval_OatLeastLessThan(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f10975,plain,
( spl0_1353
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f14408,plain,
( c_emptyset = c_SetInterval_OatLeastLessThan(v_S,v_S,tc_set(t_a))
| ~ spl0_1353
| ~ spl0_1364 ),
inference(superposition,[],[f10977,f11370]) ).
fof(f10977,plain,
( c_emptyset = c_SetInterval_OatLeastLessThan(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_1353 ),
inference(avatar_component_clause,[],[f10975]) ).
fof(f14538,plain,
spl0_1624,
inference(avatar_split_clause,[],[f3171,f14536]) ).
fof(f14536,plain,
( spl0_1624
<=> ! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X4,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f3171,plain,
! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X4,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5) ),
inference(forward_demodulation,[],[f3170,f980]) ).
fof(f980,axiom,
! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3170,plain,
! [X4,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2967,f2762]) ).
fof(f2762,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f991,f994]) ).
fof(f991,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(f2967,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f182,f994]) ).
fof(f182,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f14534,plain,
spl0_1623,
inference(avatar_split_clause,[],[f3164,f14532]) ).
fof(f14532,plain,
( spl0_1623
<=> ! [X5,X8] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f3164,plain,
! [X8,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f3163,f980]) ).
fof(f3163,plain,
! [X8,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2961,f2762]) ).
fof(f2961,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f186,f994]) ).
fof(f186,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f14530,plain,
spl0_1622,
inference(avatar_split_clause,[],[f3161,f14528]) ).
fof(f14528,plain,
( spl0_1622
<=> ! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X4,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f3161,plain,
! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X4,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5) ),
inference(forward_demodulation,[],[f3160,f980]) ).
fof(f3160,plain,
! [X4,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2959,f2762]) ).
fof(f2959,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f181,f994]) ).
fof(f181,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X4,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f14526,plain,
spl0_1621,
inference(avatar_split_clause,[],[f3154,f14524]) ).
fof(f14524,plain,
( spl0_1621
<=> ! [X5,X8] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f3154,plain,
! [X8,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X8,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f3153,f980]) ).
fof(f3153,plain,
! [X8,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5) ),
inference(forward_demodulation,[],[f2953,f2762]) ).
fof(f2953,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f185,f994]) ).
fof(f185,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X8,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X8,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f14522,plain,
spl0_1620,
inference(avatar_split_clause,[],[f3135,f14520]) ).
fof(f14520,plain,
( spl0_1620
<=> ! [X30,X19] :
( c_lessequals(c_1,c_times(X30,X19,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X19,tc_nat)
| ~ c_lessequals(c_1,X30,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f3135,plain,
! [X19,X30] :
( c_lessequals(c_1,c_times(X30,X19,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X19,tc_nat)
| ~ c_lessequals(c_1,X30,tc_nat) ),
inference(forward_demodulation,[],[f2939,f2763]) ).
fof(f2939,plain,
! [X19,X30] :
( ~ c_lessequals(c_1,X19,tc_nat)
| ~ c_lessequals(c_1,X30,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X30,X19,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f962,f1409]) ).
fof(f962,axiom,
! [X19,X30] :
( ~ c_lessequals(c_1,X19,tc_nat)
| ~ c_lessequals(c_1,X30,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f14518,plain,
spl0_1619,
inference(avatar_split_clause,[],[f3051,f14516]) ).
fof(f14516,plain,
( spl0_1619
<=> ! [X5,X40] :
( c_plus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f3051,plain,
! [X40,X5] :
( c_plus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f195,f1021]) ).
fof(f195,axiom,
! [X40,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X40,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f14514,plain,
spl0_1618,
inference(avatar_split_clause,[],[f3050,f14512]) ).
fof(f14512,plain,
( spl0_1618
<=> ! [X5,X39] :
( c_plus(c_1,c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X39),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f3050,plain,
! [X39,X5] :
( c_plus(c_1,c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X39),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f194,f1021]) ).
fof(f194,axiom,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_1,c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X39),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f14510,plain,
spl0_1617,
inference(avatar_split_clause,[],[f3023,f14508]) ).
fof(f14508,plain,
( spl0_1617
<=> ! [X6,X5] : c_List_Olistset(c_List_Olist_ONil,X5) = c_Relation_OImage(c_List_Olistrel(X6,X5),c_List_Olistset(c_List_Olist_ONil,X5),tc_List_Olist(X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f3023,plain,
! [X6,X5] : c_List_Olistset(c_List_Olist_ONil,X5) = c_Relation_OImage(c_List_Olistrel(X6,X5),c_List_Olistset(c_List_Olist_ONil,X5),tc_List_Olist(X5),tc_List_Olist(X5)),
inference(forward_demodulation,[],[f501,f504]) ).
fof(f504,axiom,
! [X21] : c_List_Olistset(c_List_Olist_ONil,X21) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f501,axiom,
! [X6,X5] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X5)) = c_Relation_OImage(c_List_Olistrel(X6,X5),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X5)),tc_List_Olist(X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f14506,plain,
spl0_1616,
inference(avatar_split_clause,[],[f3020,f14504]) ).
fof(f14504,plain,
( spl0_1616
<=> ! [X2,X5,X60] : c_Nat_Osize(c_List_Olist_OCons(X2,X60,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X60,tc_List_Olist(X5)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f3020,plain,
! [X2,X60,X5] : c_Nat_Osize(c_List_Olist_OCons(X2,X60,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X60,tc_List_Olist(X5)),c_1,tc_nat),
inference(forward_demodulation,[],[f2844,f2763]) ).
fof(f2844,plain,
! [X2,X60,X5] : c_Nat_Osize(c_List_Olist_OCons(X2,X60,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X60,tc_List_Olist(X5)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f492,f1409]) ).
fof(f492,axiom,
! [X2,X60,X5] : c_Nat_Osize(c_List_Olist_OCons(X2,X60,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X60,tc_List_Olist(X5)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f14502,plain,
( ~ spl0_1615
| ~ spl0_1364
| spl0_1463 ),
inference(avatar_split_clause,[],[f14411,f12403,f11368,f14499]) ).
fof(f14499,plain,
( spl0_1615
<=> c_less(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f14411,plain,
( ~ c_less(v_S,v_S,tc_set(t_a))
| ~ spl0_1364
| spl0_1463 ),
inference(superposition,[],[f12404,f11370]) ).
fof(f12404,plain,
( ~ c_less(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| spl0_1463 ),
inference(avatar_component_clause,[],[f12403]) ).
fof(f14497,plain,
spl0_1614,
inference(avatar_split_clause,[],[f3016,f14495]) ).
fof(f3016,plain,
! [X2,X83,X35,X5] : c_union(c_insert(X2,X35,X5),X83,X5) = c_union(X35,c_insert(X2,X83,X5),X5),
inference(forward_demodulation,[],[f1508,f1509]) ).
fof(f1509,axiom,
! [X2,X1,X35,X5] : c_union(X1,c_insert(X2,X35,X5),X5) = c_insert(X2,c_union(X1,X35,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f1508,axiom,
! [X2,X83,X35,X5] : c_union(c_insert(X2,X35,X5),X83,X5) = c_insert(X2,c_union(X35,X83,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f14493,plain,
spl0_1613,
inference(avatar_split_clause,[],[f2921,f14491]) ).
fof(f14491,plain,
( spl0_1613
<=> ! [X5,X8,X19] :
( c_List_Osublist(X8,c_SetInterval_OlessThan(X19,tc_nat),X5) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f2921,plain,
! [X8,X19,X5] :
( c_List_Osublist(X8,c_SetInterval_OlessThan(X19,tc_nat),X5) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),X19,tc_nat) ),
inference(definition_unfolding,[],[f635,f631]) ).
fof(f635,axiom,
! [X8,X19,X5] :
( c_List_Otake(X19,X8,X5) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f14473,plain,
( spl0_1612
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1611 ),
inference(avatar_split_clause,[],[f14469,f14466,f10445,f10140,f6747,f3739,f14471]) ).
fof(f14471,plain,
( spl0_1612
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),tc_nat) = c_minus(c_plus(c_1,X41,tc_nat),X77,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f14466,plain,
( spl0_1611
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X41,tc_nat),tc_nat),X77,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f14469,plain,
( ! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),tc_nat) = c_minus(c_plus(c_1,X41,tc_nat),X77,tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1611 ),
inference(forward_demodulation,[],[f14467,f11255]) ).
fof(f14467,plain,
( ! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X41,tc_nat),tc_nat),X77,tc_nat)
| ~ spl0_1611 ),
inference(avatar_component_clause,[],[f14466]) ).
fof(f14468,plain,
spl0_1611,
inference(avatar_split_clause,[],[f2815,f14466]) ).
fof(f14450,plain,
( spl0_1610
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1609 ),
inference(avatar_split_clause,[],[f14446,f14443,f10445,f10140,f6747,f3739,f14448]) ).
fof(f14443,plain,
( spl0_1609
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,c_Finite__Set_Ocard(c_SetInterval_OatMost(X77,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f14446,plain,
( ! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,c_plus(c_1,X77,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1609 ),
inference(forward_demodulation,[],[f14444,f11255]) ).
fof(f14444,plain,
( ! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,c_Finite__Set_Ocard(c_SetInterval_OatMost(X77,tc_nat),tc_nat),tc_nat)
| ~ spl0_1609 ),
inference(avatar_component_clause,[],[f14443]) ).
fof(f14445,plain,
spl0_1609,
inference(avatar_split_clause,[],[f2814,f14443]) ).
fof(f14421,plain,
( spl0_1608
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f14405,f14402,f10445,f10140,f6747,f3739,f14419]) ).
fof(f14419,plain,
( spl0_1608
<=> ! [X5,X44,X19] : c_List_Orotate1(c_List_Orotate(X19,X44,X5),X5) = c_List_Orotate(c_plus(c_1,X19,tc_nat),X44,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f14402,plain,
( spl0_1607
<=> ! [X5,X44,X19] : c_List_Orotate1(c_List_Orotate(X19,X44,X5),X5) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X44,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f14405,plain,
( ! [X19,X44,X5] : c_List_Orotate1(c_List_Orotate(X19,X44,X5),X5) = c_List_Orotate(c_plus(c_1,X19,tc_nat),X44,X5)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1607 ),
inference(forward_demodulation,[],[f14403,f11255]) ).
fof(f14403,plain,
( ! [X19,X44,X5] : c_List_Orotate1(c_List_Orotate(X19,X44,X5),X5) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X44,X5)
| ~ spl0_1607 ),
inference(avatar_component_clause,[],[f14402]) ).
fof(f14404,plain,
spl0_1607,
inference(avatar_split_clause,[],[f2813,f14402]) ).
fof(f2813,plain,
! [X19,X44,X5] : c_List_Orotate1(c_List_Orotate(X19,X44,X5),X5) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X44,X5),
inference(definition_unfolding,[],[f603,f1409]) ).
fof(f603,axiom,
! [X19,X44,X5] : c_List_Orotate(c_Suc(X19),X44,X5) = c_List_Orotate1(c_List_Orotate(X19,X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f14400,plain,
spl0_1606,
inference(avatar_split_clause,[],[f1719,f14398]) ).
fof(f14398,plain,
( spl0_1606
<=> ! [X23,X5,X91,X90] :
( ~ c_Wellfounded__Recursion_Owf(X90,X23)
| ~ c_Wellfounded__Recursion_Owf(X91,X5)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X91,X90,X5,X23),tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f1719,axiom,
! [X90,X91,X5,X23] :
( ~ c_Wellfounded__Recursion_Owf(X90,X23)
| ~ c_Wellfounded__Recursion_Owf(X91,X5)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X91,X90,X5,X23),tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f14396,plain,
spl0_1605,
inference(avatar_split_clause,[],[f1717,f14394]) ).
fof(f14394,plain,
( spl0_1605
<=> ! [X88,X23,X5,X89] :
( ~ c_Relation_Otrans(X88,X23)
| ~ c_Relation_Otrans(X89,X5)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X89,X88,X5,X23),tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f1717,axiom,
! [X88,X89,X5,X23] :
( ~ c_Relation_Otrans(X88,X23)
| ~ c_Relation_Otrans(X89,X5)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X89,X88,X5,X23),tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f14392,plain,
spl0_1604,
inference(avatar_split_clause,[],[f1672,f14390]) ).
fof(f14390,plain,
( spl0_1604
<=> ! [X5,X1,X31] :
( c_in(c_Main_OdiagE__1(X1,X31,X5),X1,X5)
| ~ c_in(X31,c_Relation_Odiag(X1,X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f1672,axiom,
! [X31,X1,X5] :
( c_in(c_Main_OdiagE__1(X1,X31,X5),X1,X5)
| ~ c_in(X31,c_Relation_Odiag(X1,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f14388,plain,
spl0_1603,
inference(avatar_split_clause,[],[f1587,f14386]) ).
fof(f14386,plain,
( spl0_1603
<=> ! [X6,X4,X5,X8] :
( c_Wellfounded__Recursion_Owf(X6,X5)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f1587,axiom,
! [X8,X6,X4,X5] :
( c_Wellfounded__Recursion_Owf(X6,X5)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f14384,plain,
spl0_1602,
inference(avatar_split_clause,[],[f1584,f14382]) ).
fof(f14382,plain,
( spl0_1602
<=> ! [X6,X4,X5,X8] :
( c_Wellfounded__Recursion_Oacyclic(X6,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f1584,axiom,
! [X8,X6,X4,X5] :
( c_Wellfounded__Recursion_Oacyclic(X6,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f14380,plain,
spl0_1601,
inference(avatar_split_clause,[],[f1522,f14378]) ).
fof(f1522,axiom,
! [X83,X1,X34,X5] :
( ~ c_in(X1,X34,X5)
| ~ c_in(X34,X83,tc_set(X5))
| c_in(X1,c_Union(X83,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f14376,plain,
spl0_1600,
inference(avatar_split_clause,[],[f1509,f14374]) ).
fof(f14372,plain,
spl0_1599,
inference(avatar_split_clause,[],[f1505,f14370]) ).
fof(f1505,axiom,
! [X31,X1,X5,X35] :
( c_in(X31,X1,X5)
| c_in(X31,X35,X5)
| ~ c_in(X31,c_union(X1,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f14368,plain,
spl0_1598,
inference(avatar_split_clause,[],[f1485,f14366]) ).
fof(f14366,plain,
( spl0_1598
<=> ! [X34,X5,X1,X83] :
( c_in(X1,X34,X5)
| ~ c_in(X34,X83,tc_set(X5))
| ~ c_in(X1,c_Inter(X83,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f1485,axiom,
! [X83,X1,X34,X5] :
( c_in(X1,X34,X5)
| ~ c_in(X34,X83,tc_set(X5))
| ~ c_in(X1,c_Inter(X83,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f14364,plain,
( spl0_1463
| spl0_1364
| ~ spl0_99
| ~ spl0_1442 ),
inference(avatar_split_clause,[],[f12751,f11689,f3665,f11368,f12403]) ).
fof(f11689,plain,
( spl0_1442
<=> ! [X5,X1,X35] :
( X1 = X35
| ~ c_lessequals(X1,X35,tc_set(X5))
| c_less(X1,X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f12751,plain,
( v_S = c_Tarski_Ointerval(v_r,v_a,v_b,t_a)
| c_less(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ spl0_99
| ~ spl0_1442 ),
inference(resolution,[],[f11690,f3667]) ).
fof(f11690,plain,
( ! [X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| X1 = X35
| c_less(X1,X35,tc_set(X5)) )
| ~ spl0_1442 ),
inference(avatar_component_clause,[],[f11689]) ).
fof(f14363,plain,
spl0_1597,
inference(avatar_split_clause,[],[f1458,f14361]) ).
fof(f14361,plain,
( spl0_1597
<=> ! [X5,X1,X35] : c_minus(X1,X35,tc_set(X5)) = c_minus(c_minus(X1,X35,tc_set(X5)),X35,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f1458,axiom,
! [X1,X35,X5] : c_minus(X1,X35,tc_set(X5)) = c_minus(c_minus(X1,X35,tc_set(X5)),X35,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f14359,plain,
spl0_1596,
inference(avatar_split_clause,[],[f1437,f14357]) ).
fof(f14357,plain,
( spl0_1596
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X4,X8,X5)
| c_lessequals(c_SetInterval_OlessThan(X4,X5),c_SetInterval_OlessThan(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f1437,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X4,X8,X5)
| c_lessequals(c_SetInterval_OlessThan(X4,X5),c_SetInterval_OlessThan(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f14355,plain,
spl0_1595,
inference(avatar_split_clause,[],[f1436,f14353]) ).
fof(f14353,plain,
( spl0_1595
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X4,X8,X5)
| ~ c_lessequals(c_SetInterval_OlessThan(X4,X5),c_SetInterval_OlessThan(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f1436,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X4,X8,X5)
| ~ c_lessequals(c_SetInterval_OlessThan(X4,X5),c_SetInterval_OlessThan(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f14351,plain,
spl0_1594,
inference(avatar_split_clause,[],[f1426,f14349]) ).
fof(f14349,plain,
( spl0_1594
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X8,X4,X5)
| c_lessequals(c_SetInterval_OgreaterThan(X4,X5),c_SetInterval_OgreaterThan(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f1426,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X8,X4,X5)
| c_lessequals(c_SetInterval_OgreaterThan(X4,X5),c_SetInterval_OgreaterThan(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f14347,plain,
spl0_1593,
inference(avatar_split_clause,[],[f1425,f14345]) ).
fof(f14345,plain,
( spl0_1593
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X8,X4,X5)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X4,X5),c_SetInterval_OgreaterThan(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f1425,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X8,X4,X5)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X4,X5),c_SetInterval_OgreaterThan(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f14343,plain,
spl0_1592,
inference(avatar_split_clause,[],[f1413,f14341]) ).
fof(f14341,plain,
( spl0_1592
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X41,c_plus(X77,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f1413,axiom,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X41,c_plus(X77,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f14339,plain,
spl0_1591,
inference(avatar_split_clause,[],[f1406,f14337]) ).
fof(f14337,plain,
( spl0_1591
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X41,X77,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f1406,axiom,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X41,X77,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f14335,plain,
spl0_1590,
inference(avatar_split_clause,[],[f1404,f14333]) ).
fof(f14333,plain,
( spl0_1590
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X4,X8,X5)
| c_lessequals(c_SetInterval_OatMost(X4,X5),c_SetInterval_OatMost(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f1404,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X4,X8,X5)
| c_lessequals(c_SetInterval_OatMost(X4,X5),c_SetInterval_OatMost(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f14331,plain,
spl0_1589,
inference(avatar_split_clause,[],[f1403,f14329]) ).
fof(f14329,plain,
( spl0_1589
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X4,X8,X5)
| ~ c_lessequals(c_SetInterval_OatMost(X4,X5),c_SetInterval_OatMost(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f1403,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X4,X8,X5)
| ~ c_lessequals(c_SetInterval_OatMost(X4,X5),c_SetInterval_OatMost(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f14327,plain,
spl0_1588,
inference(avatar_split_clause,[],[f1398,f14325]) ).
fof(f14325,plain,
( spl0_1588
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X8,X4,X5)
| c_lessequals(c_SetInterval_OatLeast(X4,X5),c_SetInterval_OatLeast(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f1398,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X8,X4,X5)
| c_lessequals(c_SetInterval_OatLeast(X4,X5),c_SetInterval_OatLeast(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f14320,plain,
spl0_1587,
inference(avatar_split_clause,[],[f1397,f14318]) ).
fof(f14318,plain,
( spl0_1587
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X8,X4,X5)
| ~ c_lessequals(c_SetInterval_OatLeast(X4,X5),c_SetInterval_OatLeast(X8,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f1397,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X8,X4,X5)
| ~ c_lessequals(c_SetInterval_OatLeast(X4,X5),c_SetInterval_OatLeast(X8,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f14316,plain,
spl0_1586,
inference(avatar_split_clause,[],[f1355,f14314]) ).
fof(f14314,plain,
( spl0_1586
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Oring(X5)
| c_uminus(c_times(X2,X7,X5),X5) = c_times(X2,c_uminus(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f1355,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_uminus(c_times(X2,X7,X5),X5) = c_times(X2,c_uminus(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f14312,plain,
spl0_1585,
inference(avatar_split_clause,[],[f1354,f14310]) ).
fof(f14310,plain,
( spl0_1585
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(c_uminus(X2,X5),X7,X5) = c_uminus(c_times(X2,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f1354,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(c_uminus(X2,X5),X7,X5) = c_uminus(c_times(X2,X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f14308,plain,
spl0_1584,
inference(avatar_split_clause,[],[f1332,f14306]) ).
fof(f14306,plain,
( spl0_1584
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(X2,X7,X5) = c_times(c_uminus(X2,X5),c_uminus(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f1332,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(X2,X7,X5) = c_times(c_uminus(X2,X5),c_uminus(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f14304,plain,
spl0_1583,
inference(avatar_split_clause,[],[f1177,f14302]) ).
fof(f14302,plain,
( spl0_1583
<=> ! [X5,X39] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X39,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f1177,axiom,
! [X39,X5] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X39,tc_nat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f14300,plain,
spl0_1582,
inference(avatar_split_clause,[],[f1171,f14298]) ).
fof(f14298,plain,
( spl0_1582
<=> ! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ c_Parity_Oeven(X4,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f1171,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ c_Parity_Oeven(X4,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f14296,plain,
spl0_1581,
inference(avatar_split_clause,[],[f1169,f14294]) ).
fof(f14294,plain,
( spl0_1581
<=> ! [X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X4,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f1169,axiom,
! [X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X4,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f14292,plain,
spl0_1580,
inference(avatar_split_clause,[],[f1074,f14290]) ).
fof(f14290,plain,
( spl0_1580
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| ~ c_less(X2,c_0,X5)
| c_less(c_plus(X2,X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f1074,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| ~ c_less(X2,c_0,X5)
| c_less(c_plus(X2,X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f14288,plain,
spl0_1579,
inference(avatar_split_clause,[],[f1073,f14286]) ).
fof(f14286,plain,
( spl0_1579
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| c_less(X2,c_0,X5)
| ~ c_less(c_plus(X2,X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f1073,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| c_less(X2,c_0,X5)
| ~ c_less(c_plus(X2,X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f14284,plain,
spl0_1578,
inference(avatar_split_clause,[],[f945,f14282]) ).
fof(f14282,plain,
( spl0_1578
<=> ! [X30,X19] :
( ~ c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,X30,tc_nat)
| c_less(c_0,c_times(X30,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f945,axiom,
! [X19,X30] :
( ~ c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,X30,tc_nat)
| c_less(c_0,c_times(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f14280,plain,
( spl0_1577
| ~ spl0_1433
| ~ spl0_1516 ),
inference(avatar_split_clause,[],[f13183,f13088,f11646,f14278]) ).
fof(f14278,plain,
( spl0_1577
<=> ! [X0] :
( ~ c_lessequals(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),X0,tc_set(t_a))
| c_lessequals(v_S,X0,tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f11646,plain,
( spl0_1433
<=> ! [X35,X5,X1,X83] :
( c_lessequals(X1,X83,tc_set(X5))
| ~ c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f13183,plain,
( ! [X0] :
( ~ c_lessequals(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),X0,tc_set(t_a))
| c_lessequals(v_S,X0,tc_set(t_a)) )
| ~ spl0_1433
| ~ spl0_1516 ),
inference(superposition,[],[f11647,f13090]) ).
fof(f11647,plain,
( ! [X83,X1,X35,X5] :
( ~ c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5))
| c_lessequals(X1,X83,tc_set(X5)) )
| ~ spl0_1433 ),
inference(avatar_component_clause,[],[f11646]) ).
fof(f14276,plain,
spl0_1576,
inference(avatar_split_clause,[],[f925,f14274]) ).
fof(f14274,plain,
( spl0_1576
<=> ! [X18,X19,X30] :
( X19 = X30
| c_0 = X18
| c_times(X19,X18,tc_nat) != c_times(X30,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f925,axiom,
! [X18,X19,X30] :
( X19 = X30
| c_0 = X18
| c_times(X19,X18,tc_nat) != c_times(X30,X18,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f14272,plain,
spl0_1575,
inference(avatar_split_clause,[],[f923,f14270]) ).
fof(f14270,plain,
( spl0_1575
<=> ! [X18,X19,X30] :
( X19 = X30
| c_0 = X18
| c_times(X18,X19,tc_nat) != c_times(X18,X30,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f923,axiom,
! [X18,X19,X30] :
( X19 = X30
| c_0 = X18
| c_times(X18,X19,tc_nat) != c_times(X18,X30,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f14268,plain,
spl0_1574,
inference(avatar_split_clause,[],[f902,f14266]) ).
fof(f14266,plain,
( spl0_1574
<=> ! [X29,X18,X55] : c_minus(c_minus(X29,X55,tc_nat),X18,tc_nat) = c_minus(X29,c_plus(X55,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f14264,plain,
spl0_1573,
inference(avatar_split_clause,[],[f893,f14262]) ).
fof(f14262,plain,
( spl0_1573
<=> ! [X19,X30] :
( c_less(c_0,X30,tc_nat)
| c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_plus(X30,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f893,axiom,
! [X19,X30] :
( c_less(c_0,X30,tc_nat)
| c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_plus(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f14260,plain,
spl0_1572,
inference(avatar_split_clause,[],[f728,f14258]) ).
fof(f14258,plain,
( spl0_1572
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f728,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f14256,plain,
spl0_1571,
inference(avatar_split_clause,[],[f725,f14254]) ).
fof(f14254,plain,
( spl0_1571
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f725,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f14252,plain,
spl0_1570,
inference(avatar_split_clause,[],[f712,f14250]) ).
fof(f14250,plain,
( spl0_1570
<=> ! [X40] :
( c_0 != c_Numeral_Onumber__of(X40,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f712,axiom,
! [X40] :
( c_0 != c_Numeral_Onumber__of(X40,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
fof(f14248,plain,
spl0_1569,
inference(avatar_split_clause,[],[f692,f14246]) ).
fof(f14246,plain,
( spl0_1569
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f692,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f14244,plain,
spl0_1568,
inference(avatar_split_clause,[],[f666,f14242]) ).
fof(f14242,plain,
( spl0_1568
<=> ! [X19,X30] :
( ~ c_less(c_0,X30,tc_nat)
| ~ c_less(c_0,X19,tc_nat)
| c_less(c_minus(X30,X19,tc_nat),X30,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f666,axiom,
! [X19,X30] :
( ~ c_less(c_0,X30,tc_nat)
| ~ c_less(c_0,X19,tc_nat)
| c_less(c_minus(X30,X19,tc_nat),X30,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f14240,plain,
spl0_1567,
inference(avatar_split_clause,[],[f614,f14238]) ).
fof(f14238,plain,
( spl0_1567
<=> ! [X45,X5,X44] : c_List_Oset(c_append(X44,X45,X5),X5) = c_union(c_List_Oset(X44,X5),c_List_Oset(X45,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f614,axiom,
! [X44,X45,X5] : c_List_Oset(c_append(X44,X45,X5),X5) = c_union(c_List_Oset(X44,X5),c_List_Oset(X45,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f14236,plain,
spl0_1566,
inference(avatar_split_clause,[],[f604,f14234]) ).
fof(f14234,plain,
( spl0_1566
<=> ! [X5,X8,X19] :
( c_List_Orotate(X19,X8,X5) = X8
| c_0 != c_Divides_Oop_Amod(X19,c_Nat_Osize(X8,tc_List_Olist(X5)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f604,axiom,
! [X8,X19,X5] :
( c_List_Orotate(X19,X8,X5) = X8
| c_0 != c_Divides_Oop_Amod(X19,c_Nat_Osize(X8,tc_List_Olist(X5)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f14232,plain,
spl0_1565,
inference(avatar_split_clause,[],[f590,f14230]) ).
fof(f14230,plain,
( spl0_1565
<=> ! [X45,X5,X44] : c_List_Orev(c_append(X44,X45,X5),X5) = c_append(c_List_Orev(X45,X5),c_List_Orev(X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f590,axiom,
! [X44,X45,X5] : c_List_Orev(c_append(X44,X45,X5),X5) = c_append(c_List_Orev(X45,X5),c_List_Orev(X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f14228,plain,
spl0_1564,
inference(avatar_split_clause,[],[f573,f14226]) ).
fof(f14226,plain,
( spl0_1564
<=> ! [X44,X4,X21,X45] : c_append(c_List_Olist_OCons(X4,X44,X21),X45,X21) = c_List_Olist_OCons(X4,c_append(X44,X45,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f573,axiom,
! [X21,X44,X45,X4] : c_append(c_List_Olist_OCons(X4,X44,X21),X45,X21) = c_List_Olist_OCons(X4,c_append(X44,X45,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f14224,plain,
spl0_1563,
inference(avatar_split_clause,[],[f561,f14222]) ).
fof(f14222,plain,
( spl0_1563
<=> ! [X44,X8,X5,X45] : c_List_Onth(c_append(X44,c_List_Olist_OCons(X8,X45,X5),X5),c_Nat_Osize(X44,tc_List_Olist(X5)),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f561,axiom,
! [X8,X44,X45,X5] : c_List_Onth(c_append(X44,c_List_Olist_OCons(X8,X45,X5),X5),c_Nat_Osize(X44,tc_List_Olist(X5)),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f14220,plain,
spl0_1562,
inference(avatar_split_clause,[],[f556,f14218]) ).
fof(f14218,plain,
( spl0_1562
<=> ! [X44,X4,X54,X5] :
( c_in(X4,c_List_Oset(X44,X5),X5)
| ~ c_in(X4,c_List_Oset(c_List_Osublist(X44,X54,X5),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f556,axiom,
! [X54,X44,X4,X5] :
( c_in(X4,c_List_Oset(X44,X5),X5)
| ~ c_in(X4,c_List_Oset(c_List_Osublist(X44,X54,X5),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f14216,plain,
spl0_1561,
inference(avatar_split_clause,[],[f555,f14214]) ).
fof(f14214,plain,
( spl0_1561
<=> ! [X44,X4,X5,X8] :
( c_in(X4,c_List_Oset(X44,X5),X5)
| ~ c_in(X4,c_List_Oset(c_List_Oremove1(X8,X44,X5),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f555,axiom,
! [X8,X44,X4,X5] :
( c_in(X4,c_List_Oset(X44,X5),X5)
| ~ c_in(X4,c_List_Oset(c_List_Oremove1(X8,X44,X5),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f14212,plain,
spl0_1560,
inference(avatar_split_clause,[],[f466,f14210]) ).
fof(f14210,plain,
( spl0_1560
<=> ! [X5,X44,X19] : c_Nat_Osize(c_List_Odrop(X19,X44,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f466,axiom,
! [X19,X44,X5] : c_Nat_Osize(c_List_Odrop(X19,X44,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f14208,plain,
spl0_1559,
inference(avatar_split_clause,[],[f442,f14206]) ).
fof(f14206,plain,
( spl0_1559
<=> ! [X5,X18,X4,X29] : c_List_Odrop(X29,c_List_Oreplicate(X18,X4,X5),X5) = c_List_Oreplicate(c_minus(X18,X29,tc_nat),X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f442,axiom,
! [X29,X18,X4,X5] : c_List_Odrop(X29,c_List_Oreplicate(X18,X4,X5),X5) = c_List_Oreplicate(c_minus(X18,X29,tc_nat),X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f14204,plain,
spl0_1558,
inference(avatar_split_clause,[],[f439,f14202]) ).
fof(f14202,plain,
( spl0_1558
<=> ! [X44,X5,X19,X30] : c_List_Odrop(X19,c_List_Odrop(X30,X44,X5),X5) = c_List_Odrop(c_plus(X19,X30,tc_nat),X44,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f439,axiom,
! [X19,X44,X5,X30] : c_List_Odrop(X19,c_List_Odrop(X30,X44,X5),X5) = c_List_Odrop(c_plus(X19,X30,tc_nat),X44,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f14200,plain,
spl0_1557,
inference(avatar_split_clause,[],[f419,f14198]) ).
fof(f14198,plain,
( spl0_1557
<=> ! [X4,X21,X44] :
( ~ c_List_Odistinct(X44,X21)
| c_List_Odistinct(c_List_Olist_OCons(X4,X44,X21),X21)
| c_in(X4,c_List_Oset(X44,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f419,axiom,
! [X21,X44,X4] :
( ~ c_List_Odistinct(X44,X21)
| c_List_Odistinct(c_List_Olist_OCons(X4,X44,X21),X21)
| c_in(X4,c_List_Oset(X44,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f14196,plain,
spl0_1556,
inference(avatar_split_clause,[],[f412,f14194]) ).
fof(f14194,plain,
( spl0_1556
<=> ! [X5,X46] :
( c_List_Olist_ONil = c_List_Oconcat(X46,X5)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X46,X5),c_List_Oset(X46,tc_List_Olist(X5)),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f412,axiom,
! [X46,X5] :
( c_List_Olist_ONil = c_List_Oconcat(X46,X5)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X46,X5),c_List_Oset(X46,tc_List_Olist(X5)),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f14192,plain,
spl0_1555,
inference(avatar_split_clause,[],[f383,f14190]) ).
fof(f14190,plain,
( spl0_1555
<=> ! [X44,X47,X5,X45] : c_append(c_append(X44,X45,X5),X47,X5) = c_append(X44,c_append(X45,X47,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f383,axiom,
! [X47,X44,X45,X5] : c_append(c_append(X44,X45,X5),X47,X5) = c_append(X44,c_append(X45,X47,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f14188,plain,
spl0_1554,
inference(avatar_split_clause,[],[f373,f14186]) ).
fof(f14186,plain,
( spl0_1554
<=> ! [X5,X46] :
( c_List_Olist_ONil = c_List_Oconcat(X46,X5)
| c_in(c_Main_ONil__eq__concat__conv__1(X46,X5),c_List_Oset(X46,tc_List_Olist(X5)),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f373,axiom,
! [X46,X5] :
( c_List_Olist_ONil = c_List_Oconcat(X46,X5)
| c_in(c_Main_ONil__eq__concat__conv__1(X46,X5),c_List_Oset(X46,tc_List_Olist(X5)),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f14184,plain,
spl0_1553,
inference(avatar_split_clause,[],[f360,f14182]) ).
fof(f14182,plain,
( spl0_1553
<=> ! [X2,X7] : c_Divides_Oop_Amod(c_uminus(X2,tc_IntDef_Oint),c_uminus(X7,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f360,axiom,
! [X2,X7] : c_Divides_Oop_Amod(c_uminus(X2,tc_IntDef_Oint),c_uminus(X7,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f14180,plain,
spl0_1552,
inference(avatar_split_clause,[],[f104,f14178]) ).
fof(f14178,plain,
( spl0_1552
<=> ! [X30,X18,X19] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_plus(X30,c_times(X19,X18,tc_nat),tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f104,axiom,
! [X18,X19,X30] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_plus(X30,c_times(X19,X18,tc_nat),tc_nat),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f14176,plain,
spl0_1551,
inference(avatar_split_clause,[],[f102,f14174]) ).
fof(f14174,plain,
( spl0_1551
<=> ! [X30,X18,X19] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_plus(X30,c_times(X18,X19,tc_nat),tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f102,axiom,
! [X18,X19,X30] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_plus(X30,c_times(X18,X19,tc_nat),tc_nat),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f14172,plain,
spl0_1550,
inference(avatar_split_clause,[],[f82,f14170]) ).
fof(f14170,plain,
( spl0_1550
<=> ! [X30,X19] :
( ~ c_less(c_1,X19,tc_nat)
| ~ c_less(c_0,X30,tc_nat)
| c_less(c_div(X30,X19,tc_nat),X30,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f82,axiom,
! [X19,X30] :
( ~ c_less(c_1,X19,tc_nat)
| ~ c_less(c_0,X30,tc_nat)
| c_less(c_div(X30,X19,tc_nat),X30,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f14147,plain,
( spl0_1549
| ~ spl0_1066
| spl0_1547 ),
inference(avatar_split_clause,[],[f13991,f13349,f8759,f14144]) ).
fof(f14144,plain,
( spl0_1549
<=> c_0 = c_Finite__Set_Ocard(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f13349,plain,
( spl0_1547
<=> c_in(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),c_Finite__Set_OFinites,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f13991,plain,
( c_0 = c_Finite__Set_Ocard(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_1066
| spl0_1547 ),
inference(resolution,[],[f13351,f8760]) ).
fof(f13351,plain,
( ~ c_in(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),c_Finite__Set_OFinites,tc_set(t_a))
| spl0_1547 ),
inference(avatar_component_clause,[],[f13349]) ).
fof(f13639,plain,
( spl0_1548
| ~ spl0_1066
| spl0_1546 ),
inference(avatar_split_clause,[],[f13501,f13345,f8759,f13636]) ).
fof(f13501,plain,
( c_0 = c_Finite__Set_Ocard(v_S,t_a)
| ~ spl0_1066
| spl0_1546 ),
inference(resolution,[],[f13346,f8760]) ).
fof(f13346,plain,
( ~ c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| spl0_1546 ),
inference(avatar_component_clause,[],[f13345]) ).
fof(f13352,plain,
( spl0_1546
| ~ spl0_1547
| ~ spl0_1361
| ~ spl0_1516 ),
inference(avatar_split_clause,[],[f13181,f13088,f11356,f13349,f13345]) ).
fof(f13181,plain,
( ~ c_in(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),c_Finite__Set_OFinites,tc_set(t_a))
| c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1361
| ~ spl0_1516 ),
inference(superposition,[],[f11357,f13090]) ).
fof(f13221,plain,
spl0_1545,
inference(avatar_split_clause,[],[f3127,f13219]) ).
fof(f13219,plain,
( spl0_1545
<=> ! [X5,X8] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f3127,plain,
! [X8,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X8,X5) ),
inference(forward_demodulation,[],[f2933,f979]) ).
fof(f2933,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X8,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f199,f994]) ).
fof(f199,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X8,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f13217,plain,
spl0_1544,
inference(avatar_split_clause,[],[f3122,f13215]) ).
fof(f13215,plain,
( spl0_1544
<=> ! [X5,X8] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f3122,plain,
! [X8,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X8),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X8,X5) ),
inference(forward_demodulation,[],[f2929,f979]) ).
fof(f2929,plain,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X8,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X8)),X5),X5) ),
inference(definition_unfolding,[],[f198,f994]) ).
fof(f198,axiom,
! [X8,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X8,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X8)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f13213,plain,
spl0_1543,
inference(avatar_split_clause,[],[f3015,f13211]) ).
fof(f13211,plain,
( spl0_1543
<=> ! [X80] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f3015,plain,
! [X80] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X80,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2837,f2763]) ).
fof(f2837,plain,
! [X80] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X80,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(X80,tc_nat),tc_nat),
inference(definition_unfolding,[],[f735,f1409]) ).
fof(f735,axiom,
! [X80] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f13209,plain,
spl0_1542,
inference(avatar_split_clause,[],[f2938,f13207]) ).
fof(f13207,plain,
( spl0_1542
<=> ! [X5,X44,X19] :
( c_List_Olist_ONil = X44
| c_0 = X19
| c_List_Olist_ONil != c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f2938,plain,
! [X44,X19,X5] :
( c_List_Olist_ONil = X44
| c_0 = X19
| c_List_Olist_ONil != c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5) ),
inference(definition_unfolding,[],[f637,f631]) ).
fof(f637,axiom,
! [X44,X19,X5] :
( c_List_Olist_ONil = X44
| c_0 = X19
| c_List_Olist_ONil != c_List_Otake(X19,X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f13201,plain,
( spl0_1541
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1540 ),
inference(avatar_split_clause,[],[f13197,f13194,f10445,f10140,f6747,f3739,f13199]) ).
fof(f13199,plain,
( spl0_1541
<=> ! [X40] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f13194,plain,
( spl0_1540
<=> ! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f13197,plain,
( ! [X40] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1540 ),
inference(forward_demodulation,[],[f13195,f11255]) ).
fof(f13195,plain,
( ! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1540 ),
inference(avatar_component_clause,[],[f13194]) ).
fof(f13196,plain,
spl0_1540,
inference(avatar_split_clause,[],[f2904,f13194]) ).
fof(f2904,plain,
! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f687,f1409]) ).
fof(f687,axiom,
! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X40,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f13192,plain,
spl0_1539,
inference(avatar_split_clause,[],[f2902,f13190]) ).
fof(f13190,plain,
( spl0_1539
<=> ! [X35,X31,X5,X1] :
( c_in(X31,X1,X5)
| ~ c_in(X31,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f2902,plain,
! [X31,X1,X5,X35] :
( c_in(X31,X1,X5)
| ~ c_in(X31,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) ),
inference(definition_unfolding,[],[f1471,f1238]) ).
fof(f1471,axiom,
! [X31,X1,X5,X35] :
( c_in(X31,X1,X5)
| ~ c_in(X31,c_inter(X1,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f13188,plain,
spl0_1538,
inference(avatar_split_clause,[],[f2901,f13186]) ).
fof(f13186,plain,
( spl0_1538
<=> ! [X35,X31,X5,X1] :
( c_in(X31,X35,X5)
| ~ c_in(X31,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f2901,plain,
! [X31,X1,X35,X5] :
( c_in(X31,X35,X5)
| ~ c_in(X31,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) ),
inference(definition_unfolding,[],[f1472,f1238]) ).
fof(f1472,axiom,
! [X31,X1,X35,X5] :
( c_in(X31,X35,X5)
| ~ c_in(X31,c_inter(X1,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f13176,plain,
spl0_1537,
inference(avatar_split_clause,[],[f2871,f13174]) ).
fof(f13174,plain,
( spl0_1537
<=> ! [X19,X30] :
( X19 = X30
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f2871,plain,
! [X19,X30] :
( X19 = X30
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f882,f1409,f1409]) ).
fof(f882,axiom,
! [X19,X30] :
( X19 = X30
| c_Suc(X19) != c_Suc(X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f13172,plain,
spl0_1536,
inference(avatar_split_clause,[],[f2819,f13170]) ).
fof(f13170,plain,
( spl0_1536
<=> ! [X5,X8,X19] : c_append(c_List_Osublist(X8,c_SetInterval_OlessThan(X19,tc_nat),X5),c_List_Odrop(X19,X8,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f2819,plain,
! [X8,X19,X5] : c_append(c_List_Osublist(X8,c_SetInterval_OlessThan(X19,tc_nat),X5),c_List_Odrop(X19,X8,X5),X5) = X8,
inference(definition_unfolding,[],[f400,f631]) ).
fof(f400,axiom,
! [X8,X19,X5] : c_append(c_List_Otake(X19,X8,X5),c_List_Odrop(X19,X8,X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f13168,plain,
spl0_1535,
inference(avatar_split_clause,[],[f1691,f13166]) ).
fof(f13166,plain,
( spl0_1535
<=> ! [X5,X1,X83] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(c_Main_OUnionE__1(X1,X83,X5),X83,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f1691,axiom,
! [X83,X1,X5] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(c_Main_OUnionE__1(X1,X83,X5),X83,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f13164,plain,
spl0_1534,
inference(avatar_split_clause,[],[f1688,f13162]) ).
fof(f13162,plain,
( spl0_1534
<=> ! [X5,X1,X83] :
( c_in(X1,c_Inter(X83,X5),X5)
| c_in(c_Main_OInterI__1(X1,X83,X5),X83,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f1688,axiom,
! [X83,X1,X5] :
( c_in(X1,c_Inter(X83,X5),X5)
| c_in(c_Main_OInterI__1(X1,X83,X5),X83,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f13160,plain,
spl0_1533,
inference(avatar_split_clause,[],[f1651,f13158]) ).
fof(f13158,plain,
( spl0_1533
<=> ! [X4,X77,X5,X1] :
( c_in(X4,X1,X5)
| ~ c_in(c_List_Olist_OCons(X4,X77,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f1651,axiom,
! [X1,X4,X77,X5] :
( c_in(X4,X1,X5)
| ~ c_in(c_List_Olist_OCons(X4,X77,X5),c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f13156,plain,
spl0_1532,
inference(avatar_split_clause,[],[f1640,f13154]) ).
fof(f13154,plain,
( spl0_1532
<=> ! [X5,X1,X44] :
( ~ c_in(c_Main_Oin__listsI__1(X1,X44,X5),X1,X5)
| c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f1640,axiom,
! [X1,X44,X5] :
( ~ c_in(c_Main_Oin__listsI__1(X1,X44,X5),X1,X5)
| c_in(X44,c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f13152,plain,
spl0_1531,
inference(avatar_split_clause,[],[f1635,f13150]) ).
fof(f13150,plain,
( spl0_1531
<=> ! [X84,X30] :
( c_0 != c_Divides_Oop_Amod(X30,X84,tc_IntDef_Oint)
| c_times(X84,c_Main_Ozmod__eq__0D__dest__1(X84,X30),tc_IntDef_Oint) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f1635,axiom,
! [X84,X30] :
( c_0 != c_Divides_Oop_Amod(X30,X84,tc_IntDef_Oint)
| c_times(X84,c_Main_Ozmod__eq__0D__dest__1(X84,X30),tc_IntDef_Oint) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f13148,plain,
spl0_1530,
inference(avatar_split_clause,[],[f1619,f13146]) ).
fof(f13146,plain,
( spl0_1530
<=> ! [X84,X30] :
( c_0 != c_Divides_Oop_Amod(X30,X84,tc_nat)
| c_times(X84,c_Main_Omod__eq__0D__dest__1(X84,X30),tc_nat) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f1619,axiom,
! [X84,X30] :
( c_0 != c_Divides_Oop_Amod(X30,X84,tc_nat)
| c_times(X84,c_Main_Omod__eq__0D__dest__1(X84,X30),tc_nat) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f13144,plain,
spl0_1529,
inference(avatar_split_clause,[],[f1592,f13142]) ).
fof(f13142,plain,
( spl0_1529
<=> ! [X4,X8] :
( ~ c_less(X4,X8,tc_nat)
| c_in(c_Pair(X4,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f1592,axiom,
! [X8,X4] :
( ~ c_less(X4,X8,tc_nat)
| c_in(c_Pair(X4,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
fof(f13140,plain,
spl0_1528,
inference(avatar_split_clause,[],[f1591,f13138]) ).
fof(f13138,plain,
( spl0_1528
<=> ! [X4,X8] :
( c_less(X4,X8,tc_nat)
| ~ c_in(c_Pair(X4,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f1591,axiom,
! [X8,X4] :
( c_less(X4,X8,tc_nat)
| ~ c_in(c_Pair(X4,X8,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
fof(f13136,plain,
( spl0_1527
| ~ spl0_800
| ~ spl0_1355
| ~ spl0_1432 ),
inference(avatar_split_clause,[],[f12673,f11642,f11157,f7294,f13133]) ).
fof(f7294,plain,
( spl0_800
<=> ! [X5,X8] : c_union(X8,c_emptyset,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f12673,plain,
( c_Tarski_Ointerval(v_r,v_a,v_b,t_a) = c_union(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,t_a)
| ~ spl0_800
| ~ spl0_1355
| ~ spl0_1432 ),
inference(forward_demodulation,[],[f12660,f7295]) ).
fof(f7295,plain,
( ! [X8,X5] : c_union(X8,c_emptyset,X5) = X8
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f7294]) ).
fof(f12660,plain,
( c_union(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,t_a) = c_union(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),c_emptyset,t_a)
| ~ spl0_1355
| ~ spl0_1432 ),
inference(superposition,[],[f11643,f11159]) ).
fof(f13131,plain,
spl0_1526,
inference(avatar_split_clause,[],[f1548,f13129]) ).
fof(f13129,plain,
( spl0_1526
<=> ! [X7,X5,X2,X1] :
( X2 = X7
| c_in(X2,X1,X5)
| ~ c_in(X2,c_insert(X7,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f1548,axiom,
! [X2,X1,X7,X5] :
( X2 = X7
| c_in(X2,X1,X5)
| ~ c_in(X2,c_insert(X7,X1,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f13127,plain,
spl0_1525,
inference(avatar_split_clause,[],[f1523,f13125]) ).
fof(f13125,plain,
( spl0_1525
<=> ! [X2,X5,X35] : c_Union(c_insert(X2,X35,tc_set(X5)),X5) = c_union(X2,c_Union(X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f1523,axiom,
! [X2,X35,X5] : c_Union(c_insert(X2,X35,tc_set(X5)),X5) = c_union(X2,c_Union(X35,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f13123,plain,
spl0_1524,
inference(avatar_split_clause,[],[f1520,f13121]) ).
fof(f13121,plain,
( spl0_1524
<=> ! [X5,X1,X83] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(c_Main_OUnion__iff__1(X1,X83,X5),X83,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f1520,axiom,
! [X83,X1,X5] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(c_Main_OUnion__iff__1(X1,X83,X5),X83,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f13119,plain,
spl0_1523,
inference(avatar_split_clause,[],[f1486,f13117]) ).
fof(f13117,plain,
( spl0_1523
<=> ! [X5,X1,X83] :
( c_in(X1,c_Inter(X83,X5),X5)
| c_in(c_Main_OInter__iff__1(X1,X83,X5),X83,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f1486,axiom,
! [X83,X1,X5] :
( c_in(X1,c_Inter(X83,X5),X5)
| c_in(c_Main_OInter__iff__1(X1,X83,X5),X83,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f13115,plain,
spl0_1522,
inference(avatar_split_clause,[],[f1353,f13113]) ).
fof(f13113,plain,
( spl0_1522
<=> ! [X2,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_0 = X2
| c_0 = X7
| c_0 != c_times(X2,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f1353,axiom,
! [X2,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_0 = X2
| c_0 = X7
| c_0 != c_times(X2,X7,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f13111,plain,
spl0_1521,
inference(avatar_split_clause,[],[f1337,f13109]) ).
fof(f13109,plain,
( spl0_1521
<=> ! [X5,X7,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X7
| c_0 = X31
| c_times(X7,X31,X5) != X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f1337,axiom,
! [X31,X7,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X7
| c_0 = X31
| c_times(X7,X31,X5) != X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
fof(f13107,plain,
spl0_1520,
inference(avatar_split_clause,[],[f1336,f13105]) ).
fof(f13105,plain,
( spl0_1520
<=> ! [X2,X5,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X2
| c_0 = X31
| c_times(X31,X2,X5) != X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f1336,axiom,
! [X2,X31,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X2
| c_0 = X31
| c_times(X31,X2,X5) != X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
fof(f13103,plain,
spl0_1519,
inference(avatar_split_clause,[],[f1228,f13101]) ).
fof(f13101,plain,
( spl0_1519
<=> ! [X2,X81,X7,X5,X22,X23] :
( X7 = X81
| c_Pair(X2,X7,X5,X23) != c_Pair(X22,X81,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f1228,axiom,
! [X2,X81,X7,X5,X22,X23] :
( X7 = X81
| c_Pair(X2,X7,X5,X23) != c_Pair(X22,X81,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f13099,plain,
spl0_1518,
inference(avatar_split_clause,[],[f1227,f13097]) ).
fof(f13097,plain,
( spl0_1518
<=> ! [X2,X81,X23,X5,X22,X7] :
( X2 = X22
| c_Pair(X2,X7,X5,X23) != c_Pair(X22,X81,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f1227,axiom,
! [X2,X81,X7,X22,X5,X23] :
( X2 = X22
| c_Pair(X2,X7,X5,X23) != c_Pair(X22,X81,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f13095,plain,
spl0_1517,
inference(avatar_split_clause,[],[f1214,f13093]) ).
fof(f13093,plain,
( spl0_1517
<=> ! [X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X19,tc_nat)
| c_0 = c_Nat_Opower(c_0,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f1214,axiom,
! [X19,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X19,tc_nat)
| c_0 = c_Nat_Opower(c_0,X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f13091,plain,
( spl0_1516
| ~ spl0_799
| ~ spl0_1355
| ~ spl0_1431 ),
inference(avatar_split_clause,[],[f12655,f11638,f11157,f7290,f13088]) ).
fof(f7290,plain,
( spl0_799
<=> ! [X5,X8] : c_union(c_emptyset,X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f12655,plain,
( c_Tarski_Ointerval(v_r,v_a,v_b,t_a) = c_union(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_799
| ~ spl0_1355
| ~ spl0_1431 ),
inference(forward_demodulation,[],[f12642,f7291]) ).
fof(f7291,plain,
( ! [X8,X5] : c_union(c_emptyset,X8,X5) = X8
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7290]) ).
fof(f12642,plain,
( c_union(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) = c_union(c_emptyset,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_1355
| ~ spl0_1431 ),
inference(superposition,[],[f11639,f11159]) ).
fof(f13086,plain,
spl0_1515,
inference(avatar_split_clause,[],[f1213,f13084]) ).
fof(f13084,plain,
( spl0_1515
<=> ! [X2,X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X19,tc_nat)
| c_0 != c_Nat_Opower(X2,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f1213,axiom,
! [X2,X19,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X19,tc_nat)
| c_0 != c_Nat_Opower(X2,X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f13082,plain,
spl0_1514,
inference(avatar_split_clause,[],[f1133,f13080]) ).
fof(f13080,plain,
( spl0_1514
<=> ! [X4,X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omax(X4,X8,X23) = c_Orderings_Omax(X4,c_Orderings_Omax(X4,X8,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f1133,axiom,
! [X8,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omax(X4,X8,X23) = c_Orderings_Omax(X4,c_Orderings_Omax(X4,X8,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f13078,plain,
spl0_1513,
inference(avatar_split_clause,[],[f1128,f13076]) ).
fof(f13076,plain,
( spl0_1513
<=> ! [X4,X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omin(X4,X8,X23) = c_Orderings_Omin(X4,c_Orderings_Omin(X4,X8,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f1128,axiom,
! [X8,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omin(X4,X8,X23) = c_Orderings_Omin(X4,c_Orderings_Omin(X4,X8,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f13074,plain,
spl0_1512,
inference(avatar_split_clause,[],[f1111,f13072]) ).
fof(f13072,plain,
( spl0_1512
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_OrderedGroup_Opprt(X2,X5),c_OrderedGroup_Opprt(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f1111,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_OrderedGroup_Opprt(X2,X5),c_OrderedGroup_Opprt(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f13070,plain,
spl0_1511,
inference(avatar_split_clause,[],[f1107,f13068]) ).
fof(f13068,plain,
( spl0_1511
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_OrderedGroup_Onprt(X2,X5),c_OrderedGroup_Onprt(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f1107,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_OrderedGroup_Onprt(X2,X5),c_OrderedGroup_Onprt(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f13066,plain,
spl0_1510,
inference(avatar_split_clause,[],[f1101,f13064]) ).
fof(f13064,plain,
( spl0_1510
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_uminus(X7,X5),c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f1101,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_uminus(X7,X5),c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f13062,plain,
spl0_1509,
inference(avatar_split_clause,[],[f1100,f13060]) ).
fof(f13060,plain,
( spl0_1509
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_uminus(X7,X5),c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f1100,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_uminus(X7,X5),c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f13058,plain,
spl0_1508,
inference(avatar_split_clause,[],[f1097,f13056]) ).
fof(f13056,plain,
( spl0_1508
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_uminus(X7,X5),c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f1097,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_uminus(X7,X5),c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f13054,plain,
spl0_1507,
inference(avatar_split_clause,[],[f1096,f13052]) ).
fof(f13052,plain,
( spl0_1507
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_uminus(X7,X5),c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f1096,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_uminus(X7,X5),c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f13050,plain,
spl0_1506,
inference(avatar_split_clause,[],[f1060,f13048]) ).
fof(f13048,plain,
( spl0_1506
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X31
| c_plus(X31,X2,X5) != c_plus(X7,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f1060,axiom,
! [X31,X2,X7,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X31
| c_plus(X31,X2,X5) != c_plus(X7,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f13046,plain,
spl0_1505,
inference(avatar_split_clause,[],[f1055,f13044]) ).
fof(f13044,plain,
( spl0_1505
<=> ! [X31,X7,X5,X2] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X31
| c_plus(X2,X7,X5) != c_plus(X2,X31,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f1055,axiom,
! [X31,X2,X7,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X31
| c_plus(X2,X7,X5) != c_plus(X2,X31,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f13042,plain,
spl0_1504,
inference(avatar_split_clause,[],[f976,f13040]) ).
fof(f13040,plain,
( spl0_1504
<=> ! [X40,X39] : c_Numeral_Obin__add(c_Numeral_OBit(X40,c_Numeral_Obit_OB1),c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X40,c_Numeral_Obin__succ(X39)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f976,axiom,
! [X40,X39] : c_Numeral_Obin__add(c_Numeral_OBit(X40,c_Numeral_Obit_OB1),c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X40,c_Numeral_Obin__succ(X39)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f13038,plain,
spl0_1503,
inference(avatar_split_clause,[],[f950,f13036]) ).
fof(f13036,plain,
( spl0_1503
<=> ! [X30,X18,X19] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f950,axiom,
! [X18,X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f13034,plain,
spl0_1502,
inference(avatar_split_clause,[],[f949,f13032]) ).
fof(f13032,plain,
( spl0_1502
<=> ! [X30,X18,X19] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f949,axiom,
! [X18,X19,X30] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f13030,plain,
spl0_1501,
inference(avatar_split_clause,[],[f948,f13028]) ).
fof(f13028,plain,
( spl0_1501
<=> ! [X30,X18,X19] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f948,axiom,
! [X18,X19,X30] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f13026,plain,
spl0_1500,
inference(avatar_split_clause,[],[f947,f13024]) ).
fof(f13024,plain,
( spl0_1500
<=> ! [X30,X18,X19] :
( c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f947,axiom,
! [X18,X19,X30] :
( c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_plus(X18,X30,tc_nat),c_plus(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f13022,plain,
spl0_1499,
inference(avatar_split_clause,[],[f941,f13020]) ).
fof(f13020,plain,
( spl0_1499
<=> ! [X30,X18,X19] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f941,axiom,
! [X18,X19,X30] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f13018,plain,
spl0_1498,
inference(avatar_split_clause,[],[f940,f13016]) ).
fof(f13016,plain,
( spl0_1498
<=> ! [X30,X18,X19] :
( c_less(c_0,X18,tc_nat)
| ~ c_less(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f940,axiom,
! [X18,X19,X30] :
( c_less(c_0,X18,tc_nat)
| ~ c_less(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f13014,plain,
spl0_1497,
inference(avatar_split_clause,[],[f938,f13012]) ).
fof(f13012,plain,
( spl0_1497
<=> ! [X30,X18,X19] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f938,axiom,
! [X18,X19,X30] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f13010,plain,
spl0_1496,
inference(avatar_split_clause,[],[f937,f13008]) ).
fof(f13008,plain,
( spl0_1496
<=> ! [X30,X18,X19] :
( c_less(c_0,X18,tc_nat)
| ~ c_less(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f937,axiom,
! [X18,X19,X30] :
( c_less(c_0,X18,tc_nat)
| ~ c_less(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f13006,plain,
spl0_1495,
inference(avatar_split_clause,[],[f936,f13004]) ).
fof(f13004,plain,
( spl0_1495
<=> ! [X30,X18,X19] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f936,axiom,
! [X18,X19,X30] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f13002,plain,
spl0_1494,
inference(avatar_split_clause,[],[f935,f13000]) ).
fof(f13000,plain,
( spl0_1494
<=> ! [X30,X18,X19] :
( c_less(c_0,X18,tc_nat)
| c_lessequals(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f935,axiom,
! [X18,X19,X30] :
( c_less(c_0,X18,tc_nat)
| c_lessequals(c_times(X30,X18,tc_nat),c_times(X19,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f12998,plain,
spl0_1493,
inference(avatar_split_clause,[],[f933,f12996]) ).
fof(f12996,plain,
( spl0_1493
<=> ! [X30,X18,X19] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f933,axiom,
! [X18,X19,X30] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f12994,plain,
spl0_1492,
inference(avatar_split_clause,[],[f932,f12992]) ).
fof(f12992,plain,
( spl0_1492
<=> ! [X30,X18,X19] :
( c_less(c_0,X18,tc_nat)
| c_lessequals(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f932,axiom,
! [X18,X19,X30] :
( c_less(c_0,X18,tc_nat)
| c_lessequals(c_times(X18,X30,tc_nat),c_times(X18,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f12990,plain,
spl0_1491,
inference(avatar_split_clause,[],[f792,f12988]) ).
fof(f12988,plain,
( spl0_1491
<=> ! [X23,X7] :
( ~ class_HOL_Oone(X23)
| ~ class_OrderedGroup_Oab__group__add(X23)
| c_1 != c_uminus(X7,X23)
| c_uminus(c_1,X23) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f792,axiom,
! [X7,X23] :
( ~ class_HOL_Oone(X23)
| ~ class_OrderedGroup_Oab__group__add(X23)
| c_1 != c_uminus(X7,X23)
| c_uminus(c_1,X23) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f12986,plain,
spl0_1490,
inference(avatar_split_clause,[],[f733,f12984]) ).
fof(f12984,plain,
( spl0_1490
<=> ! [X5,X40] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X40,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f733,axiom,
! [X40,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X40,tc_nat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f12982,plain,
spl0_1489,
inference(avatar_split_clause,[],[f685,f12980]) ).
fof(f12980,plain,
( spl0_1489
<=> ! [X30,X5,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X30,X19,tc_nat)
| c_less(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f685,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X30,X19,tc_nat)
| c_less(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f12978,plain,
spl0_1488,
inference(avatar_split_clause,[],[f684,f12976]) ).
fof(f12976,plain,
( spl0_1488
<=> ! [X30,X5,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(X30,X19,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f684,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(X30,X19,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f12974,plain,
spl0_1487,
inference(avatar_split_clause,[],[f682,f12972]) ).
fof(f12972,plain,
( spl0_1487
<=> ! [X30,X5,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f682,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f12970,plain,
spl0_1486,
inference(avatar_split_clause,[],[f681,f12968]) ).
fof(f12968,plain,
( spl0_1486
<=> ! [X30,X5,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f681,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X30,X5),c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f12966,plain,
( spl0_1485
| ~ spl0_1112
| ~ spl0_1438 ),
inference(avatar_split_clause,[],[f12718,f11673,f8945,f12964]) ).
fof(f12964,plain,
( spl0_1485
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f8945,plain,
( spl0_1112
<=> ! [X4,X5] : c_in(c_Pair(X4,X4,X5,X5),c_Relation_OId,tc_prod(X5,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f11673,plain,
( spl0_1438
<=> ! [X6,X2,X5] :
( ~ c_Wellfounded__Recursion_Owf(X6,X5)
| ~ c_in(c_Pair(X2,X2,X5,X5),X6,tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f12718,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1112
| ~ spl0_1438 ),
inference(resolution,[],[f11674,f8946]) ).
fof(f8946,plain,
( ! [X4,X5] : c_in(c_Pair(X4,X4,X5,X5),c_Relation_OId,tc_prod(X5,X5))
| ~ spl0_1112 ),
inference(avatar_component_clause,[],[f8945]) ).
fof(f11674,plain,
( ! [X2,X6,X5] :
( ~ c_in(c_Pair(X2,X2,X5,X5),X6,tc_prod(X5,X5))
| ~ c_Wellfounded__Recursion_Owf(X6,X5) )
| ~ spl0_1438 ),
inference(avatar_component_clause,[],[f11673]) ).
fof(f12962,plain,
spl0_1484,
inference(avatar_split_clause,[],[f621,f12960]) ).
fof(f12960,plain,
( spl0_1484
<=> ! [X4,X5,X19] :
( c_0 = X19
| c_insert(X4,c_emptyset,X5) = c_List_Oset(c_List_Oreplicate(X19,X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f621,axiom,
! [X19,X4,X5] :
( c_0 = X19
| c_insert(X4,c_emptyset,X5) = c_List_Oset(c_List_Oreplicate(X19,X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f12958,plain,
spl0_1483,
inference(avatar_split_clause,[],[f598,f12956]) ).
fof(f12956,plain,
( spl0_1483
<=> ! [X4,X5,X44] :
( c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) = X44
| c_List_Orev(X44,X5) != c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f598,axiom,
! [X44,X4,X5] :
( c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) = X44
| c_List_Orev(X44,X5) != c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).
fof(f12954,plain,
spl0_1482,
inference(avatar_split_clause,[],[f575,f12952]) ).
fof(f12952,plain,
( spl0_1482
<=> ! [X8,X4,X21,X45] :
( X4 = X8
| c_List_Oop_Amem(X4,X45,X21)
| ~ c_List_Oop_Amem(X4,c_List_Olist_OCons(X8,X45,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f575,axiom,
! [X21,X8,X45,X4] :
( X4 = X8
| c_List_Oop_Amem(X4,X45,X21)
| ~ c_List_Oop_Amem(X4,c_List_Olist_OCons(X8,X45,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f12950,plain,
spl0_1481,
inference(avatar_split_clause,[],[f505,f12948]) ).
fof(f12948,plain,
( spl0_1481
<=> ! [X21,X1,X62] : c_List_Olistset(c_List_Olist_OCons(X1,X62,tc_set(X21)),X21) = c_List_Oset__Cons(X1,c_List_Olistset(X62,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f505,axiom,
! [X21,X1,X62] : c_List_Olistset(c_List_Olist_OCons(X1,X62,tc_set(X21)),X21) = c_List_Oset__Cons(X1,c_List_Olistset(X62,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f12946,plain,
spl0_1480,
inference(avatar_split_clause,[],[f497,f12944]) ).
fof(f12944,plain,
( spl0_1480
<=> ! [X5,X4,X29,X8] :
( ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),X29,tc_nat)
| c_List_Olist__update(X8,X29,X4,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f497,axiom,
! [X29,X8,X4,X5] :
( ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),X29,tc_nat)
| c_List_Olist__update(X8,X29,X4,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f12942,plain,
spl0_1479,
inference(avatar_split_clause,[],[f477,f12940]) ).
fof(f12940,plain,
( spl0_1479
<=> ! [X5,X44] : c_minus(c_Nat_Osize(X44,tc_List_Olist(X5)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X44,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f477,axiom,
! [X44,X5] : c_minus(c_Nat_Osize(X44,tc_List_Olist(X5)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X44,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f12938,plain,
spl0_1478,
inference(avatar_split_clause,[],[f465,f12936]) ).
fof(f12936,plain,
( spl0_1478
<=> ! [X5,X44] : c_Nat_Osize(c_List_Obutlast(X44,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X44,tc_List_Olist(X5)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f465,axiom,
! [X44,X5] : c_Nat_Osize(c_List_Obutlast(X44,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X44,tc_List_Olist(X5)),c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f12934,plain,
spl0_1477,
inference(avatar_split_clause,[],[f461,f12932]) ).
fof(f12932,plain,
( spl0_1477
<=> ! [X29,X55] :
( ~ c_less(X29,X55,tc_nat)
| c_List_Olast(c_List_Oupt(X29,X55),tc_nat) = c_minus(X55,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f461,axiom,
! [X29,X55] :
( ~ c_less(X29,X55,tc_nat)
| c_List_Olast(c_List_Oupt(X29,X55),tc_nat) = c_minus(X55,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f12930,plain,
spl0_1476,
inference(avatar_split_clause,[],[f409,f12928]) ).
fof(f12928,plain,
( spl0_1476
<=> ! [X4,X21,X44] : c_List_Oconcat(c_List_Olist_OCons(X4,X44,tc_List_Olist(X21)),X21) = c_append(X4,c_List_Oconcat(X44,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f409,axiom,
! [X21,X44,X4] : c_List_Oconcat(c_List_Olist_OCons(X4,X44,tc_List_Olist(X21)),X21) = c_append(X4,c_List_Oconcat(X44,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f12926,plain,
spl0_1475,
inference(avatar_split_clause,[],[f321,f12924]) ).
fof(f12924,plain,
( spl0_1475
<=> ! [X6,X42] : c_IntDiv_OnegateSnd(c_Pair(X42,X6,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X42,c_uminus(X6,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f321,axiom,
! [X6,X42] : c_IntDiv_OnegateSnd(c_Pair(X42,X6,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X42,c_uminus(X6,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f12922,plain,
( spl0_1474
| ~ spl0_130
| ~ spl0_1438 ),
inference(avatar_split_clause,[],[f12715,f11673,f3804,f12920]) ).
fof(f12920,plain,
( spl0_1474
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f3804,plain,
( spl0_130
<=> ! [X4,X5] : c_in(X4,c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f12715,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_130
| ~ spl0_1438 ),
inference(resolution,[],[f11674,f3805]) ).
fof(f3805,plain,
( ! [X4,X5] : c_in(X4,c_UNIV,X5)
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f3804]) ).
fof(f12918,plain,
spl0_1473,
inference(avatar_split_clause,[],[f296,f12916]) ).
fof(f12916,plain,
( spl0_1473
<=> ! [X9,X39] :
( ~ c_less(X39,X9,tc_IntDef_Oint)
| ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X39),c_IntDef_Onat(X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f296,axiom,
! [X39,X9] :
( ~ c_less(X39,X9,tc_IntDef_Oint)
| ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X39),c_IntDef_Onat(X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f12914,plain,
spl0_1472,
inference(avatar_split_clause,[],[f280,f12912]) ).
fof(f12912,plain,
( spl0_1472
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X39,X9,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f280,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X39,X9,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f12910,plain,
spl0_1471,
inference(avatar_split_clause,[],[f279,f12908]) ).
fof(f12908,plain,
( spl0_1471
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X39,X9,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f279,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X39,X9,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f12906,plain,
spl0_1470,
inference(avatar_split_clause,[],[f276,f12904]) ).
fof(f12904,plain,
( spl0_1470
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X39,X9,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f276,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X39,X9,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f12902,plain,
spl0_1469,
inference(avatar_split_clause,[],[f275,f12900]) ).
fof(f12900,plain,
( spl0_1469
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X39,X9,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f275,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X39,X9,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X39,X5),c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f12898,plain,
spl0_1468,
inference(avatar_split_clause,[],[f146,f12896]) ).
fof(f12896,plain,
( spl0_1468
<=> ! [X36,X5,X35] :
( ~ c_in(X35,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X35,X36,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f146,axiom,
! [X36,X35,X5] :
( ~ c_in(X35,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X35,X36,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f12894,plain,
spl0_1467,
inference(avatar_split_clause,[],[f63,f12892]) ).
fof(f12892,plain,
( spl0_1467
<=> ! [X28,X24,X23,X5,X27,X25] :
( X25 = X28
| c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_OScons(X27,X28,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f63,axiom,
! [X28,X27,X24,X5,X25,X23] :
( X25 = X28
| c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_OScons(X27,X28,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f12890,plain,
spl0_1466,
inference(avatar_split_clause,[],[f62,f12888]) ).
fof(f12888,plain,
( spl0_1466
<=> ! [X24,X23,X5,X27,X25,X28] :
( X24 = X27
| c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_OScons(X27,X28,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f62,axiom,
! [X28,X27,X24,X5,X25,X23] :
( X24 = X27
| c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_OScons(X27,X28,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f12776,plain,
( spl0_1465
| ~ spl0_99
| ~ spl0_1443 ),
inference(avatar_split_clause,[],[f12772,f11693,f3665,f12774]) ).
fof(f11693,plain,
( spl0_1443
<=> ! [X35,X31,X5,X1] :
( ~ c_in(X31,X1,X5)
| c_in(X31,X35,X5)
| ~ c_lessequals(X1,X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f12772,plain,
( ! [X0] :
( c_in(X0,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ c_in(X0,v_S,t_a) )
| ~ spl0_99
| ~ spl0_1443 ),
inference(resolution,[],[f11694,f3667]) ).
fof(f11694,plain,
( ! [X31,X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_in(X31,X35,X5)
| ~ c_in(X31,X1,X5) )
| ~ spl0_1443 ),
inference(avatar_component_clause,[],[f11693]) ).
fof(f12410,plain,
( ~ spl0_1462
| spl0_1463
| ~ spl0_1464
| ~ spl0_1355
| ~ spl0_1392 ),
inference(avatar_split_clause,[],[f12294,f11481,f11157,f12407,f12403,f12399]) ).
fof(f12399,plain,
( spl0_1462
<=> class_OrderedGroup_Opordered__ab__group__add(tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f12407,plain,
( spl0_1464
<=> c_less(c_emptyset,c_0,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f11481,plain,
( spl0_1392
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_minus(X2,X7,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f12294,plain,
( ~ c_less(c_emptyset,c_0,tc_set(t_a))
| c_less(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_set(t_a))
| ~ spl0_1355
| ~ spl0_1392 ),
inference(superposition,[],[f11482,f11159]) ).
fof(f11482,plain,
( ! [X2,X7,X5] :
( ~ c_less(c_minus(X2,X7,X5),c_0,X5)
| c_less(X2,X7,X5)
| ~ class_OrderedGroup_Opordered__ab__group__add(X5) )
| ~ spl0_1392 ),
inference(avatar_component_clause,[],[f11481]) ).
fof(f11829,plain,
spl0_1461,
inference(avatar_split_clause,[],[f3081,f11827]) ).
fof(f11827,plain,
( spl0_1461
<=> ! [X80] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f3081,plain,
! [X80] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X80,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2905,f2763]) ).
fof(f2905,plain,
! [X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,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(X80,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f736,f1409,f1409]) ).
fof(f736,axiom,
! [X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f11825,plain,
spl0_1460,
inference(avatar_split_clause,[],[f3065,f11823]) ).
fof(f11823,plain,
( spl0_1460
<=> ! [X29,X19] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X29,X19,tc_nat),tc_nat),X19,tc_nat)
| ~ c_less(c_0,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f3065,plain,
! [X29,X19] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X29,X19,tc_nat),tc_nat),X19,tc_nat)
| ~ c_less(c_0,X19,tc_nat) ),
inference(forward_demodulation,[],[f2885,f2814]) ).
fof(f2885,plain,
! [X29,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_minus(X19,c_Finite__Set_Ocard(c_SetInterval_OatMost(X29,tc_nat),tc_nat),tc_nat),X19,tc_nat) ),
inference(definition_unfolding,[],[f901,f1409]) ).
fof(f901,axiom,
! [X29,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_minus(X19,c_Suc(X29),tc_nat),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f11821,plain,
spl0_1459,
inference(avatar_split_clause,[],[f3019,f11819]) ).
fof(f11819,plain,
( spl0_1459
<=> ! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f3019,plain,
! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X8,
inference(forward_demodulation,[],[f3018,f1021]) ).
fof(f3018,plain,
! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X8,
inference(forward_demodulation,[],[f3017,f1019]) ).
fof(f3017,plain,
! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X8,
inference(forward_demodulation,[],[f748,f1021]) ).
fof(f748,axiom,
! [X8] : c_div(c_plus(X8,X8,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f11817,plain,
spl0_1458,
inference(avatar_split_clause,[],[f3007,f11815]) ).
fof(f11815,plain,
( spl0_1458
<=> ! [X40,X39] : c_Numeral_Obin__mult(c_Numeral_OBit(X40,c_Numeral_Obit_OB1),X39) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),X39),X39) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f3007,plain,
! [X40,X39] : c_Numeral_Obin__mult(c_Numeral_OBit(X40,c_Numeral_Obit_OB1),X39) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),X39),X39),
inference(forward_demodulation,[],[f993,f992]) ).
fof(f992,axiom,
! [X40,X39] : c_Numeral_Obin__mult(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),X39) = c_Numeral_OBit(c_Numeral_Obin__mult(X40,X39),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f993,axiom,
! [X40,X39] : c_Numeral_Obin__mult(c_Numeral_OBit(X40,c_Numeral_Obit_OB1),X39) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X40,X39),c_Numeral_Obit_OB0),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f11813,plain,
spl0_1457,
inference(avatar_split_clause,[],[f3004,f11811]) ).
fof(f3004,plain,
! [X39] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X39)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2805,f2778]) ).
fof(f2778,plain,
! [X39] : c_Numeral_Obin__add(c_Numeral_OMin,X39) = c_Numeral_Obin__add(X39,c_Numeral_OMin),
inference(definition_unfolding,[],[f977,f978]) ).
fof(f978,axiom,
! [X39] : c_Numeral_Obin__pred(X39) = c_Numeral_Obin__add(X39,c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f977,axiom,
! [X39] : c_Numeral_Obin__add(c_Numeral_OMin,X39) = c_Numeral_Obin__pred(X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2805,plain,
! [X39] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X39),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f989,f994,f978,f994]) ).
fof(f989,axiom,
! [X39] : c_Numeral_Obin__minus(c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X39)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f11809,plain,
spl0_1456,
inference(avatar_split_clause,[],[f2915,f11807]) ).
fof(f11807,plain,
( spl0_1456
<=> ! [X40] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X40),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f2915,plain,
! [X40] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X40),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f718,f994]) ).
fof(f718,axiom,
! [X40] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X40),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f11805,plain,
spl0_1455,
inference(avatar_split_clause,[],[f2913,f11803]) ).
fof(f11803,plain,
( spl0_1455
<=> ! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X40,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2913,plain,
! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X40,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f719,f994]) ).
fof(f719,axiom,
! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X40),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X40,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f11758,plain,
( spl0_1454
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1453 ),
inference(avatar_split_clause,[],[f11754,f11751,f10445,f10140,f6747,f3739,f11756]) ).
fof(f11756,plain,
( spl0_1454
<=> ! [X29,X55] :
( c_List_Olist_ONil = c_List_Oupt(X29,c_plus(c_1,X55,tc_nat))
| c_lessequals(X29,X55,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f11751,plain,
( spl0_1453
<=> ! [X29,X55] :
( c_lessequals(X29,X55,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X29,c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f11754,plain,
( ! [X29,X55] :
( c_List_Olist_ONil = c_List_Oupt(X29,c_plus(c_1,X55,tc_nat))
| c_lessequals(X29,X55,tc_nat) )
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1453 ),
inference(forward_demodulation,[],[f11752,f11255]) ).
fof(f11752,plain,
( ! [X29,X55] :
( c_lessequals(X29,X55,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X29,c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat)) )
| ~ spl0_1453 ),
inference(avatar_component_clause,[],[f11751]) ).
fof(f11753,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2896,f11751]) ).
fof(f2896,plain,
! [X29,X55] :
( c_lessequals(X29,X55,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X29,c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f648,f1409]) ).
fof(f648,axiom,
! [X29,X55] :
( c_lessequals(X29,X55,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X29,c_Suc(X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f11749,plain,
spl0_1452,
inference(avatar_split_clause,[],[f2861,f11747]) ).
fof(f2861,plain,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X39),X5) ),
inference(definition_unfolding,[],[f982,f994]) ).
fof(f982,axiom,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X39,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X39),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f11741,plain,
( spl0_1451
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1450 ),
inference(avatar_split_clause,[],[f11737,f11734,f10445,f10140,f6747,f3739,f11739]) ).
fof(f11739,plain,
( spl0_1451
<=> ! [X30] : c_insert(X30,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X30,c_plus(c_1,X30,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f11734,plain,
( spl0_1450
<=> ! [X30] : c_insert(X30,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f11737,plain,
( ! [X30] : c_insert(X30,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X30,c_plus(c_1,X30,tc_nat),tc_nat)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1450 ),
inference(forward_demodulation,[],[f11735,f11255]) ).
fof(f11735,plain,
( ! [X30] : c_insert(X30,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat)
| ~ spl0_1450 ),
inference(avatar_component_clause,[],[f11734]) ).
fof(f11736,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2806,f11734]) ).
fof(f2806,plain,
! [X30] : c_insert(X30,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1392,f1409]) ).
fof(f1392,axiom,
! [X30] : c_SetInterval_OatLeastLessThan(X30,c_Suc(X30),tc_nat) = c_insert(X30,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f11732,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2804,f11730]) ).
fof(f11730,plain,
( spl0_1449
<=> ! [X5,X1,X35] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),c_minus(X35,X1,tc_set(X5)),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f2804,plain,
! [X1,X5,X35] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),c_minus(X35,X1,tc_set(X5)),X5,X5),
inference(definition_unfolding,[],[f1454,f1238]) ).
fof(f1454,axiom,
! [X1,X35,X5] : c_emptyset = c_inter(X1,c_minus(X35,X1,tc_set(X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f11728,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2793,f11726]) ).
fof(f11726,plain,
( spl0_1448
<=> ! [X82,X5] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f2793,plain,
! [X82,X5] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5),
inference(definition_unfolding,[],[f1571,f1581]) ).
fof(f1571,axiom,
! [X82,X5] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X82,X5),X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f11724,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2792,f11722]) ).
fof(f11722,plain,
( spl0_1447
<=> ! [X82,X5] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f2792,plain,
! [X82,X5] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5),
inference(definition_unfolding,[],[f1572,f1581]) ).
fof(f1572,axiom,
! [X82,X5] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X82,X5),X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f11708,plain,
( spl0_1446
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1445 ),
inference(avatar_split_clause,[],[f11704,f11701,f10445,f10140,f6747,f3739,f11706]) ).
fof(f11706,plain,
( spl0_1446
<=> ! [X19] : c_plus(c_1,X19,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X19,tc_nat),X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f11701,plain,
( spl0_1445
<=> ! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f11704,plain,
( ! [X19] : c_plus(c_1,X19,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X19,tc_nat),X19)
| ~ spl0_115
| ~ spl0_673
| ~ spl0_1267
| ~ spl0_1343
| ~ spl0_1445 ),
inference(forward_demodulation,[],[f11702,f11255]) ).
fof(f11702,plain,
( ! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X19)
| ~ spl0_1445 ),
inference(avatar_component_clause,[],[f11701]) ).
fof(f11703,plain,
spl0_1445,
inference(avatar_split_clause,[],[f2788,f11701]) ).
fof(f2788,plain,
! [X19] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X19),
inference(definition_unfolding,[],[f28,f1409,f1409]) ).
fof(f28,axiom,
! [X19] : c_Suc(X19) = c_Binomial_Obinomial(c_Suc(X19),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f11699,plain,
spl0_1444,
inference(avatar_split_clause,[],[f1703,f11697]) ).
fof(f11697,plain,
( spl0_1444
<=> ! [X5,X1,X35] :
( X1 = X35
| ~ c_lessequals(X1,X35,tc_set(X5))
| ~ c_lessequals(X35,X1,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f1703,axiom,
! [X1,X35,X5] :
( X1 = X35
| ~ c_lessequals(X1,X35,tc_set(X5))
| ~ c_lessequals(X35,X1,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f11695,plain,
spl0_1443,
inference(avatar_split_clause,[],[f1700,f11693]) ).
fof(f1700,axiom,
! [X31,X1,X5,X35] :
( ~ c_in(X31,X1,X5)
| c_in(X31,X35,X5)
| ~ c_lessequals(X1,X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11691,plain,
spl0_1442,
inference(avatar_split_clause,[],[f1696,f11689]) ).
fof(f1696,axiom,
! [X1,X35,X5] :
( X1 = X35
| ~ c_lessequals(X1,X35,tc_set(X5))
| c_less(X1,X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f11687,plain,
spl0_1441,
inference(avatar_split_clause,[],[f1692,f11685]) ).
fof(f11685,plain,
( spl0_1441
<=> ! [X5,X1,X83] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(X1,c_Main_OUnionE__1(X1,X83,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f1692,axiom,
! [X83,X1,X5] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(X1,c_Main_OUnionE__1(X1,X83,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f11683,plain,
spl0_1440,
inference(avatar_split_clause,[],[f1689,f11681]) ).
fof(f11681,plain,
( spl0_1440
<=> ! [X5,X1,X83] :
( c_in(X1,c_Inter(X83,X5),X5)
| ~ c_in(X1,c_Main_OInterI__1(X1,X83,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f1689,axiom,
! [X83,X1,X5] :
( c_in(X1,c_Inter(X83,X5),X5)
| ~ c_in(X1,c_Main_OInterI__1(X1,X83,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f11679,plain,
spl0_1439,
inference(avatar_split_clause,[],[f1621,f11677]) ).
fof(f11677,plain,
( spl0_1439
<=> ! [X2,X5,X1] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_insert(X2,X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f1621,axiom,
! [X2,X1,X5] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_insert(X2,X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f11675,plain,
spl0_1438,
inference(avatar_split_clause,[],[f1590,f11673]) ).
fof(f1590,axiom,
! [X2,X6,X5] :
( ~ c_Wellfounded__Recursion_Owf(X6,X5)
| ~ c_in(c_Pair(X2,X2,X5,X5),X6,tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f11664,plain,
spl0_1437,
inference(avatar_split_clause,[],[f1554,f11662]) ).
fof(f11662,plain,
( spl0_1437
<=> ! [X4,X5,X1,X35] :
( c_lessequals(X1,X35,tc_set(X5))
| ~ c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f1554,axiom,
! [X1,X4,X35,X5] :
( c_lessequals(X1,X35,tc_set(X5))
| ~ c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f11660,plain,
spl0_1436,
inference(avatar_split_clause,[],[f1534,f11658]) ).
fof(f11658,plain,
( spl0_1436
<=> ! [X34,X5,X1] :
( c_emptyset = X34
| c_emptyset != c_Union(X1,X5)
| ~ c_in(X34,X1,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f1534,axiom,
! [X1,X34,X5] :
( c_emptyset = X34
| c_emptyset != c_Union(X1,X5)
| ~ c_in(X34,X1,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
fof(f11656,plain,
spl0_1435,
inference(avatar_split_clause,[],[f1521,f11654]) ).
fof(f11654,plain,
( spl0_1435
<=> ! [X5,X1,X83] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(X1,c_Main_OUnion__iff__1(X1,X83,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f1521,axiom,
! [X83,X1,X5] :
( ~ c_in(X1,c_Union(X83,X5),X5)
| c_in(X1,c_Main_OUnion__iff__1(X1,X83,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f11652,plain,
spl0_1434,
inference(avatar_split_clause,[],[f1511,f11650]) ).
fof(f11650,plain,
( spl0_1434
<=> ! [X5,X1,X83,X35] :
( c_lessequals(X35,X83,tc_set(X5))
| ~ c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f1511,axiom,
! [X83,X1,X35,X5] :
( c_lessequals(X35,X83,tc_set(X5))
| ~ c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f11648,plain,
spl0_1433,
inference(avatar_split_clause,[],[f1510,f11646]) ).
fof(f1510,axiom,
! [X83,X1,X5,X35] :
( c_lessequals(X1,X83,tc_set(X5))
| ~ c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f11644,plain,
spl0_1432,
inference(avatar_split_clause,[],[f1496,f11642]) ).
fof(f1496,axiom,
! [X1,X35,X5] : c_union(X1,X35,X5) = c_union(X1,c_minus(X35,X1,tc_set(X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f11640,plain,
spl0_1431,
inference(avatar_split_clause,[],[f1495,f11638]) ).
fof(f1495,axiom,
! [X1,X35,X5] : c_union(c_minus(X35,X1,tc_set(X5)),X1,X5) = c_union(X35,X1,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f11636,plain,
spl0_1430,
inference(avatar_split_clause,[],[f1487,f11634]) ).
fof(f11634,plain,
( spl0_1430
<=> ! [X5,X1,X83] :
( c_in(X1,c_Inter(X83,X5),X5)
| ~ c_in(X1,c_Main_OInter__iff__1(X1,X83,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f1487,axiom,
! [X83,X1,X5] :
( c_in(X1,c_Inter(X83,X5),X5)
| ~ c_in(X1,c_Main_OInter__iff__1(X1,X83,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f11632,plain,
spl0_1429,
inference(avatar_split_clause,[],[f1478,f11630]) ).
fof(f11630,plain,
( spl0_1429
<=> ! [X34,X5,X1] :
( c_UNIV = X34
| c_UNIV != c_Inter(X1,X5)
| ~ c_in(X34,X1,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f1478,axiom,
! [X1,X34,X5] :
( c_UNIV = X34
| c_UNIV != c_Inter(X1,X5)
| ~ c_in(X34,X1,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
fof(f11628,plain,
spl0_1428,
inference(avatar_split_clause,[],[f1420,f11626]) ).
fof(f11626,plain,
( spl0_1428
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_less(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanLessThan(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1420,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanLessThan(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f11624,plain,
( spl0_1427
| ~ spl0_1047
| ~ spl0_1340 ),
inference(avatar_split_clause,[],[f11196,f10433,f8492,f11622]) ).
fof(f11622,plain,
( spl0_1427
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f8492,plain,
( spl0_1047
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f11196,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1047
| ~ spl0_1340 ),
inference(resolution,[],[f10434,f8493]) ).
fof(f8493,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1047 ),
inference(avatar_component_clause,[],[f8492]) ).
fof(f11620,plain,
spl0_1426,
inference(avatar_split_clause,[],[f1419,f11618]) ).
fof(f11618,plain,
( spl0_1426
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_less(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanLessThan(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f1419,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanLessThan(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f11616,plain,
spl0_1425,
inference(avatar_split_clause,[],[f1417,f11614]) ).
fof(f11614,plain,
( spl0_1425
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanAtMost(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f1417,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanAtMost(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f11612,plain,
spl0_1424,
inference(avatar_split_clause,[],[f1416,f11610]) ).
fof(f11610,plain,
( spl0_1424
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_less(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanAtMost(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f1416,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThanAtMost(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f11608,plain,
spl0_1423,
inference(avatar_split_clause,[],[f1390,f11606]) ).
fof(f11606,plain,
( spl0_1423
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_less(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OatLeastLessThan(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f1390,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OatLeastLessThan(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f11604,plain,
spl0_1422,
inference(avatar_split_clause,[],[f1389,f11602]) ).
fof(f11602,plain,
( spl0_1422
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OatLeastLessThan(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f1389,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OatLeastLessThan(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f11600,plain,
spl0_1421,
inference(avatar_split_clause,[],[f1385,f11598]) ).
fof(f11598,plain,
( spl0_1421
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OatLeastAtMost(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1385,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X29,X41,X5)
| ~ c_in(X29,c_SetInterval_OatLeastAtMost(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f11596,plain,
spl0_1420,
inference(avatar_split_clause,[],[f1384,f11594]) ).
fof(f11594,plain,
( spl0_1420
<=> ! [X5,X41,X77,X29] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OatLeastAtMost(X77,X41,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f1384,axiom,
! [X41,X29,X77,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X77,X29,X5)
| ~ c_in(X29,c_SetInterval_OatLeastAtMost(X77,X41,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f11592,plain,
spl0_1419,
inference(avatar_split_clause,[],[f1252,f11590]) ).
fof(f11590,plain,
( spl0_1419
<=> ! [X2,X5,X7] :
( X2 = X7
| ~ c_in(c_Pair(X2,X7,X5,X5),c_Relation_OId,tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f1252,axiom,
! [X2,X7,X5] :
( X2 = X7
| ~ c_in(c_Pair(X2,X7,X5,X5),c_Relation_OId,tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f11588,plain,
spl0_1418,
inference(avatar_split_clause,[],[f1232,f11586]) ).
fof(f11586,plain,
( spl0_1418
<=> ! [X9,X5,X23] : c_Pair(c_Main_Osurj__pair__1(X9,X5,X23),c_Main_Osurj__pair__2(X9,X5,X23),X5,X23) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f1232,axiom,
! [X9,X5,X23] : c_Pair(c_Main_Osurj__pair__1(X9,X5,X23),c_Main_Osurj__pair__2(X9,X5,X23),X5,X23) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f11584,plain,
spl0_1417,
inference(avatar_split_clause,[],[f1230,f11582]) ).
fof(f11582,plain,
( spl0_1417
<=> ! [X5,X8,X23] : c_Pair(c_fst(X8,X5,X23),c_snd(X8,X5,X23),X5,X23) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f1230,axiom,
! [X8,X5,X23] : c_Pair(c_fst(X8,X5,X23),c_snd(X8,X5,X23),X5,X23) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f11580,plain,
spl0_1416,
inference(avatar_split_clause,[],[f1226,f11578]) ).
fof(f11578,plain,
( spl0_1416
<=> ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,X5),c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f1226,axiom,
! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X2,X5),c_0,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f11576,plain,
spl0_1415,
inference(avatar_split_clause,[],[f1223,f11574]) ).
fof(f11574,plain,
( spl0_1415
<=> ! [X2,X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X2,X5),X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f1223,axiom,
! [X2,X19,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X2,X5),X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f11572,plain,
spl0_1414,
inference(avatar_split_clause,[],[f1212,f11570]) ).
fof(f11570,plain,
( spl0_1414
<=> ! [X2,X5,X19] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X2
| c_0 != c_Nat_Opower(X2,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f1212,axiom,
! [X2,X19,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X2
| c_0 != c_Nat_Opower(X2,X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f11568,plain,
spl0_1413,
inference(avatar_split_clause,[],[f1204,f11566]) ).
fof(f11566,plain,
( spl0_1413
<=> ! [X4,X39] :
( ~ c_less(c_0,X4,tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f1204,axiom,
! [X39,X4] :
( ~ c_less(c_0,X4,tc_nat)
| c_less(c_0,c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f11564,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1160,f11562]) ).
fof(f11562,plain,
( spl0_1412
<=> ! [X4,X19] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_less(c_0,X19,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X4,X19,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1160,axiom,
! [X19,X4] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_less(c_0,X19,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X4,X19,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f11560,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1147,f11558]) ).
fof(f11558,plain,
( spl0_1411
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X4,tc_nat)
| ~ c_less(c_0,X8,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f1147,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X4,tc_nat)
| ~ c_less(c_0,X8,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f11556,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1130,f11554]) ).
fof(f11554,plain,
( spl0_1410
<=> ! [X9,X4,X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X8,X9,X23)
| ~ c_lessequals(c_Orderings_Omax(X4,X8,X23),X9,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f1130,axiom,
! [X8,X9,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X8,X9,X23)
| ~ c_lessequals(c_Orderings_Omax(X4,X8,X23),X9,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f11552,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1129,f11550]) ).
fof(f11550,plain,
( spl0_1409
<=> ! [X4,X23,X9,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X4,X9,X23)
| ~ c_lessequals(c_Orderings_Omax(X4,X8,X23),X9,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1129,axiom,
! [X8,X9,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X4,X9,X23)
| ~ c_lessequals(c_Orderings_Omax(X4,X8,X23),X9,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f11548,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1125,f11546]) ).
fof(f11546,plain,
( spl0_1408
<=> ! [X4,X23,X9,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X4,X9,X23)
| ~ c_lessequals(X4,c_Orderings_Omin(X8,X9,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f1125,axiom,
! [X8,X9,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X4,X9,X23)
| ~ c_lessequals(X4,c_Orderings_Omin(X8,X9,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f11544,plain,
spl0_1407,
inference(avatar_split_clause,[],[f1124,f11542]) ).
fof(f11542,plain,
( spl0_1407
<=> ! [X4,X23,X9,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X4,X8,X23)
| ~ c_lessequals(X4,c_Orderings_Omin(X8,X9,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f1124,axiom,
! [X8,X9,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_lessequals(X4,X8,X23)
| ~ c_lessequals(X4,c_Orderings_Omin(X8,X9,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f11540,plain,
( spl0_1406
| ~ spl0_1354
| ~ spl0_99
| ~ spl0_1313 ),
inference(avatar_split_clause,[],[f11021,f10325,f3665,f10979,f11537]) ).
fof(f10325,plain,
( spl0_1313
<=> ! [X77,X18,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X77,X18,X5)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X18,X77,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f11021,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_99
| ~ spl0_1313 ),
inference(resolution,[],[f10326,f3667]) ).
fof(f10326,plain,
( ! [X18,X77,X5] :
( ~ c_lessequals(X77,X18,X5)
| ~ class_Orderings_Oorder(X5)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X18,X77,X5) )
| ~ spl0_1313 ),
inference(avatar_component_clause,[],[f10325]) ).
fof(f11535,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1122,f11533]) ).
fof(f11533,plain,
( spl0_1405
<=> ! [X5,X4,X9,X8] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X9,X8,X5)
| ~ c_less(X9,c_Orderings_Omin(X4,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1122,axiom,
! [X8,X9,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X9,X8,X5)
| ~ c_less(X9,c_Orderings_Omin(X4,X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f11531,plain,
spl0_1404,
inference(avatar_split_clause,[],[f1121,f11529]) ).
fof(f11529,plain,
( spl0_1404
<=> ! [X4,X9,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X9,X4,X5)
| ~ c_less(X9,c_Orderings_Omin(X4,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f1121,axiom,
! [X8,X9,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X9,X4,X5)
| ~ c_less(X9,c_Orderings_Omin(X4,X8,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f11527,plain,
spl0_1403,
inference(avatar_split_clause,[],[f1119,f11525]) ).
fof(f11525,plain,
( spl0_1403
<=> ! [X9,X5,X8,X4] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_Orderings_Omax(X4,X8,X5),X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f1119,axiom,
! [X8,X9,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_Orderings_Omax(X4,X8,X5),X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f11523,plain,
spl0_1402,
inference(avatar_split_clause,[],[f1118,f11521]) ).
fof(f11521,plain,
( spl0_1402
<=> ! [X5,X4,X9,X8] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X4,X9,X5)
| ~ c_less(c_Orderings_Omax(X4,X8,X5),X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f1118,axiom,
! [X8,X9,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X4,X9,X5)
| ~ c_less(c_Orderings_Omax(X4,X8,X5),X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f11519,plain,
spl0_1401,
inference(avatar_split_clause,[],[f1114,f11517]) ).
fof(f11517,plain,
( spl0_1401
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X2,X5)
| c_lessequals(c_0,c_plus(X2,X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f1114,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X2,X5)
| c_lessequals(c_0,c_plus(X2,X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f11515,plain,
spl0_1400,
inference(avatar_split_clause,[],[f1113,f11513]) ).
fof(f11513,plain,
( spl0_1400
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,X2,X5)
| ~ c_lessequals(c_0,c_plus(X2,X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f1113,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,X2,X5)
| ~ c_lessequals(c_0,c_plus(X2,X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f11511,plain,
spl0_1399,
inference(avatar_split_clause,[],[f1080,f11509]) ).
fof(f11509,plain,
( spl0_1399
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_minus(X2,X7,X5),X5) = c_minus(X7,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f1080,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_minus(X2,X7,X5),X5) = c_minus(X7,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f11507,plain,
spl0_1398,
inference(avatar_split_clause,[],[f1077,f11505]) ).
fof(f11505,plain,
( spl0_1398
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X2
| c_0 != c_LOrder_Omeet(X2,c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f1077,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X2
| c_0 != c_LOrder_Omeet(X2,c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f11503,plain,
spl0_1397,
inference(avatar_split_clause,[],[f1075,f11501]) ).
fof(f11501,plain,
( spl0_1397
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X2
| c_0 != c_LOrder_Ojoin(X2,c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f1075,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X2
| c_0 != c_LOrder_Ojoin(X2,c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f11499,plain,
spl0_1396,
inference(avatar_split_clause,[],[f1072,f11497]) ).
fof(f11497,plain,
( spl0_1396
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X2,c_0,X5)
| c_lessequals(c_plus(X2,X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f1072,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X2,c_0,X5)
| c_lessequals(c_plus(X2,X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f11495,plain,
spl0_1395,
inference(avatar_split_clause,[],[f1071,f11493]) ).
fof(f11493,plain,
( spl0_1395
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(X2,c_0,X5)
| ~ c_lessequals(c_plus(X2,X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f1071,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(X2,c_0,X5)
| ~ c_lessequals(c_plus(X2,X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f11491,plain,
spl0_1394,
inference(avatar_split_clause,[],[f1069,f11489]) ).
fof(f11489,plain,
( spl0_1394
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_plus(X2,X7,X5) = c_minus(X2,c_uminus(X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f1069,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_plus(X2,X7,X5) = c_minus(X2,c_uminus(X7,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f11487,plain,
spl0_1393,
inference(avatar_split_clause,[],[f1068,f11485]) ).
fof(f11485,plain,
( spl0_1393
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_minus(X2,X7,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f1068,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X2,X7,X5)
| c_less(c_minus(X2,X7,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f11483,plain,
spl0_1392,
inference(avatar_split_clause,[],[f1067,f11481]) ).
fof(f1067,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X2,X7,X5)
| ~ c_less(c_minus(X2,X7,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f11479,plain,
spl0_1391,
inference(avatar_split_clause,[],[f1066,f11477]) ).
fof(f11477,plain,
( spl0_1391
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_minus(X2,X7,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f1066,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(c_minus(X2,X7,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f11475,plain,
spl0_1390,
inference(avatar_split_clause,[],[f1065,f11473]) ).
fof(f11473,plain,
( spl0_1390
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_minus(X2,X7,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f1065,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(c_minus(X2,X7,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f11471,plain,
spl0_1389,
inference(avatar_split_clause,[],[f1049,f11469]) ).
fof(f11469,plain,
( spl0_1389
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(X2,c_0,X5)
| c_uminus(X2,X5) = c_HOL_Oabs(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f1049,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(X2,c_0,X5)
| c_uminus(X2,X5) = c_HOL_Oabs(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f11467,plain,
spl0_1388,
inference(avatar_split_clause,[],[f975,f11465]) ).
fof(f11465,plain,
( spl0_1388
<=> ! [X40,X39] : c_Numeral_Obin__add(c_Numeral_OBit(X40,c_Numeral_Obit_OB1),c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X40,X39),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f975,axiom,
! [X40,X39] : c_Numeral_Obin__add(c_Numeral_OBit(X40,c_Numeral_Obit_OB1),c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X40,X39),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f11463,plain,
spl0_1387,
inference(avatar_split_clause,[],[f974,f11461]) ).
fof(f11461,plain,
( spl0_1387
<=> ! [X39,X40,X8] : c_Numeral_Obin__add(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),c_Numeral_OBit(X39,X8)) = c_Numeral_OBit(c_Numeral_Obin__add(X40,X39),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f974,axiom,
! [X40,X39,X8] : c_Numeral_Obin__add(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),c_Numeral_OBit(X39,X8)) = c_Numeral_OBit(c_Numeral_Obin__add(X40,X39),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f11459,plain,
spl0_1386,
inference(avatar_split_clause,[],[f910,f11457]) ).
fof(f11457,plain,
( spl0_1386
<=> ! [X8,X19] :
( ~ c_lessequals(X19,X8,tc_nat)
| c_plus(X19,c_minus(X8,X19,tc_nat),tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f910,axiom,
! [X8,X19] :
( ~ c_lessequals(X19,X8,tc_nat)
| c_plus(X19,c_minus(X8,X19,tc_nat),tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f11455,plain,
spl0_1385,
inference(avatar_split_clause,[],[f909,f11453]) ).
fof(f11453,plain,
( spl0_1385
<=> ! [X8,X19] :
( ~ c_lessequals(X19,X8,tc_nat)
| c_plus(c_minus(X8,X19,tc_nat),X19,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f909,axiom,
! [X8,X19] :
( ~ c_lessequals(X19,X8,tc_nat)
| c_plus(c_minus(X8,X19,tc_nat),X19,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f11451,plain,
spl0_1384,
inference(avatar_split_clause,[],[f717,f11449]) ).
fof(f11449,plain,
( spl0_1384
<=> ! [X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X40,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f717,axiom,
! [X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X40,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X40,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f11447,plain,
spl0_1383,
inference(avatar_split_clause,[],[f664,f11445]) ).
fof(f11445,plain,
( spl0_1383
<=> ! [X8,X19] :
( ~ c_lessequals(X8,X19,tc_nat)
| c_minus(X19,c_minus(X19,X8,tc_nat),tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f664,axiom,
! [X8,X19] :
( ~ c_lessequals(X8,X19,tc_nat)
| c_minus(X19,c_minus(X19,X8,tc_nat),tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f11443,plain,
spl0_1382,
inference(avatar_split_clause,[],[f630,f11441]) ).
fof(f11441,plain,
( spl0_1382
<=> ! [X4,X5,X1] :
( c_in(c_0,X1,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f630,axiom,
! [X1,X4,X5] :
( c_in(c_0,X1,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f11439,plain,
spl0_1381,
inference(avatar_split_clause,[],[f613,f11437]) ).
fof(f11437,plain,
( spl0_1381
<=> ! [X4,X21,X44] : c_List_Oset(c_List_Olist_OCons(X4,X44,X21),X21) = c_insert(X4,c_List_Oset(X44,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f613,axiom,
! [X21,X44,X4] : c_List_Oset(c_List_Olist_OCons(X4,X44,X21),X21) = c_insert(X4,c_List_Oset(X44,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f11435,plain,
spl0_1380,
inference(avatar_split_clause,[],[f607,f11433]) ).
fof(f11433,plain,
( spl0_1380
<=> ! [X5,X8,X19] :
( c_List_Orotate(X19,X8,X5) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f607,axiom,
! [X8,X19,X5] :
( c_List_Orotate(X19,X8,X5) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f11431,plain,
spl0_1379,
inference(avatar_split_clause,[],[f567,f11429]) ).
fof(f11429,plain,
( spl0_1379
<=> ! [X5,X19,X29,X8] :
( ~ c_less(X29,X19,tc_nat)
| c_List_Onth(c_List_Oreplicate(X19,X8,X5),X29,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f567,axiom,
! [X29,X8,X19,X5] :
( ~ c_less(X29,X19,tc_nat)
| c_List_Onth(c_List_Oreplicate(X19,X8,X5),X29,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f11427,plain,
spl0_1378,
inference(avatar_split_clause,[],[f469,f11425]) ).
fof(f11425,plain,
( spl0_1378
<=> ! [X5,X44,X4,X29] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Olist__update(X44,X29,X4,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f469,axiom,
! [X29,X44,X4,X5] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Olist__update(X44,X29,X4,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f11423,plain,
spl0_1377,
inference(avatar_split_clause,[],[f456,f11421]) ).
fof(f11421,plain,
( spl0_1377
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X45
| c_List_Olast(c_append(X44,X45,X5),X5) = c_List_Olast(X45,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f456,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X45
| c_List_Olast(c_append(X44,X45,X5),X5) = c_List_Olast(X45,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f11419,plain,
spl0_1376,
inference(avatar_split_clause,[],[f454,f11417]) ).
fof(f11417,plain,
( spl0_1376
<=> ! [X4,X5,X44] :
( c_List_Olist_ONil = X44
| c_List_Olast(c_List_Olist_OCons(X4,X44,X5),X5) = c_List_Olast(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f454,axiom,
! [X44,X4,X5] :
( c_List_Olist_ONil = X44
| c_List_Olast(c_List_Olist_OCons(X4,X44,X5),X5) = c_List_Olast(X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f11415,plain,
spl0_1375,
inference(avatar_split_clause,[],[f446,f11413]) ).
fof(f11413,plain,
( spl0_1375
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X44
| c_List_Ohd(c_append(X44,X45,X5),X5) = c_List_Ohd(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f446,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X44
| c_List_Ohd(c_append(X44,X45,X5),X5) = c_List_Ohd(X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f11411,plain,
spl0_1374,
inference(avatar_split_clause,[],[f445,f11409]) ).
fof(f11409,plain,
( spl0_1374
<=> ! [X5,X8] :
( c_List_Olist_ONil = X8
| c_List_Olist_OCons(c_List_Ohd(X8,X5),c_List_Otl(X8,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f445,axiom,
! [X8,X5] :
( c_List_Olist_ONil = X8
| c_List_Olist_OCons(c_List_Ohd(X8,X5),c_List_Otl(X8,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f11407,plain,
spl0_1373,
inference(avatar_split_clause,[],[f443,f11405]) ).
fof(f11405,plain,
( spl0_1373
<=> ! [X29,X55,X30] : c_List_Odrop(X30,c_List_Oupt(X29,X55),tc_nat) = c_List_Oupt(c_plus(X29,X30,tc_nat),X55) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f443,axiom,
! [X29,X55,X30] : c_List_Odrop(X30,c_List_Oupt(X29,X55),tc_nat) = c_List_Oupt(c_plus(X29,X30,tc_nat),X55),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f11403,plain,
spl0_1372,
inference(avatar_split_clause,[],[f441,f11401]) ).
fof(f11401,plain,
( spl0_1372
<=> ! [X5,X44,X19] :
( c_List_Olist_ONil = c_List_Odrop(X19,X44,X5)
| ~ c_lessequals(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f441,axiom,
! [X19,X44,X5] :
( c_List_Olist_ONil = c_List_Odrop(X19,X44,X5)
| ~ c_lessequals(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f11399,plain,
spl0_1371,
inference(avatar_split_clause,[],[f440,f11397]) ).
fof(f11397,plain,
( spl0_1371
<=> ! [X5,X44,X19] :
( c_List_Olist_ONil != c_List_Odrop(X19,X44,X5)
| c_lessequals(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f440,axiom,
! [X19,X44,X5] :
( c_List_Olist_ONil != c_List_Odrop(X19,X44,X5)
| c_lessequals(c_Nat_Osize(X44,tc_List_Olist(X5)),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f11395,plain,
spl0_1370,
inference(avatar_split_clause,[],[f340,f11393]) ).
fof(f11393,plain,
( spl0_1370
<=> ! [X2,X7] : c_div(c_uminus(X2,tc_IntDef_Oint),c_uminus(X7,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X2,X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f340,axiom,
! [X2,X7] : c_div(c_uminus(X2,tc_IntDef_Oint),c_uminus(X7,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X2,X7,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f11391,plain,
spl0_1369,
inference(avatar_split_clause,[],[f281,f11389]) ).
fof(f11389,plain,
( spl0_1369
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_uminus(X9,tc_IntDef_Oint),X5) = c_uminus(c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f281,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_uminus(X9,tc_IntDef_Oint),X5) = c_uminus(c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f11387,plain,
spl0_1368,
inference(avatar_split_clause,[],[f170,f11385]) ).
fof(f11385,plain,
( spl0_1368
<=> ! [X30,X18,X19] :
( c_Divides_Oop_Advd(X18,X19,tc_nat)
| ~ c_Divides_Oop_Advd(X18,c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f170,axiom,
! [X18,X19,X30] :
( c_Divides_Oop_Advd(X18,X19,tc_nat)
| ~ c_Divides_Oop_Advd(X18,c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f11383,plain,
spl0_1367,
inference(avatar_split_clause,[],[f169,f11381]) ).
fof(f11381,plain,
( spl0_1367
<=> ! [X18,X19,X30] :
( c_Divides_Oop_Advd(X18,X30,tc_nat)
| ~ c_Divides_Oop_Advd(X18,c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f169,axiom,
! [X18,X19,X30] :
( c_Divides_Oop_Advd(X18,X30,tc_nat)
| ~ c_Divides_Oop_Advd(X18,c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f11379,plain,
spl0_1366,
inference(avatar_split_clause,[],[f156,f11377]) ).
fof(f11377,plain,
( spl0_1366
<=> ! [X2,X5,X1] :
( c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_insert(X2,X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f156,axiom,
! [X2,X1,X5] :
( c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_insert(X2,X1,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f11375,plain,
( ~ spl0_1363
| spl0_1364
| ~ spl0_1365
| ~ spl0_1189
| ~ spl0_1355 ),
inference(avatar_split_clause,[],[f11325,f11157,f9454,f11372,f11368,f11364]) ).
fof(f11364,plain,
( spl0_1363
<=> class_OrderedGroup_Oab__group__add(tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f11372,plain,
( spl0_1365
<=> c_emptyset = c_0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f9454,plain,
( spl0_1189
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X2 = X7
| c_0 != c_minus(X2,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f11325,plain,
( c_emptyset != c_0
| v_S = c_Tarski_Ointerval(v_r,v_a,v_b,t_a)
| ~ class_OrderedGroup_Oab__group__add(tc_set(t_a))
| ~ spl0_1189
| ~ spl0_1355 ),
inference(superposition,[],[f9455,f11159]) ).
fof(f9455,plain,
( ! [X2,X7,X5] :
( c_0 != c_minus(X2,X7,X5)
| X2 = X7
| ~ class_OrderedGroup_Oab__group__add(X5) )
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f9454]) ).
fof(f11362,plain,
spl0_1362,
inference(avatar_split_clause,[],[f152,f11360]) ).
fof(f11360,plain,
( spl0_1362
<=> ! [X38,X5,X37] :
( c_in(X38,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f152,axiom,
! [X38,X37,X5] :
( c_in(X38,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f11358,plain,
spl0_1361,
inference(avatar_split_clause,[],[f151,f11356]) ).
fof(f151,axiom,
! [X38,X37,X5] :
( c_in(X37,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X37,X38,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f11354,plain,
spl0_1360,
inference(avatar_split_clause,[],[f150,f11352]) ).
fof(f11352,plain,
( spl0_1360
<=> ! [X5,X1] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Pow(X1,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f150,axiom,
! [X1,X5] :
( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Pow(X1,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f11350,plain,
spl0_1359,
inference(avatar_split_clause,[],[f149,f11348]) ).
fof(f11348,plain,
( spl0_1359
<=> ! [X5,X1] :
( c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_Pow(X1,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f149,axiom,
! [X1,X5] :
( c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_Pow(X1,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f11346,plain,
spl0_1358,
inference(avatar_split_clause,[],[f141,f11344]) ).
fof(f141,axiom,
! [X1,X5] :
( c_emptyset = X1
| c_0 != c_Finite__Set_Ocard(X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f11342,plain,
spl0_1357,
inference(avatar_split_clause,[],[f88,f11340]) ).
fof(f11340,plain,
( spl0_1357
<=> ! [X8,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_times(X8,X19,tc_nat),X19,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f88,axiom,
! [X8,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_times(X8,X19,tc_nat),X19,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f11338,plain,
spl0_1356,
inference(avatar_split_clause,[],[f86,f11336]) ).
fof(f11336,plain,
( spl0_1356
<=> ! [X8,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_times(X19,X8,tc_nat),X19,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f86,axiom,
! [X8,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_times(X19,X8,tc_nat),X19,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f11160,plain,
( spl0_1355
| ~ spl0_99
| ~ spl0_1322 ),
inference(avatar_split_clause,[],[f11066,f10361,f3665,f11157]) ).
fof(f10361,plain,
( spl0_1322
<=> ! [X5,X1,X35] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_emptyset = c_minus(X1,X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f11066,plain,
( c_emptyset = c_minus(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ spl0_99
| ~ spl0_1322 ),
inference(resolution,[],[f10362,f3667]) ).
fof(f10362,plain,
( ! [X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_emptyset = c_minus(X1,X35,tc_set(X5)) )
| ~ spl0_1322 ),
inference(avatar_component_clause,[],[f10361]) ).
fof(f11028,plain,
( ~ spl0_113
| spl0_1354 ),
inference(avatar_contradiction_clause,[],[f11027]) ).
fof(f11027,plain,
( $false
| ~ spl0_113
| spl0_1354 ),
inference(resolution,[],[f10981,f3732]) ).
fof(f3732,plain,
( ! [X92] : class_Orderings_Oorder(tc_set(X92))
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f3731]) ).
fof(f3731,plain,
( spl0_113
<=> ! [X92] : class_Orderings_Oorder(tc_set(X92)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f10981,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| spl0_1354 ),
inference(avatar_component_clause,[],[f10979]) ).
fof(f10982,plain,
( spl0_1353
| ~ spl0_1354
| ~ spl0_99
| ~ spl0_1303 ),
inference(avatar_split_clause,[],[f10967,f10284,f3665,f10979,f10975]) ).
fof(f10284,plain,
( spl0_1303
<=> ! [X5,X19,X30] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X19,X30,X5)
| c_emptyset = c_SetInterval_OatLeastLessThan(X30,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f10967,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| c_emptyset = c_SetInterval_OatLeastLessThan(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_99
| ~ spl0_1303 ),
inference(resolution,[],[f10285,f3667]) ).
fof(f10285,plain,
( ! [X19,X5,X30] :
( ~ c_lessequals(X19,X30,X5)
| ~ class_Orderings_Oorder(X5)
| c_emptyset = c_SetInterval_OatLeastLessThan(X30,X19,X5) )
| ~ spl0_1303 ),
inference(avatar_component_clause,[],[f10284]) ).
fof(f10879,plain,
( spl0_1352
| ~ spl0_712
| ~ spl0_1111 ),
inference(avatar_split_clause,[],[f9215,f8941,f6924,f10877]) ).
fof(f10877,plain,
( spl0_1352
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f6924,plain,
( spl0_712
<=> ! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f8941,plain,
( spl0_1111
<=> ! [X5,X1] : c_Relation_Odiag(X1,X5) = c_Relation_Oconverse(c_Relation_Odiag(X1,X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f9215,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_712
| ~ spl0_1111 ),
inference(superposition,[],[f8942,f6925]) ).
fof(f6925,plain,
( ! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5)
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f6924]) ).
fof(f8942,plain,
( ! [X1,X5] : c_Relation_Odiag(X1,X5) = c_Relation_Oconverse(c_Relation_Odiag(X1,X5),X5,X5)
| ~ spl0_1111 ),
inference(avatar_component_clause,[],[f8941]) ).
fof(f10683,plain,
( spl0_1351
| ~ spl0_119
| ~ spl0_1082 ),
inference(avatar_split_clause,[],[f9132,f8824,f3758,f10681]) ).
fof(f10681,plain,
( spl0_1351
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f3758,plain,
( spl0_119
<=> ! [X30] : c_Divides_Oop_Advd(X30,X30,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f8824,plain,
( spl0_1082
<=> ! [X9,X39] :
( c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X9,tc_IntDef_Oint),X39,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f9132,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_119
| ~ spl0_1082 ),
inference(resolution,[],[f8825,f3759]) ).
fof(f3759,plain,
( ! [X30] : c_Divides_Oop_Advd(X30,X30,tc_IntDef_Oint)
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f3758]) ).
fof(f8825,plain,
( ! [X39,X9] :
( ~ c_Divides_Oop_Advd(c_uminus(X9,tc_IntDef_Oint),X39,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint) )
| ~ spl0_1082 ),
inference(avatar_component_clause,[],[f8824]) ).
fof(f10622,plain,
( spl0_1350
| ~ spl0_119
| ~ spl0_1078 ),
inference(avatar_split_clause,[],[f9122,f8807,f3758,f10620]) ).
fof(f10620,plain,
( spl0_1350
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f8807,plain,
( spl0_1078
<=> ! [X9,X39] :
( c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X9,c_uminus(X39,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f9122,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_119
| ~ spl0_1078 ),
inference(resolution,[],[f8808,f3759]) ).
fof(f8808,plain,
( ! [X39,X9] :
( ~ c_Divides_Oop_Advd(X9,c_uminus(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint) )
| ~ spl0_1078 ),
inference(avatar_component_clause,[],[f8807]) ).
fof(f10474,plain,
spl0_1349,
inference(avatar_split_clause,[],[f3126,f10472]) ).
fof(f10472,plain,
( spl0_1349
<=> ! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X4,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f3126,plain,
! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X4,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X4,X5) ),
inference(forward_demodulation,[],[f3125,f980]) ).
fof(f3125,plain,
! [X4,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X4,X5) ),
inference(forward_demodulation,[],[f2932,f2762]) ).
fof(f2932,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X4,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f203,f994]) ).
fof(f203,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X4,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f10470,plain,
spl0_1348,
inference(avatar_split_clause,[],[f3056,f10468]) ).
fof(f10468,plain,
( spl0_1348
<=> ! [X5] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X5)
| ~ class_Power_Orecpower(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f3056,plain,
! [X5] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X5)
| ~ class_Power_Orecpower(X5) ),
inference(forward_demodulation,[],[f3055,f1021]) ).
fof(f3055,plain,
! [X5] :
( 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),X5)
| ~ class_Power_Orecpower(X5) ),
inference(forward_demodulation,[],[f3054,f1019]) ).
fof(f3054,plain,
! [X5] :
( 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),X5)
| ~ class_Power_Orecpower(X5) ),
inference(forward_demodulation,[],[f743,f1021]) ).
fof(f743,axiom,
! [X5] :
( ~ class_Power_Orecpower(X5)
| 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),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f10466,plain,
spl0_1347,
inference(avatar_split_clause,[],[f3049,f10464]) ).
fof(f3049,plain,
! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f3048,f1021]) ).
fof(f3048,plain,
! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f3047,f1019]) ).
fof(f3047,plain,
! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f193,f1021]) ).
fof(f193,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f10462,plain,
spl0_1346,
inference(avatar_split_clause,[],[f2873,f10460]) ).
fof(f10460,plain,
( spl0_1346
<=> ! [X5,X1,X35] :
( c_UNIV = X35
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f2873,plain,
! [X1,X35,X5] :
( c_UNIV = X35
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5) ),
inference(definition_unfolding,[],[f1464,f1238]) ).
fof(f1464,axiom,
! [X1,X35,X5] :
( c_UNIV = X35
| c_UNIV != c_inter(X1,X35,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f10458,plain,
spl0_1345,
inference(avatar_split_clause,[],[f2872,f10456]) ).
fof(f10456,plain,
( spl0_1345
<=> ! [X5,X1,X35] :
( c_UNIV = X1
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f2872,plain,
! [X1,X5,X35] :
( c_UNIV = X1
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5) ),
inference(definition_unfolding,[],[f1463,f1238]) ).
fof(f1463,axiom,
! [X1,X35,X5] :
( c_UNIV = X1
| c_UNIV != c_inter(X1,X35,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f10451,plain,
spl0_1344,
inference(avatar_split_clause,[],[f2867,f10449]) ).
fof(f10449,plain,
( spl0_1344
<=> ! [X5,X19] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f2867,plain,
! [X19,X5] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),X5) ),
inference(definition_unfolding,[],[f1211,f1409]) ).
fof(f1211,axiom,
! [X19,X5] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Nat_Opower(c_0,c_Suc(X19),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f10447,plain,
spl0_1343,
inference(avatar_split_clause,[],[f2799,f10445]) ).
fof(f2799,plain,
! [X30] : c_plus(c_1,c_IntDef_Oint(X30),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f237,f1409]) ).
fof(f237,axiom,
! [X30] : c_IntDef_Oint(c_Suc(X30)) = c_plus(c_1,c_IntDef_Oint(X30),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f10443,plain,
spl0_1342,
inference(avatar_split_clause,[],[f2796,f10441]) ).
fof(f10441,plain,
( spl0_1342
<=> ! [X5,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X1,tc_set(X5)),X5),X1,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f2796,plain,
! [X1,X5] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X1,tc_set(X5)),X5),X1,X5,X5),
inference(definition_unfolding,[],[f1443,f1238]) ).
fof(f1443,axiom,
! [X1,X5] : c_emptyset = c_inter(c_uminus(X1,tc_set(X5)),X1,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f10439,plain,
spl0_1341,
inference(avatar_split_clause,[],[f2795,f10437]) ).
fof(f10437,plain,
( spl0_1341
<=> ! [X5,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),c_uminus(X1,tc_set(X5)),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f2795,plain,
! [X1,X5] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X1,X5),c_uminus(X1,tc_set(X5)),X5,X5),
inference(definition_unfolding,[],[f1444,f1238]) ).
fof(f1444,axiom,
! [X1,X5] : c_emptyset = c_inter(X1,c_uminus(X1,tc_set(X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f10435,plain,
spl0_1340,
inference(avatar_split_clause,[],[f1702,f10433]) ).
fof(f1702,axiom,
! [X1,X35,X5] :
( c_lessequals(X1,X35,tc_set(X5))
| ~ c_in(c_Main_OsubsetI__1(X1,X35,X5),X35,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10431,plain,
spl0_1339,
inference(avatar_split_clause,[],[f1701,f10429]) ).
fof(f10429,plain,
( spl0_1339
<=> ! [X5,X1,X35] :
( c_lessequals(X1,X35,tc_set(X5))
| c_in(c_Main_OsubsetI__1(X1,X35,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f1701,axiom,
! [X1,X35,X5] :
( c_lessequals(X1,X35,tc_set(X5))
| c_in(c_Main_OsubsetI__1(X1,X35,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10427,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1641,f10425]) ).
fof(f10425,plain,
( spl0_1338
<=> ! [X5,X44] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X44,X5),tc_List_Olist(X5)),c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f1641,axiom,
! [X44,X5] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X44,X5),tc_List_Olist(X5)),c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10423,plain,
spl0_1337,
inference(avatar_split_clause,[],[f1594,f10421]) ).
fof(f10421,plain,
( spl0_1337
<=> ! [X4,X23,X5,X8] :
( X4 = X8
| c_Datatype__Universe_ONumb(X4,X5,X23) != c_Datatype__Universe_ONumb(X8,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f1594,axiom,
! [X8,X4,X5,X23] :
( X4 = X8
| c_Datatype__Universe_ONumb(X4,X5,X23) != c_Datatype__Universe_ONumb(X8,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10419,plain,
spl0_1336,
inference(avatar_split_clause,[],[f1593,f10417]) ).
fof(f10417,plain,
( spl0_1336
<=> ! [X4,X23,X5,X8] :
( X4 = X8
| c_Datatype__Universe_OLeaf(X4,X5,X23) != c_Datatype__Universe_OLeaf(X8,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f1593,axiom,
! [X8,X4,X5,X23] :
( X4 = X8
| c_Datatype__Universe_OLeaf(X4,X5,X23) != c_Datatype__Universe_OLeaf(X8,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f10415,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1568,f10413]) ).
fof(f10413,plain,
( spl0_1335
<=> ! [X4,X23,X5,X8] :
( X4 = X8
| c_Sum__Type_OInr(X4,X23,X5) != c_Sum__Type_OInr(X8,X23,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f1568,axiom,
! [X8,X4,X5,X23] :
( X4 = X8
| c_Sum__Type_OInr(X4,X23,X5) != c_Sum__Type_OInr(X8,X23,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f10411,plain,
spl0_1334,
inference(avatar_split_clause,[],[f1566,f10409]) ).
fof(f10409,plain,
( spl0_1334
<=> ! [X4,X23,X5,X8] :
( X4 = X8
| c_Sum__Type_OInl(X4,X5,X23) != c_Sum__Type_OInl(X8,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f1566,axiom,
! [X8,X4,X5,X23] :
( X4 = X8
| c_Sum__Type_OInl(X4,X5,X23) != c_Sum__Type_OInl(X8,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f10407,plain,
spl0_1333,
inference(avatar_split_clause,[],[f1560,f10405]) ).
fof(f1560,axiom,
! [X2,X1,X7,X5] :
( X2 = X7
| c_insert(X2,X1,X5) != c_insert(X7,c_emptyset,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
fof(f10403,plain,
spl0_1332,
inference(avatar_split_clause,[],[f1553,f10401]) ).
fof(f1553,axiom,
! [X1,X4,X35,X5] :
( c_in(X4,X35,X5)
| ~ c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f10399,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1541,f10397]) ).
fof(f10397,plain,
( spl0_1331
<=> ! [X4,X5,X1] : c_insert(X4,X1,X5) = c_insert(X4,c_insert(X4,X1,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f1541,axiom,
! [X1,X4,X5] : c_insert(X4,X1,X5) = c_insert(X4,c_insert(X4,X1,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f10395,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1535,f10393]) ).
fof(f10393,plain,
( spl0_1330
<=> ! [X5,X1] :
( c_emptyset = c_Union(X1,X5)
| c_in(c_Main_Oempty__Union__conv__1(X1,X5),X1,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f1535,axiom,
! [X1,X5] :
( c_emptyset = c_Union(X1,X5)
| c_in(c_Main_Oempty__Union__conv__1(X1,X5),X1,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f10391,plain,
spl0_1329,
inference(avatar_split_clause,[],[f1518,f10389]) ).
fof(f10389,plain,
( spl0_1329
<=> ! [X5,X1] :
( c_emptyset = c_Union(X1,X5)
| c_in(c_Main_OUnion__empty__conv__1(X1,X5),X1,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f1518,axiom,
! [X1,X5] :
( c_emptyset = c_Union(X1,X5)
| c_in(c_Main_OUnion__empty__conv__1(X1,X5),X1,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f10387,plain,
spl0_1328,
inference(avatar_split_clause,[],[f1493,f10385]) ).
fof(f10385,plain,
( spl0_1328
<=> ! [X5,X1,X35] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_in(X1,c_Pow(X35,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f1493,axiom,
! [X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_in(X1,c_Pow(X35,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f10383,plain,
spl0_1327,
inference(avatar_split_clause,[],[f1492,f10381]) ).
fof(f10381,plain,
( spl0_1327
<=> ! [X5,X1,X35] :
( c_lessequals(X1,X35,tc_set(X5))
| ~ c_in(X1,c_Pow(X35,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f1492,axiom,
! [X1,X35,X5] :
( c_lessequals(X1,X35,tc_set(X5))
| ~ c_in(X1,c_Pow(X35,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f10379,plain,
spl0_1326,
inference(avatar_split_clause,[],[f1482,f10377]) ).
fof(f10377,plain,
( spl0_1326
<=> ! [X5,X1] :
( c_UNIV = c_Inter(X1,X5)
| c_in(c_Main_OInter__UNIV__conv__2__1(X1,X5),X1,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f1482,axiom,
! [X1,X5] :
( c_UNIV = c_Inter(X1,X5)
| c_in(c_Main_OInter__UNIV__conv__2__1(X1,X5),X1,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f10375,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1479,f10373]) ).
fof(f10373,plain,
( spl0_1325
<=> ! [X5,X1] :
( c_UNIV = c_Inter(X1,X5)
| c_in(c_Main_OInter__UNIV__conv__1__1(X1,X5),X1,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f1479,axiom,
! [X1,X5] :
( c_UNIV = c_Inter(X1,X5)
| c_in(c_Main_OInter__UNIV__conv__1__1(X1,X5),X1,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f10371,plain,
spl0_1324,
inference(avatar_split_clause,[],[f1460,f10369]) ).
fof(f10369,plain,
( spl0_1324
<=> ! [X35,X31,X5,X1] :
( ~ c_in(X31,X35,X5)
| ~ c_in(X31,c_minus(X1,X35,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f1460,axiom,
! [X31,X1,X35,X5] :
( ~ c_in(X31,X35,X5)
| ~ c_in(X31,c_minus(X1,X35,tc_set(X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f10367,plain,
spl0_1323,
inference(avatar_split_clause,[],[f1459,f10365]) ).
fof(f10365,plain,
( spl0_1323
<=> ! [X35,X31,X5,X1] :
( c_in(X31,X1,X5)
| ~ c_in(X31,c_minus(X1,X35,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f1459,axiom,
! [X31,X1,X5,X35] :
( c_in(X31,X1,X5)
| ~ c_in(X31,c_minus(X1,X35,tc_set(X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f10363,plain,
spl0_1322,
inference(avatar_split_clause,[],[f1457,f10361]) ).
fof(f1457,axiom,
! [X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_emptyset = c_minus(X1,X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f10359,plain,
spl0_1321,
inference(avatar_split_clause,[],[f1456,f10357]) ).
fof(f10357,plain,
( spl0_1321
<=> ! [X5,X1,X35] :
( c_lessequals(X1,X35,tc_set(X5))
| c_emptyset != c_minus(X1,X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f1456,axiom,
! [X1,X35,X5] :
( c_lessequals(X1,X35,tc_set(X5))
| c_emptyset != c_minus(X1,X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f10355,plain,
spl0_1320,
inference(avatar_split_clause,[],[f1446,f10353]) ).
fof(f10353,plain,
( spl0_1320
<=> ! [X5,X1,X35] :
( X1 = X35
| c_uminus(X1,tc_set(X5)) != c_uminus(X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f1446,axiom,
! [X1,X35,X5] :
( X1 = X35
| c_uminus(X1,tc_set(X5)) != c_uminus(X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f10351,plain,
spl0_1319,
inference(avatar_split_clause,[],[f1435,f10349]) ).
fof(f10349,plain,
( spl0_1319
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X29,X18,X5)
| c_in(X29,c_SetInterval_OlessThan(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f1435,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X29,X18,X5)
| c_in(X29,c_SetInterval_OlessThan(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f10347,plain,
spl0_1318,
inference(avatar_split_clause,[],[f1434,f10345]) ).
fof(f10345,plain,
( spl0_1318
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X29,X18,X5)
| ~ c_in(X29,c_SetInterval_OlessThan(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f1434,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X29,X18,X5)
| ~ c_in(X29,c_SetInterval_OlessThan(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f10343,plain,
spl0_1317,
inference(avatar_split_clause,[],[f1433,f10341]) ).
fof(f10341,plain,
( spl0_1317
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OlessThan(X4,X5) != c_SetInterval_OlessThan(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f1433,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OlessThan(X4,X5) != c_SetInterval_OlessThan(X8,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f10339,plain,
spl0_1316,
inference(avatar_split_clause,[],[f1424,f10337]) ).
fof(f10337,plain,
( spl0_1316
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X18,X29,X5)
| c_in(X29,c_SetInterval_OgreaterThan(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f1424,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X18,X29,X5)
| c_in(X29,c_SetInterval_OgreaterThan(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f10335,plain,
spl0_1315,
inference(avatar_split_clause,[],[f1423,f10333]) ).
fof(f10333,plain,
( spl0_1315
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X18,X29,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThan(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f1423,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X18,X29,X5)
| ~ c_in(X29,c_SetInterval_OgreaterThan(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f10331,plain,
spl0_1314,
inference(avatar_split_clause,[],[f1422,f10329]) ).
fof(f10329,plain,
( spl0_1314
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OgreaterThan(X4,X5) != c_SetInterval_OgreaterThan(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f1422,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OgreaterThan(X4,X5) != c_SetInterval_OgreaterThan(X8,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f10327,plain,
spl0_1313,
inference(avatar_split_clause,[],[f1415,f10325]) ).
fof(f1415,axiom,
! [X18,X77,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X77,X18,X5)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X18,X77,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f10323,plain,
spl0_1312,
inference(avatar_split_clause,[],[f1411,f10321]) ).
fof(f10321,plain,
( spl0_1312
<=> ! [X77,X41] : c_IntDef_Onat(c_minus(X41,X77,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1411,axiom,
! [X41,X77] : c_IntDef_Onat(c_minus(X41,X77,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f10319,plain,
spl0_1311,
inference(avatar_split_clause,[],[f1408,f10317]) ).
fof(f10317,plain,
( spl0_1311
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X41,X77,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f1408,axiom,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X77,X41,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X41,X77,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f10315,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1402,f10313]) ).
fof(f10313,plain,
( spl0_1310
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X29,X18,X5)
| c_in(X29,c_SetInterval_OatMost(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f1402,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X29,X18,X5)
| c_in(X29,c_SetInterval_OatMost(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f10311,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1401,f10309]) ).
fof(f10309,plain,
( spl0_1309
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X29,X18,X5)
| ~ c_in(X29,c_SetInterval_OatMost(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1401,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X29,X18,X5)
| ~ c_in(X29,c_SetInterval_OatMost(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f10307,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1400,f10305]) ).
fof(f10305,plain,
( spl0_1308
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OatMost(X4,X5) != c_SetInterval_OatMost(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1400,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OatMost(X4,X5) != c_SetInterval_OatMost(X8,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f10303,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1396,f10301]) ).
fof(f10301,plain,
( spl0_1307
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X18,X29,X5)
| c_in(X29,c_SetInterval_OatLeast(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f1396,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X18,X29,X5)
| c_in(X29,c_SetInterval_OatLeast(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f10299,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1395,f10297]) ).
fof(f10297,plain,
( spl0_1306
<=> ! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X18,X29,X5)
| ~ c_in(X29,c_SetInterval_OatLeast(X18,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f1395,axiom,
! [X29,X18,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X18,X29,X5)
| ~ c_in(X29,c_SetInterval_OatLeast(X18,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f10295,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1394,f10293]) ).
fof(f10293,plain,
( spl0_1305
<=> ! [X4,X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OatLeast(X4,X5) != c_SetInterval_OatLeast(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f1394,axiom,
! [X8,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| X4 = X8
| c_SetInterval_OatLeast(X4,X5) != c_SetInterval_OatLeast(X8,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f10291,plain,
( spl0_1304
| ~ spl0_703
| ~ spl0_782
| ~ spl0_1042 ),
inference(avatar_split_clause,[],[f8685,f8464,f7221,f6885,f10288]) ).
fof(f10288,plain,
( spl0_1304
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f6885,plain,
( spl0_703
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f8464,plain,
( spl0_1042
<=> ! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X39,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f8685,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_703
| ~ spl0_782
| ~ spl0_1042 ),
inference(forward_demodulation,[],[f8682,f6887]) ).
fof(f6887,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_703 ),
inference(avatar_component_clause,[],[f6885]) ).
fof(f8682,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_782
| ~ spl0_1042 ),
inference(superposition,[],[f8465,f7223]) ).
fof(f8465,plain,
( ! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X39,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1042 ),
inference(avatar_component_clause,[],[f8464]) ).
fof(f10286,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1388,f10284]) ).
fof(f1388,axiom,
! [X19,X5,X30] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X19,X30,X5)
| c_emptyset = c_SetInterval_OatLeastLessThan(X30,X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f10282,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1383,f10280]) ).
fof(f1383,axiom,
! [X19,X5,X30] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X19,X30,X5)
| c_emptyset = c_SetInterval_OatLeastAtMost(X30,X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f10278,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1382,f10276]) ).
fof(f10276,plain,
( spl0_1301
<=> ! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatLeast(X18,X5) = c_uminus(c_SetInterval_OlessThan(X18,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1382,axiom,
! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatLeast(X18,X5) = c_uminus(c_SetInterval_OlessThan(X18,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f10274,plain,
spl0_1300,
inference(avatar_split_clause,[],[f1381,f10272]) ).
fof(f10272,plain,
( spl0_1300
<=> ! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatMost(X18,X5) = c_uminus(c_SetInterval_OgreaterThan(X18,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1381,axiom,
! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatMost(X18,X5) = c_uminus(c_SetInterval_OgreaterThan(X18,X5),tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f10270,plain,
spl0_1299,
inference(avatar_split_clause,[],[f1380,f10268]) ).
fof(f10268,plain,
( spl0_1299
<=> ! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatMost(X18,X5),tc_set(X5)) = c_SetInterval_OgreaterThan(X18,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f1380,axiom,
! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatMost(X18,X5),tc_set(X5)) = c_SetInterval_OgreaterThan(X18,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f10266,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1379,f10264]) ).
fof(f10264,plain,
( spl0_1298
<=> ! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatLeast(X18,X5),tc_set(X5)) = c_SetInterval_OlessThan(X18,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1379,axiom,
! [X18,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatLeast(X18,X5),tc_set(X5)) = c_SetInterval_OlessThan(X18,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f10262,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1167,f10260]) ).
fof(f10260,plain,
( spl0_1297
<=> ! [X4,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1167,axiom,
! [X8,X4] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f10258,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1166,f10256]) ).
fof(f10256,plain,
( spl0_1296
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1166,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f10254,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1165,f10252]) ).
fof(f10252,plain,
( spl0_1295
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1165,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f10250,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1164,f10248]) ).
fof(f10248,plain,
( spl0_1294
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1164,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f10246,plain,
spl0_1293,
inference(avatar_split_clause,[],[f1161,f10244]) ).
fof(f10244,plain,
( spl0_1293
<=> ! [X4,X8] :
( c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f1161,axiom,
! [X8,X4] :
( c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f10242,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1154,f10240]) ).
fof(f10240,plain,
( spl0_1292
<=> ! [X4,X8] :
( c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f1154,axiom,
! [X8,X4] :
( c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f10238,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1153,f10236]) ).
fof(f10236,plain,
( spl0_1291
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1153,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f10234,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1152,f10232]) ).
fof(f10232,plain,
( spl0_1290
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1152,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f10230,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1151,f10228]) ).
fof(f10228,plain,
( spl0_1289
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f1151,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven(c_plus(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10226,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1148,f10224]) ).
fof(f10224,plain,
( spl0_1288
<=> ! [X4,X8] :
( c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_times(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f1148,axiom,
! [X8,X4] :
( c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_times(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10222,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1142,f10220]) ).
fof(f10220,plain,
( spl0_1287
<=> ! [X4,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f1142,axiom,
! [X8,X4] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10218,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1141,f10216]) ).
fof(f10216,plain,
( spl0_1286
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1141,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10214,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1140,f10212]) ).
fof(f10212,plain,
( spl0_1285
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1140,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10210,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1139,f10208]) ).
fof(f10208,plain,
( spl0_1284
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1139,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10206,plain,
( spl0_1282
| ~ spl0_1283
| ~ spl0_784
| ~ spl0_1014 ),
inference(avatar_split_clause,[],[f8630,f8351,f7230,f10203,f10200]) ).
fof(f10200,plain,
( spl0_1282
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f10203,plain,
( spl0_1283
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f7230,plain,
( spl0_784
<=> ! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f8351,plain,
( spl0_1014
<=> ! [X4,X8] :
( c_Parity_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f8630,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_784
| ~ spl0_1014 ),
inference(superposition,[],[f8352,f7231]) ).
fof(f7231,plain,
( ! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_nat)
| ~ spl0_784 ),
inference(avatar_component_clause,[],[f7230]) ).
fof(f8352,plain,
( ! [X8,X4] :
( ~ c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat)
| c_Parity_Oeven(X4,tc_nat) )
| ~ spl0_1014 ),
inference(avatar_component_clause,[],[f8351]) ).
fof(f10198,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1099,f10196]) ).
fof(f10196,plain,
( spl0_1281
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(c_0,X2,X5)
| c_less(c_uminus(X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1099,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(c_0,X2,X5)
| c_less(c_uminus(X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10194,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1098,f10192]) ).
fof(f10192,plain,
( spl0_1280
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(c_0,X2,X5)
| ~ c_less(c_uminus(X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1098,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(c_0,X2,X5)
| ~ c_less(c_uminus(X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10190,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1095,f10188]) ).
fof(f10188,plain,
( spl0_1279
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(c_0,X2,X5)
| c_lessequals(c_uminus(X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1095,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(c_0,X2,X5)
| c_lessequals(c_uminus(X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10186,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1094,f10184]) ).
fof(f10184,plain,
( spl0_1278
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(c_0,X2,X5)
| ~ c_lessequals(c_uminus(X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1094,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(c_0,X2,X5)
| ~ c_lessequals(c_uminus(X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10182,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1092,f10180]) ).
fof(f10180,plain,
( spl0_1277
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X2 = X7
| c_uminus(X2,X5) != c_uminus(X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1092,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X2 = X7
| c_uminus(X2,X5) != c_uminus(X7,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10178,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1089,f10176]) ).
fof(f10176,plain,
( spl0_1276
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X2,c_0,X5)
| c_less(c_0,c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1089,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X2,c_0,X5)
| c_less(c_0,c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10174,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1088,f10172]) ).
fof(f10172,plain,
( spl0_1275
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X2,c_0,X5)
| ~ c_less(c_0,c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1088,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X2,c_0,X5)
| ~ c_less(c_0,c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10170,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1087,f10168]) ).
fof(f10168,plain,
( spl0_1274
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X2,c_0,X5)
| c_lessequals(c_0,c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1087,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X2,c_0,X5)
| c_lessequals(c_0,c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10166,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1086,f10164]) ).
fof(f10164,plain,
( spl0_1273
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X2,c_0,X5)
| ~ c_lessequals(c_0,c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f1086,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X2,c_0,X5)
| ~ c_lessequals(c_0,c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10162,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1032,f10160]) ).
fof(f10160,plain,
( spl0_1272
<=> ! [X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(X9,X5) = c_times(X9,c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1032,axiom,
! [X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(X9,X5) = c_times(X9,c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10158,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1031,f10156]) ).
fof(f10156,plain,
( spl0_1271
<=> ! [X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X9,X5) = c_uminus(X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f1031,axiom,
! [X9,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X9,X5) = c_uminus(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10154,plain,
spl0_1270,
inference(avatar_split_clause,[],[f951,f10152]) ).
fof(f10152,plain,
( spl0_1270
<=> ! [X18,X19,X30] :
( X19 = X30
| c_plus(X30,X18,tc_nat) != c_plus(X19,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f951,axiom,
! [X18,X19,X30] :
( X19 = X30
| c_plus(X30,X18,tc_nat) != c_plus(X19,X18,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10150,plain,
spl0_1269,
inference(avatar_split_clause,[],[f946,f10148]) ).
fof(f10148,plain,
( spl0_1269
<=> ! [X18,X19,X30] :
( X19 = X30
| c_plus(X18,X30,tc_nat) != c_plus(X18,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f946,axiom,
! [X18,X19,X30] :
( X19 = X30
| c_plus(X18,X30,tc_nat) != c_plus(X18,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10146,plain,
spl0_1268,
inference(avatar_split_clause,[],[f930,f10144]) ).
fof(f10144,plain,
( spl0_1268
<=> ! [X19,X30] :
( c_0 = X30
| c_0 = X19
| c_0 != c_times(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f930,axiom,
! [X19,X30] :
( c_0 = X30
| c_0 = X19
| c_0 != c_times(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10142,plain,
spl0_1267,
inference(avatar_split_clause,[],[f715,f10140]) ).
fof(f715,axiom,
! [X19,X30] : c_IntDef_Oint(c_plus(X30,X19,tc_nat)) = c_plus(c_IntDef_Oint(X30),c_IntDef_Oint(X19),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(f10138,plain,
spl0_1266,
inference(avatar_split_clause,[],[f678,f10136]) ).
fof(f10136,plain,
( spl0_1266
<=> ! [X5,X19,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X19 = X30
| c_NatArith_Oof__nat(X19,X5) != c_NatArith_Oof__nat(X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f678,axiom,
! [X19,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X19 = X30
| c_NatArith_Oof__nat(X19,X5) != c_NatArith_Oof__nat(X30,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10134,plain,
spl0_1265,
inference(avatar_split_clause,[],[f672,f10132]) ).
fof(f10132,plain,
( spl0_1265
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_0,X19,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f672,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_0,X19,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10130,plain,
spl0_1264,
inference(avatar_split_clause,[],[f671,f10128]) ).
fof(f10128,plain,
( spl0_1264
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f671,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10126,plain,
spl0_1263,
inference(avatar_split_clause,[],[f649,f10124]) ).
fof(f10124,plain,
( spl0_1263
<=> ! [X29,X55] :
( c_0 = X55
| c_lessequals(X55,X29,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X29,X55) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f649,axiom,
! [X29,X55] :
( c_0 = X55
| c_lessequals(X55,X29,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X29,X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10122,plain,
spl0_1262,
inference(avatar_split_clause,[],[f608,f10120]) ).
fof(f10120,plain,
( spl0_1262
<=> ! [X44,X47,X5,X45] :
( X45 = X47
| c_append(X44,X45,X5) != c_append(X44,X47,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f608,axiom,
! [X47,X44,X45,X5] :
( X45 = X47
| c_append(X44,X45,X5) != c_append(X44,X47,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10118,plain,
( spl0_1261
| ~ spl0_750
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f8541,f8210,f7093,f10116]) ).
fof(f10116,plain,
( spl0_1261
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f7093,plain,
( spl0_750
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f8210,plain,
( spl0_979
<=> ! [X2,X7] : c_0 = c_div(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f8541,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_750
| ~ spl0_979 ),
inference(superposition,[],[f8211,f7094]) ).
fof(f7094,plain,
( ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8
| ~ spl0_750 ),
inference(avatar_component_clause,[],[f7093]) ).
fof(f8211,plain,
( ! [X2,X7] : c_0 = c_div(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint)
| ~ spl0_979 ),
inference(avatar_component_clause,[],[f8210]) ).
fof(f10114,plain,
spl0_1260,
inference(avatar_split_clause,[],[f602,f10112]) ).
fof(f10112,plain,
( spl0_1260
<=> ! [X5,X8] :
( c_List_Orotate1(X8,X5) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f602,axiom,
! [X8,X5] :
( c_List_Orotate1(X8,X5) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X5)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10110,plain,
spl0_1259,
inference(avatar_split_clause,[],[f491,f10108]) ).
fof(f10108,plain,
( spl0_1259
<=> ! [X59,X60,X22,X5,X2] :
( X59 = X60
| c_List_Olist_OCons(X22,X59,X5) != c_List_Olist_OCons(X2,X60,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f491,axiom,
! [X2,X59,X60,X22,X5] :
( X59 = X60
| c_List_Olist_OCons(X22,X59,X5) != c_List_Olist_OCons(X2,X60,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10106,plain,
spl0_1258,
inference(avatar_split_clause,[],[f490,f10104]) ).
fof(f10104,plain,
( spl0_1258
<=> ! [X2,X59,X60,X5,X22] :
( X2 = X22
| c_List_Olist_OCons(X22,X59,X5) != c_List_Olist_OCons(X2,X60,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f490,axiom,
! [X2,X59,X22,X5,X60] :
( X2 = X22
| c_List_Olist_OCons(X22,X59,X5) != c_List_Olist_OCons(X2,X60,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10102,plain,
spl0_1257,
inference(avatar_split_clause,[],[f475,f10100]) ).
fof(f10100,plain,
( spl0_1257
<=> ! [X5,X44,X19] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate(X19,X44,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f475,axiom,
! [X44,X19,X5] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate(X19,X44,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10098,plain,
spl0_1256,
inference(avatar_split_clause,[],[f417,f10096]) ).
fof(f10096,plain,
( spl0_1256
<=> ! [X4,X21,X44] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X4,X44,X21),X21)
| ~ c_in(X4,c_List_Oset(X44,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f417,axiom,
! [X21,X44,X4] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X4,X44,X21),X21)
| ~ c_in(X4,c_List_Oset(X44,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10094,plain,
spl0_1255,
inference(avatar_split_clause,[],[f395,f10092]) ).
fof(f10092,plain,
( spl0_1255
<=> ! [X44,X47,X5,X45] :
( X45 = X47
| c_append(X45,X44,X5) != c_append(X47,X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f395,axiom,
! [X47,X44,X45,X5] :
( X45 = X47
| c_append(X45,X44,X5) != c_append(X47,X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10090,plain,
spl0_1254,
inference(avatar_split_clause,[],[f358,f10088]) ).
fof(f10088,plain,
( spl0_1254
<=> ! [X2,X7] : c_Divides_Oop_Amod(X7,X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X7,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f358,axiom,
! [X2,X7] : c_Divides_Oop_Amod(X7,X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X7,X2,tc_IntDef_Oint),X2,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10086,plain,
spl0_1253,
inference(avatar_split_clause,[],[f357,f10084]) ).
fof(f10084,plain,
( spl0_1253
<=> ! [X2,X7] : c_Divides_Oop_Amod(c_plus(X2,X7,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X7,X2,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f357,axiom,
! [X2,X7] : c_Divides_Oop_Amod(c_plus(X2,X7,tc_IntDef_Oint),X2,tc_IntDef_Oint) = c_Divides_Oop_Amod(X7,X2,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10082,plain,
spl0_1252,
inference(avatar_split_clause,[],[f350,f10080]) ).
fof(f10080,plain,
( spl0_1252
<=> ! [X4,X19] :
( c_0 = X4
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X4,tc_IntDef_Oint),X19,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f350,axiom,
! [X19,X4] :
( c_0 = X4
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X4,tc_IntDef_Oint),X19,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10071,plain,
( spl0_1251
| ~ spl0_875
| ~ spl0_1250 ),
inference(avatar_split_clause,[],[f10067,f10064,f7640,f10069]) ).
fof(f10069,plain,
( spl0_1251
<=> ! [X19] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X19,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f7640,plain,
( spl0_875
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f10064,plain,
( spl0_1250
<=> ! [X19] :
( c_0 = X19
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X19,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f10067,plain,
( ! [X19] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X19,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X19 )
| ~ spl0_875
| ~ spl0_1250 ),
inference(forward_demodulation,[],[f10065,f7642]) ).
fof(f7642,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f7640]) ).
fof(f10065,plain,
( ! [X19] :
( c_0 = X19
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X19,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1250 ),
inference(avatar_component_clause,[],[f10064]) ).
fof(f10066,plain,
spl0_1250,
inference(avatar_split_clause,[],[f349,f10064]) ).
fof(f349,axiom,
! [X19] :
( c_0 = X19
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X19,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10062,plain,
spl0_1249,
inference(avatar_split_clause,[],[f342,f10060]) ).
fof(f10060,plain,
( spl0_1249
<=> ! [X7,X8] :
( c_0 = X7
| c_div(c_times(X7,X8,tc_IntDef_Oint),X7,tc_IntDef_Oint) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f342,axiom,
! [X8,X7] :
( c_0 = X7
| c_div(c_times(X7,X8,tc_IntDef_Oint),X7,tc_IntDef_Oint) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10058,plain,
spl0_1248,
inference(avatar_split_clause,[],[f341,f10056]) ).
fof(f10056,plain,
( spl0_1248
<=> ! [X7,X8] :
( c_0 = X7
| c_div(c_times(X8,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f341,axiom,
! [X8,X7] :
( c_0 = X7
| c_div(c_times(X8,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10054,plain,
spl0_1247,
inference(avatar_split_clause,[],[f322,f10052]) ).
fof(f10052,plain,
( spl0_1247
<=> ! [X7] : c_IntDiv_OposDivAlg(c_Pair(c_0,X7,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_1247])]) ).
fof(f322,axiom,
! [X7] : c_IntDiv_OposDivAlg(c_Pair(c_0,X7,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(f10050,plain,
spl0_1246,
inference(avatar_split_clause,[],[f307,f10048]) ).
fof(f10048,plain,
( spl0_1246
<=> ! [X2,X7] : c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f307,axiom,
! [X2,X7] : c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f10046,plain,
spl0_1245,
inference(avatar_split_clause,[],[f278,f10044]) ).
fof(f10044,plain,
( spl0_1245
<=> ! [X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X39,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X39,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f278,axiom,
! [X39,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X39,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X39,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f10042,plain,
spl0_1244,
inference(avatar_split_clause,[],[f277,f10040]) ).
fof(f10040,plain,
( spl0_1244
<=> ! [X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X39,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X39,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f277,axiom,
! [X39,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X39,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X39,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f10038,plain,
spl0_1243,
inference(avatar_split_clause,[],[f274,f10036]) ).
fof(f10036,plain,
( spl0_1243
<=> ! [X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X39,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X39,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f274,axiom,
! [X39,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X39,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X39,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f10034,plain,
spl0_1242,
inference(avatar_split_clause,[],[f273,f10032]) ).
fof(f10032,plain,
( spl0_1242
<=> ! [X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X39,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X39,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f273,axiom,
! [X39,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X39,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X39,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f10024,plain,
spl0_1241,
inference(avatar_split_clause,[],[f271,f10022]) ).
fof(f10022,plain,
( spl0_1241
<=> ! [X9,X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| X9 = X39
| c_IntDef_Oof__int(X9,X5) != c_IntDef_Oof__int(X39,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f271,axiom,
! [X39,X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| X9 = X39
| c_IntDef_Oof__int(X9,X5) != c_IntDef_Oof__int(X39,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f10020,plain,
spl0_1240,
inference(avatar_split_clause,[],[f265,f10018]) ).
fof(f10018,plain,
( spl0_1240
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f265,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f10016,plain,
spl0_1239,
inference(avatar_split_clause,[],[f264,f10014]) ).
fof(f10014,plain,
( spl0_1239
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X9,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f264,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X9,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f10012,plain,
spl0_1238,
inference(avatar_split_clause,[],[f263,f10010]) ).
fof(f10010,plain,
( spl0_1238
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X9,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f263,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X9,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f10008,plain,
spl0_1237,
inference(avatar_split_clause,[],[f262,f10006]) ).
fof(f10006,plain,
( spl0_1237
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X9,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f262,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X9,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X9,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f10004,plain,
spl0_1236,
inference(avatar_split_clause,[],[f226,f10002]) ).
fof(f10002,plain,
( spl0_1236
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| c_in(c_uminus(X2,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f226,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X2,c_IntDef_OInts,X5)
| c_in(c_uminus(X2,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f10000,plain,
spl0_1235,
inference(avatar_split_clause,[],[f221,f9998]) ).
fof(f9998,plain,
( spl0_1235
<=> ! [X8] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X8)) = X8
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f221,axiom,
! [X8] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X8)) = X8
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f9996,plain,
spl0_1234,
inference(avatar_split_clause,[],[f207,f9994]) ).
fof(f9994,plain,
( spl0_1234
<=> ! [X40,X30] :
( c_IntDef_Oint(X30) != c_Numeral_Onumber__of(X40,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f207,axiom,
! [X40,X30] :
( c_IntDef_Oint(X30) != c_Numeral_Onumber__of(X40,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f9992,plain,
spl0_1233,
inference(avatar_split_clause,[],[f206,f9990]) ).
fof(f9990,plain,
( spl0_1233
<=> ! [X40,X30] :
( c_IntDef_Oint(X30) != c_Numeral_Onumber__of(X40,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X40,tc_IntDef_Oint)) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f206,axiom,
! [X40,X30] :
( c_IntDef_Oint(X30) != c_Numeral_Onumber__of(X40,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X40,tc_IntDef_Oint)) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f9988,plain,
spl0_1232,
inference(avatar_split_clause,[],[f108,f9986]) ).
fof(f9986,plain,
( spl0_1232
<=> ! [X30,X19] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f108,axiom,
! [X19,X30] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f9979,plain,
spl0_1231,
inference(avatar_split_clause,[],[f98,f9977]) ).
fof(f9977,plain,
( spl0_1231
<=> ! [X30,X19] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_plus(X30,X19,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f98,axiom,
! [X19,X30] : c_Divides_Oop_Amod(X30,X19,tc_nat) = c_Divides_Oop_Amod(c_plus(X30,X19,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f9975,plain,
spl0_1230,
inference(avatar_split_clause,[],[f97,f9973]) ).
fof(f9973,plain,
( spl0_1230
<=> ! [X30,X19] : c_Divides_Oop_Amod(c_plus(X19,X30,tc_nat),X19,tc_nat) = c_Divides_Oop_Amod(X30,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f97,axiom,
! [X19,X30] : c_Divides_Oop_Amod(c_plus(X19,X30,tc_nat),X19,tc_nat) = c_Divides_Oop_Amod(X30,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f9971,plain,
spl0_1229,
inference(avatar_split_clause,[],[f56,f9969]) ).
fof(f9969,plain,
( spl0_1229
<=> ! [X24,X23,X5,X25] :
( X24 = X25
| c_Datatype__Universe_OIn1(X25,X5,X23) != c_Datatype__Universe_OIn1(X24,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f56,axiom,
! [X24,X5,X25,X23] :
( X24 = X25
| c_Datatype__Universe_OIn1(X25,X5,X23) != c_Datatype__Universe_OIn1(X24,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f9967,plain,
spl0_1228,
inference(avatar_split_clause,[],[f54,f9965]) ).
fof(f9965,plain,
( spl0_1228
<=> ! [X24,X23,X5,X25] :
( X24 = X25
| c_Datatype__Universe_OIn0(X24,X5,X23) != c_Datatype__Universe_OIn0(X25,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f54,axiom,
! [X24,X5,X25,X23] :
( X24 = X25
| c_Datatype__Universe_OIn0(X24,X5,X23) != c_Datatype__Universe_OIn0(X25,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f9963,plain,
spl0_1227,
inference(avatar_split_clause,[],[f50,f9961]) ).
fof(f9961,plain,
( spl0_1227
<=> ! [X23,X7,X5,X2] :
( X2 = X7
| c_Datatype__Universe_OAtom(X2,X5,X23) != c_Datatype__Universe_OAtom(X7,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f50,axiom,
! [X2,X7,X5,X23] :
( X2 = X7
| c_Datatype__Universe_OAtom(X2,X5,X23) != c_Datatype__Universe_OAtom(X7,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f9959,plain,
spl0_1226,
inference(avatar_split_clause,[],[f14,f9957]) ).
fof(f9957,plain,
( spl0_1226
<=> ! [X5,X10] :
( ~ c_in(X10,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X5,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(X10,X5,tc_Product__Type_Ounit),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f14,axiom,
! [X10,X5] :
( ~ c_in(X10,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X5,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(X10,X5,tc_Product__Type_Ounit),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
fof(f9946,plain,
( spl0_1225
| ~ spl0_58
| ~ spl0_962 ),
inference(avatar_split_clause,[],[f8150,f8024,f3460,f9943]) ).
fof(f9943,plain,
( spl0_1225
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f8024,plain,
( spl0_962
<=> ! [X5] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f8150,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_962 ),
inference(resolution,[],[f8025,f3462]) ).
fof(f8025,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X5) )
| ~ spl0_962 ),
inference(avatar_component_clause,[],[f8024]) ).
fof(f9806,plain,
( ~ spl0_1223
| spl0_1224
| ~ spl0_772
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f9798,f9454,f7181,f9804,f9800]) ).
fof(f9800,plain,
( spl0_1223
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f9804,plain,
( spl0_1224
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f7181,plain,
( spl0_772
<=> ! [X19] : c_0 = c_minus(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f9798,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_772
| ~ spl0_1189 ),
inference(trivial_inequality_removal,[],[f9791]) ).
fof(f9791,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_772
| ~ spl0_1189 ),
inference(superposition,[],[f9455,f7182]) ).
fof(f7182,plain,
( ! [X19] : c_0 = c_minus(c_0,X19,tc_nat)
| ~ spl0_772 ),
inference(avatar_component_clause,[],[f7181]) ).
fof(f9739,plain,
( spl0_1222
| ~ spl0_857
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8133,f7942,f7525,f9736]) ).
fof(f9736,plain,
( spl0_1222
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f7525,plain,
( spl0_857
<=> ! [X4,X5,X1] : c_in(X4,c_insert(X4,X1,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f7942,plain,
( spl0_942
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f8133,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_857
| ~ spl0_942 ),
inference(superposition,[],[f7526,f7944]) ).
fof(f7944,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f7942]) ).
fof(f7526,plain,
( ! [X1,X4,X5] : c_in(X4,c_insert(X4,X1,X5),X5)
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f7525]) ).
fof(f9691,plain,
( spl0_1221
| ~ spl0_93
| ~ spl0_930 ),
inference(avatar_split_clause,[],[f8117,f7893,f3635,f9689]) ).
fof(f9689,plain,
( spl0_1221
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f3635,plain,
( spl0_93
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f7893,plain,
( spl0_930
<=> ! [X5,X8] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X8,c_1,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f8117,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_93
| ~ spl0_930 ),
inference(resolution,[],[f7894,f3637]) ).
fof(f3637,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f3635]) ).
fof(f7894,plain,
( ! [X8,X5] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X8,c_1,X5) = X8 )
| ~ spl0_930 ),
inference(avatar_component_clause,[],[f7893]) ).
fof(f9639,plain,
( spl0_1220
| ~ spl0_59
| ~ spl0_930 ),
inference(avatar_split_clause,[],[f8116,f7893,f3465,f9637]) ).
fof(f9637,plain,
( spl0_1220
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f3465,plain,
( spl0_59
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f8116,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_59
| ~ spl0_930 ),
inference(resolution,[],[f7894,f3467]) ).
fof(f3467,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f9611,plain,
( spl0_1219
| ~ spl0_58
| ~ spl0_1009
| ~ spl0_1147 ),
inference(avatar_split_clause,[],[f9288,f9285,f8331,f3460,f9609]) ).
fof(f9609,plain,
( spl0_1219
<=> ! [X5] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f9285,plain,
( spl0_1147
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f9288,plain,
( ! [X5] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_58
| ~ spl0_1009
| ~ spl0_1147 ),
inference(forward_demodulation,[],[f9286,f8621]) ).
fof(f9286,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X5) )
| ~ spl0_1147 ),
inference(avatar_component_clause,[],[f9285]) ).
fof(f9605,plain,
( spl0_1218
| ~ spl0_93
| ~ spl0_929 ),
inference(avatar_split_clause,[],[f8115,f7889,f3635,f9603]) ).
fof(f9603,plain,
( spl0_1218
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f7889,plain,
( spl0_929
<=> ! [X5,X19] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f8115,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_93
| ~ spl0_929 ),
inference(resolution,[],[f7890,f3637]) ).
fof(f7890,plain,
( ! [X19,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X19,X5) )
| ~ spl0_929 ),
inference(avatar_component_clause,[],[f7889]) ).
fof(f9573,plain,
spl0_1217,
inference(avatar_split_clause,[],[f3073,f9571]) ).
fof(f9571,plain,
( spl0_1217
<=> ! [X30,X19] :
( ~ c_lessequals(c_1,c_times(X30,X19,tc_nat),tc_nat)
| c_lessequals(c_1,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f3073,plain,
! [X19,X30] :
( ~ c_lessequals(c_1,c_times(X30,X19,tc_nat),tc_nat)
| c_lessequals(c_1,X19,tc_nat) ),
inference(forward_demodulation,[],[f2898,f2763]) ).
fof(f2898,plain,
! [X19,X30] :
( c_lessequals(c_1,X19,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X30,X19,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f961,f1409]) ).
fof(f961,axiom,
! [X19,X30] :
( c_lessequals(c_1,X19,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f9569,plain,
spl0_1216,
inference(avatar_split_clause,[],[f3072,f9567]) ).
fof(f9567,plain,
( spl0_1216
<=> ! [X30,X19] :
( ~ c_lessequals(c_1,c_times(X30,X19,tc_nat),tc_nat)
| c_lessequals(c_1,X30,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f3072,plain,
! [X19,X30] :
( ~ c_lessequals(c_1,c_times(X30,X19,tc_nat),tc_nat)
| c_lessequals(c_1,X30,tc_nat) ),
inference(forward_demodulation,[],[f2897,f2763]) ).
fof(f2897,plain,
! [X19,X30] :
( c_lessequals(c_1,X30,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X30,X19,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f960,f1409]) ).
fof(f960,axiom,
! [X19,X30] :
( c_lessequals(c_1,X30,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f9565,plain,
( spl0_1215
| ~ spl0_59
| ~ spl0_929 ),
inference(avatar_split_clause,[],[f8114,f7889,f3465,f9563]) ).
fof(f9563,plain,
( spl0_1215
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f8114,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_929 ),
inference(resolution,[],[f7890,f3467]) ).
fof(f9561,plain,
spl0_1214,
inference(avatar_split_clause,[],[f3062,f9559]) ).
fof(f9559,plain,
( spl0_1214
<=> ! [X29,X19] :
( c_lessequals(c_1,c_Nat_Opower(X29,X19,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X29,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f3062,plain,
! [X29,X19] :
( c_lessequals(c_1,c_Nat_Opower(X29,X19,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X29,tc_nat) ),
inference(forward_demodulation,[],[f2880,f2763]) ).
fof(f2880,plain,
! [X29,X19] :
( ~ c_lessequals(c_1,X29,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X29,X19,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1205,f1409]) ).
fof(f1205,axiom,
! [X29,X19] :
( ~ c_lessequals(c_1,X29,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X29,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f9557,plain,
spl0_1213,
inference(avatar_split_clause,[],[f3003,f9555]) ).
fof(f9555,plain,
( spl0_1213
<=> ! [X19,X30] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X19),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X30),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f3003,plain,
! [X19,X30] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X19),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X30),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2803,f2799]) ).
fof(f2803,plain,
! [X19,X30] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X30),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1630,f1409]) ).
fof(f1630,axiom,
! [X19,X30] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X19)),tc_IntDef_Oint),c_IntDef_Oint(X30),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f9553,plain,
spl0_1212,
inference(avatar_split_clause,[],[f2999,f9551]) ).
fof(f9551,plain,
( spl0_1212
<=> ! [X39] : c_Numeral_OBit(c_Numeral_Obin__add(X39,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f2999,plain,
! [X39] : c_Numeral_OBit(c_Numeral_Obin__add(X39,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2801,f2778]) ).
fof(f2801,plain,
! [X39] : c_Numeral_Obin__add(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X39,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f996,f978,f978]) ).
fof(f996,axiom,
! [X39] : c_Numeral_Obin__pred(c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X39),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f9549,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2802,f9547]) ).
fof(f9547,plain,
( spl0_1211
<=> ! [X39] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X39),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f2802,plain,
! [X39] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X39),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f988,f994,f994]) ).
fof(f988,axiom,
! [X39] : c_Numeral_Obin__minus(c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X39),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f9541,plain,
( spl0_1210
| ~ spl0_1209 ),
inference(avatar_split_clause,[],[f9537,f9534,f9539]) ).
fof(f9539,plain,
( spl0_1210
<=> ! [X19] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X19),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f9534,plain,
( spl0_1209
<=> ! [X19] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f9537,plain,
( ! [X19] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X19),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1209 ),
inference(forward_demodulation,[],[f9535,f2799]) ).
fof(f9535,plain,
( ! [X19] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1209 ),
inference(avatar_component_clause,[],[f9534]) ).
fof(f9536,plain,
spl0_1209,
inference(avatar_split_clause,[],[f2791,f9534]) ).
fof(f2791,plain,
! [X19] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f259,f1409]) ).
fof(f259,axiom,
! [X19] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X19)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9532,plain,
spl0_1208,
inference(avatar_split_clause,[],[f1580,f9530]) ).
fof(f9530,plain,
( spl0_1208
<=> ! [X6,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X6,X5),X5,X5) = c_Relation_ORange(X6,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f1580,axiom,
! [X6,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X6,X5),X5,X5) = c_Relation_ORange(X6,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f9528,plain,
spl0_1207,
inference(avatar_split_clause,[],[f1578,f9526]) ).
fof(f9526,plain,
( spl0_1207
<=> ! [X6,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X6,X5),X5,X5) = c_Relation_ODomain(X6,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f1578,axiom,
! [X6,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X6,X5),X5,X5) = c_Relation_ODomain(X6,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f9524,plain,
spl0_1206,
inference(avatar_split_clause,[],[f1550,f9522]) ).
fof(f9522,plain,
( spl0_1206
<=> ! [X7,X5,X2,X1] :
( ~ c_in(X2,X1,X5)
| c_in(X2,c_insert(X7,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f1550,axiom,
! [X2,X1,X7,X5] :
( ~ c_in(X2,X1,X5)
| c_in(X2,c_insert(X7,X1,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f9520,plain,
( spl0_1205
| ~ spl0_97
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8110,f7877,f3655,f9518]) ).
fof(f9518,plain,
( spl0_1205
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f3655,plain,
( spl0_97
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f7877,plain,
( spl0_926
<=> ! [X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omax(X8,X8,X23) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f8110,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_97
| ~ spl0_926 ),
inference(resolution,[],[f7878,f3657]) ).
fof(f3657,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f3655]) ).
fof(f7878,plain,
( ! [X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omax(X8,X8,X23) = X8 )
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f7877]) ).
fof(f9516,plain,
spl0_1204,
inference(avatar_split_clause,[],[f1507,f9514]) ).
fof(f9514,plain,
( spl0_1204
<=> ! [X35,X31,X5,X1] :
( ~ c_in(X31,X35,X5)
| c_in(X31,c_union(X1,X35,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f1507,axiom,
! [X31,X1,X35,X5] :
( ~ c_in(X31,X35,X5)
| c_in(X31,c_union(X1,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f9512,plain,
spl0_1203,
inference(avatar_split_clause,[],[f1506,f9510]) ).
fof(f1506,axiom,
! [X31,X1,X5,X35] :
( ~ c_in(X31,X1,X5)
| c_in(X31,c_union(X1,X35,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f9508,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1448,f9506]) ).
fof(f9506,plain,
( spl0_1202
<=> ! [X5,X1,X31] :
( c_in(X31,X1,X5)
| c_in(X31,c_uminus(X1,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1448,axiom,
! [X31,X1,X5] :
( c_in(X31,X1,X5)
| c_in(X31,c_uminus(X1,tc_set(X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f9504,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1447,f9502]) ).
fof(f9502,plain,
( spl0_1201
<=> ! [X5,X1,X31] :
( ~ c_in(X31,X1,X5)
| ~ c_in(X31,c_uminus(X1,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1447,axiom,
! [X31,X1,X5] :
( ~ c_in(X31,X1,X5)
| ~ c_in(X31,c_uminus(X1,tc_set(X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f9500,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1410,f9498]) ).
fof(f9498,plain,
( spl0_1200
<=> ! [X77,X41] : c_minus(X41,X77,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X77,X41,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1410,axiom,
! [X41,X77] : c_minus(X41,X77,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X77,X41,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f9496,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1407,f9494]) ).
fof(f9494,plain,
( spl0_1199
<=> ! [X77,X41] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,X77,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1407,axiom,
! [X41,X77] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X77,X41,tc_nat),tc_nat) = c_minus(X41,X77,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f9492,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1387,f9490]) ).
fof(f9490,plain,
( spl0_1198
<=> ! [X2,X5] :
( ~ class_Orderings_Oorder(X5)
| c_SetInterval_OatLeastAtMost(X2,X2,X5) = c_insert(X2,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f1387,axiom,
! [X2,X5] :
( ~ class_Orderings_Oorder(X5)
| c_SetInterval_OatLeastAtMost(X2,X2,X5) = c_insert(X2,c_emptyset,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f9488,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1136,f9486]) ).
fof(f9486,plain,
( spl0_1197
<=> ! [X40] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X40,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1136,axiom,
! [X40] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X40,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(f9484,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1135,f9482]) ).
fof(f9482,plain,
( spl0_1196
<=> ! [X40] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X40,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1135,axiom,
! [X40] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X40,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(f9480,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1117,f9478]) ).
fof(f9478,plain,
( spl0_1195
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X2
| c_less(c_0,c_HOL_Oabs(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1117,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X2
| c_less(c_0,c_HOL_Oabs(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f9476,plain,
( spl0_1194
| ~ spl0_33
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8109,f7877,f3335,f9474]) ).
fof(f9474,plain,
( spl0_1194
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f3335,plain,
( spl0_33
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f8109,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_33
| ~ spl0_926 ),
inference(resolution,[],[f7878,f3337]) ).
fof(f3337,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f3335]) ).
fof(f9472,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1110,f9470]) ).
fof(f9470,plain,
( spl0_1193
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_OrderedGroup_Opprt(X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1110,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_OrderedGroup_Opprt(X8,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f9468,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1109,f9466]) ).
fof(f9466,plain,
( spl0_1192
<=> ! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X4,c_0,X5)
| c_0 = c_OrderedGroup_Opprt(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1109,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X4,c_0,X5)
| c_0 = c_OrderedGroup_Opprt(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f9464,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1105,f9462]) ).
fof(f9462,plain,
( spl0_1191
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_OrderedGroup_Onprt(X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1105,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_OrderedGroup_Onprt(X8,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f9460,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1104,f9458]) ).
fof(f9458,plain,
( spl0_1190
<=> ! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X4,X5)
| c_0 = c_OrderedGroup_Onprt(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1104,axiom,
! [X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X4,X5)
| c_0 = c_OrderedGroup_Onprt(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f9456,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1064,f9454]) ).
fof(f1064,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X2 = X7
| c_0 != c_minus(X2,X7,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f9452,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1048,f9450]) ).
fof(f9450,plain,
( spl0_1188
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_HOL_Oabs(X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1048,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_HOL_Oabs(X8,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f9448,plain,
spl0_1187,
inference(avatar_split_clause,[],[f1046,f9446]) ).
fof(f9446,plain,
( spl0_1187
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X2,X5) = c_HOL_Oabs(c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f1046,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X2,X5) = c_HOL_Oabs(c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f9444,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1044,f9442]) ).
fof(f9442,plain,
( spl0_1186
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X2
| ~ c_lessequals(c_HOL_Oabs(X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f1044,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X2
| ~ c_lessequals(c_HOL_Oabs(X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f9440,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1043,f9438]) ).
fof(f9438,plain,
( spl0_1185
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X2,X5) = c_HOL_Oabs(c_HOL_Oabs(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1043,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X2,X5) = c_HOL_Oabs(c_HOL_Oabs(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f9436,plain,
spl0_1184,
inference(avatar_split_clause,[],[f1012,f9434]) ).
fof(f9434,plain,
( spl0_1184
<=> ! [X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB1),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1012,axiom,
! [X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB1),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f9432,plain,
( spl0_1183
| ~ spl0_97
| ~ spl0_925 ),
inference(avatar_split_clause,[],[f8108,f7873,f3655,f9430]) ).
fof(f9430,plain,
( spl0_1183
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f7873,plain,
( spl0_925
<=> ! [X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omin(X8,X8,X23) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f8108,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_97
| ~ spl0_925 ),
inference(resolution,[],[f7874,f3657]) ).
fof(f7874,plain,
( ! [X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omin(X8,X8,X23) = X8 )
| ~ spl0_925 ),
inference(avatar_component_clause,[],[f7873]) ).
fof(f9428,plain,
spl0_1182,
inference(avatar_split_clause,[],[f992,f9426]) ).
fof(f9426,plain,
( spl0_1182
<=> ! [X40,X39] : c_Numeral_Obin__mult(c_Numeral_OBit(X40,c_Numeral_Obit_OB0),X39) = c_Numeral_OBit(c_Numeral_Obin__mult(X40,X39),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f9424,plain,
spl0_1181,
inference(avatar_split_clause,[],[f969,f9422]) ).
fof(f9422,plain,
( spl0_1181
<=> ! [X30,X19] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_0,c_minus(X19,X30,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f969,axiom,
! [X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_0,c_minus(X19,X30,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f9420,plain,
spl0_1180,
inference(avatar_split_clause,[],[f968,f9418]) ).
fof(f9418,plain,
( spl0_1180
<=> ! [X30,X19] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_0,c_minus(X19,X30,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f968,axiom,
! [X19,X30] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_0,c_minus(X19,X30,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f9416,plain,
spl0_1179,
inference(avatar_split_clause,[],[f944,f9414]) ).
fof(f9414,plain,
( spl0_1179
<=> ! [X30,X19] :
( c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_times(X30,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f944,axiom,
! [X19,X30] :
( c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_times(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f9412,plain,
spl0_1178,
inference(avatar_split_clause,[],[f943,f9410]) ).
fof(f9410,plain,
( spl0_1178
<=> ! [X19,X30] :
( c_less(c_0,X30,tc_nat)
| ~ c_less(c_0,c_times(X30,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f943,axiom,
! [X19,X30] :
( c_less(c_0,X30,tc_nat)
| ~ c_less(c_0,c_times(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f9408,plain,
spl0_1177,
inference(avatar_split_clause,[],[f895,f9406]) ).
fof(f9406,plain,
( spl0_1177
<=> ! [X30,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_0,c_plus(X30,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f895,axiom,
! [X19,X30] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_0,c_plus(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f9404,plain,
spl0_1176,
inference(avatar_split_clause,[],[f894,f9402]) ).
fof(f9402,plain,
( spl0_1176
<=> ! [X19,X30] :
( ~ c_less(c_0,X30,tc_nat)
| c_less(c_0,c_plus(X30,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f894,axiom,
! [X19,X30] :
( ~ c_less(c_0,X30,tc_nat)
| c_less(c_0,c_plus(X30,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f9400,plain,
spl0_1175,
inference(avatar_split_clause,[],[f716,f9398]) ).
fof(f9398,plain,
( spl0_1175
<=> ! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X40,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f716,axiom,
! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X40,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f9396,plain,
spl0_1174,
inference(avatar_split_clause,[],[f679,f9394]) ).
fof(f9394,plain,
( spl0_1174
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X30
| ~ c_lessequals(c_NatArith_Oof__nat(X30,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f679,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X30
| ~ c_lessequals(c_NatArith_Oof__nat(X30,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f9392,plain,
spl0_1173,
inference(avatar_split_clause,[],[f599,f9390]) ).
fof(f9390,plain,
( spl0_1173
<=> ! [X4,X5] : c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) = c_List_Orev(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f599,axiom,
! [X4,X5] : c_List_Olist_OCons(X4,c_List_Olist_ONil,X5) = c_List_Orev(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f9388,plain,
( spl0_1172
| ~ spl0_33
| ~ spl0_925 ),
inference(avatar_split_clause,[],[f8107,f7873,f3335,f9386]) ).
fof(f9386,plain,
( spl0_1172
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f8107,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_33
| ~ spl0_925 ),
inference(resolution,[],[f7874,f3337]) ).
fof(f9384,plain,
spl0_1171,
inference(avatar_split_clause,[],[f596,f9382]) ).
fof(f9382,plain,
( spl0_1171
<=> ! [X4,X5,X19] : c_List_Oreplicate(X19,X4,X5) = c_List_Orev(c_List_Oreplicate(X19,X4,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f596,axiom,
! [X19,X4,X5] : c_List_Oreplicate(X19,X4,X5) = c_List_Orev(c_List_Oreplicate(X19,X4,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f9380,plain,
spl0_1170,
inference(avatar_split_clause,[],[f577,f9378]) ).
fof(f9378,plain,
( spl0_1170
<=> ! [X8,X4,X21,X45] :
( ~ c_List_Oop_Amem(X4,X45,X21)
| c_List_Oop_Amem(X4,c_List_Olist_OCons(X8,X45,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f577,axiom,
! [X21,X8,X45,X4] :
( ~ c_List_Oop_Amem(X4,X45,X21)
| c_List_Oop_Amem(X4,c_List_Olist_OCons(X8,X45,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f9376,plain,
spl0_1169,
inference(avatar_split_clause,[],[f478,f9374]) ).
fof(f9374,plain,
( spl0_1169
<=> ! [X29,X55] : c_Nat_Osize(c_List_Oupt(X29,X55),tc_List_Olist(tc_nat)) = c_minus(X55,X29,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f478,axiom,
! [X29,X55] : c_Nat_Osize(c_List_Oupt(X29,X55),tc_List_Olist(tc_nat)) = c_minus(X55,X29,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f9372,plain,
spl0_1168,
inference(avatar_split_clause,[],[f474,f9370]) ).
fof(f9370,plain,
( spl0_1168
<=> ! [X5,X44] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate1(X44,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f474,axiom,
! [X44,X5] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate1(X44,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f9368,plain,
spl0_1167,
inference(avatar_split_clause,[],[f473,f9366]) ).
fof(f9366,plain,
( spl0_1167
<=> ! [X5,X44] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orev(X44,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f473,axiom,
! [X44,X5] : c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orev(X44,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f9364,plain,
spl0_1166,
inference(avatar_split_clause,[],[f460,f9362]) ).
fof(f9362,plain,
( spl0_1166
<=> ! [X5,X44,X8] : c_List_Olast(c_append(X44,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f460,axiom,
! [X8,X44,X5] : c_List_Olast(c_append(X44,c_List_Olist_OCons(X8,c_List_Olist_ONil,X5),X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f9360,plain,
spl0_1165,
inference(avatar_split_clause,[],[f459,f9358]) ).
fof(f9358,plain,
( spl0_1165
<=> ! [X5,X8,X19] :
( c_0 = X19
| c_List_Olast(c_List_Oreplicate(X19,X8,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f459,axiom,
! [X8,X19,X5] :
( c_0 = X19
| c_List_Olast(c_List_Oreplicate(X19,X8,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f9356,plain,
spl0_1164,
inference(avatar_split_clause,[],[f458,f9354]) ).
fof(f9354,plain,
( spl0_1164
<=> ! [X5,X56] :
( c_List_Olist_ONil = X56
| c_in(c_List_Olast(X56,X5),c_List_Oset(X56,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f458,axiom,
! [X56,X5] :
( c_List_Olist_ONil = X56
| c_in(c_List_Olast(X56,X5),c_List_Oset(X56,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f9352,plain,
spl0_1163,
inference(avatar_split_clause,[],[f449,f9350]) ).
fof(f9350,plain,
( spl0_1163
<=> ! [X55,X8] :
( ~ c_less(X8,X55,tc_nat)
| c_List_Ohd(c_List_Oupt(X8,X55),tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f449,axiom,
! [X8,X55] :
( ~ c_less(X8,X55,tc_nat)
| c_List_Ohd(c_List_Oupt(X8,X55),tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f9348,plain,
spl0_1162,
inference(avatar_split_clause,[],[f448,f9346]) ).
fof(f9346,plain,
( spl0_1162
<=> ! [X5,X8,X19] :
( c_0 = X19
| c_List_Ohd(c_List_Oreplicate(X19,X8,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f448,axiom,
! [X8,X19,X5] :
( c_0 = X19
| c_List_Ohd(c_List_Oreplicate(X19,X8,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f9344,plain,
( spl0_1161
| ~ spl0_70
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8098,f7857,f3520,f9342]) ).
fof(f9342,plain,
( spl0_1161
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f3520,plain,
( spl0_70
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f7857,plain,
( spl0_921
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X8,c_1,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f8098,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_70
| ~ spl0_921 ),
inference(resolution,[],[f7858,f3522]) ).
fof(f3522,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f3520]) ).
fof(f7858,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X8,c_1,X5) = X8 )
| ~ spl0_921 ),
inference(avatar_component_clause,[],[f7857]) ).
fof(f9340,plain,
spl0_1160,
inference(avatar_split_clause,[],[f447,f9338]) ).
fof(f9338,plain,
( spl0_1160
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_in(c_List_Ohd(X44,X5),c_List_Oset(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f447,axiom,
! [X44,X5] :
( c_List_Olist_ONil = X44
| c_in(c_List_Ohd(X44,X5),c_List_Oset(X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f9336,plain,
spl0_1159,
inference(avatar_split_clause,[],[f404,f9334]) ).
fof(f9334,plain,
( spl0_1159
<=> ! [X4,X5,X8] : c_List_Obutlast(c_append(X8,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f404,axiom,
! [X8,X4,X5] : c_List_Obutlast(c_append(X8,c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f9332,plain,
spl0_1158,
inference(avatar_split_clause,[],[f328,f9330]) ).
fof(f9330,plain,
( spl0_1158
<=> ! [X2,X7] :
( ~ c_less(c_0,X7,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f328,axiom,
! [X2,X7] :
( ~ c_less(c_0,X7,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f9328,plain,
spl0_1157,
inference(avatar_split_clause,[],[f327,f9326]) ).
fof(f9326,plain,
( spl0_1157
<=> ! [X2,X7] :
( ~ c_less(c_0,X7,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f327,axiom,
! [X2,X7] :
( ~ c_less(c_0,X7,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f9324,plain,
spl0_1156,
inference(avatar_split_clause,[],[f320,f9322]) ).
fof(f9322,plain,
( spl0_1156
<=> ! [X2,X7] :
( ~ c_less(X7,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f320,axiom,
! [X2,X7] :
( ~ c_less(X7,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f9320,plain,
spl0_1155,
inference(avatar_split_clause,[],[f319,f9318]) ).
fof(f9318,plain,
( spl0_1155
<=> ! [X2,X7] :
( ~ c_less(X7,c_0,tc_IntDef_Oint)
| c_less(X7,c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f319,axiom,
! [X2,X7] :
( ~ c_less(X7,c_0,tc_IntDef_Oint)
| c_less(X7,c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f9316,plain,
spl0_1154,
inference(avatar_split_clause,[],[f283,f9314]) ).
fof(f9314,plain,
( spl0_1154
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_NatArith_Oof__nat(X19,X5) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X19,tc_IntDef_Oint),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f283,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_NatArith_Oof__nat(X19,X5) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X19,tc_IntDef_Oint),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f9312,plain,
spl0_1153,
inference(avatar_split_clause,[],[f219,f9310]) ).
fof(f9310,plain,
( spl0_1153
<=> ! [X9,X39] :
( ~ c_less(X39,X9,tc_IntDef_Oint)
| c_lessequals(X39,c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f219,axiom,
! [X39,X9] :
( ~ c_less(X39,X9,tc_IntDef_Oint)
| c_lessequals(X39,c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f9308,plain,
spl0_1152,
inference(avatar_split_clause,[],[f218,f9306]) ).
fof(f9306,plain,
( spl0_1152
<=> ! [X9,X39] :
( c_less(X39,X9,tc_IntDef_Oint)
| ~ c_lessequals(X39,c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f218,axiom,
! [X39,X9] :
( c_less(X39,X9,tc_IntDef_Oint)
| ~ c_lessequals(X39,c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f9304,plain,
spl0_1151,
inference(avatar_split_clause,[],[f217,f9302]) ).
fof(f9302,plain,
( spl0_1151
<=> ! [X9,X39] :
( ~ c_lessequals(X39,X9,tc_IntDef_Oint)
| c_less(X39,c_plus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f217,axiom,
! [X39,X9] :
( ~ c_lessequals(X39,X9,tc_IntDef_Oint)
| c_less(X39,c_plus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f9300,plain,
( spl0_1150
| ~ spl0_21
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8097,f7857,f3275,f9298]) ).
fof(f9298,plain,
( spl0_1150
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f3275,plain,
( spl0_21
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f8097,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_21
| ~ spl0_921 ),
inference(resolution,[],[f7858,f3277]) ).
fof(f3277,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f3275]) ).
fof(f9296,plain,
spl0_1149,
inference(avatar_split_clause,[],[f216,f9294]) ).
fof(f9294,plain,
( spl0_1149
<=> ! [X9,X39] :
( c_lessequals(X39,X9,tc_IntDef_Oint)
| ~ c_less(X39,c_plus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f216,axiom,
! [X39,X9] :
( c_lessequals(X39,X9,tc_IntDef_Oint)
| ~ c_less(X39,c_plus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f9292,plain,
spl0_1148,
inference(avatar_split_clause,[],[f213,f9290]) ).
fof(f9290,plain,
( spl0_1148
<=> ! [X9,X39] : c_plus(X9,c_uminus(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X9,X39,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f213,axiom,
! [X39,X9] : c_plus(X9,c_uminus(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X9,X39,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(f9287,plain,
spl0_1147,
inference(avatar_split_clause,[],[f210,f9285]) ).
fof(f210,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f9283,plain,
spl0_1146,
inference(avatar_split_clause,[],[f175,f9281]) ).
fof(f9281,plain,
( spl0_1146
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f175,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f9279,plain,
spl0_1145,
inference(avatar_split_clause,[],[f172,f9277]) ).
fof(f9277,plain,
( spl0_1145
<=> ! [X8,X19] : c_GCD_Ogcd(c_Pair(X8,c_times(X8,X19,tc_nat),tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f172,axiom,
! [X8,X19] : c_GCD_Ogcd(c_Pair(X8,c_times(X8,X19,tc_nat),tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9275,plain,
spl0_1144,
inference(avatar_split_clause,[],[f101,f9273]) ).
fof(f9273,plain,
( spl0_1144
<=> ! [X30,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f101,axiom,
! [X19,X30] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9271,plain,
spl0_1143,
inference(avatar_split_clause,[],[f99,f9269]) ).
fof(f9269,plain,
( spl0_1143
<=> ! [X30,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f99,axiom,
! [X19,X30] :
( ~ c_less(c_0,X19,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9267,plain,
spl0_1142,
inference(avatar_split_clause,[],[f43,f9265]) ).
fof(f9265,plain,
( spl0_1142
<=> ! [X2,X5,X23,X7] : c_0 = c_Nat_Osize(c_Pair(X2,X7,X5,X23),tc_prod(X5,X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f43,axiom,
! [X2,X7,X5,X23] : c_0 = c_Nat_Osize(c_Pair(X2,X7,X5,X23),tc_prod(X5,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9263,plain,
spl0_1141,
inference(avatar_split_clause,[],[f31,f9261]) ).
fof(f9261,plain,
( spl0_1141
<=> ! [X20,X5,X4] :
( c_Datatype_Ooption_OSome(X4,X5) = X20
| ~ c_in(X4,c_Datatype_Oo2s(X20,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f31,axiom,
! [X4,X5,X20] :
( c_Datatype_Ooption_OSome(X4,X5) = X20
| ~ c_in(X4,c_Datatype_Oo2s(X20,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9259,plain,
spl0_1140,
inference(avatar_split_clause,[],[f21,f9257]) ).
fof(f9257,plain,
( spl0_1140
<=> ! [X11,X5,X12,X8] : c_Tarski_Opotype_Omore(c_Tarski_Opotype_Opotype__ext(X11,X12,X8,X5,X5),X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f21,axiom,
! [X11,X8,X5,X12] : c_Tarski_Opotype_Omore(c_Tarski_Opotype_Opotype__ext(X11,X12,X8,X5,X5),X5,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__3_0) ).
fof(f9255,plain,
( spl0_1139
| ~ spl0_70
| ~ spl0_920 ),
inference(avatar_split_clause,[],[f8096,f7853,f3520,f9253]) ).
fof(f9253,plain,
( spl0_1139
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f7853,plain,
( spl0_920
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f8096,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_70
| ~ spl0_920 ),
inference(resolution,[],[f7854,f3522]) ).
fof(f7854,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X8,X5) = X8 )
| ~ spl0_920 ),
inference(avatar_component_clause,[],[f7853]) ).
fof(f9251,plain,
spl0_1138,
inference(avatar_split_clause,[],[f20,f9249]) ).
fof(f9249,plain,
( spl0_1138
<=> ! [X11,X13,X14,X5,X8] : c_Tarski_Opotype_Oorder(c_Tarski_Opotype_Opotype__ext(X11,X8,X13,X5,X14),X5,X14) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f20,axiom,
! [X11,X8,X14,X5,X13] : c_Tarski_Opotype_Oorder(c_Tarski_Opotype_Opotype__ext(X11,X8,X13,X5,X14),X5,X14) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__2_0) ).
fof(f9247,plain,
spl0_1137,
inference(avatar_split_clause,[],[f19,f9245]) ).
fof(f9245,plain,
( spl0_1137
<=> ! [X13,X14,X12,X5,X8] : c_Tarski_Opotype_Opset(c_Tarski_Opotype_Opotype__ext(X8,X12,X13,X5,X14),X5,X14) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f19,axiom,
! [X8,X14,X5,X12,X13] : c_Tarski_Opotype_Opset(c_Tarski_Opotype_Opotype__ext(X8,X12,X13,X5,X14),X5,X14) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__1_0) ).
fof(f9223,plain,
( spl0_1136
| ~ spl0_21
| ~ spl0_920 ),
inference(avatar_split_clause,[],[f8095,f7853,f3275,f9221]) ).
fof(f9221,plain,
( spl0_1136
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f8095,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_21
| ~ spl0_920 ),
inference(resolution,[],[f7854,f3277]) ).
fof(f9209,plain,
( spl0_1135
| ~ spl0_15
| ~ spl0_919 ),
inference(avatar_split_clause,[],[f8094,f7849,f3245,f9207]) ).
fof(f9207,plain,
( spl0_1135
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f3245,plain,
( spl0_15
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f7849,plain,
( spl0_919
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X2,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f8094,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_15
| ~ spl0_919 ),
inference(resolution,[],[f7850,f3247]) ).
fof(f3247,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f3245]) ).
fof(f7850,plain,
( ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X2,X2,X5) )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f7849]) ).
fof(f9185,plain,
( spl0_1134
| ~ spl0_15
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8093,f7845,f3245,f9183]) ).
fof(f9183,plain,
( spl0_1134
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f7845,plain,
( spl0_918
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X8,c_0,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f8093,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_15
| ~ spl0_918 ),
inference(resolution,[],[f7846,f3247]) ).
fof(f7846,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X8,c_0,X5) = X8 )
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f7845]) ).
fof(f9131,plain,
( spl0_1133
| ~ spl0_58
| ~ spl0_1009
| ~ spl0_1081 ),
inference(avatar_split_clause,[],[f8822,f8819,f8331,f3460,f9129]) ).
fof(f9129,plain,
( spl0_1133
<=> ! [X2] : c_uminus(X2,tc_IntDef_Oint) = c_div(X2,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f8819,plain,
( spl0_1081
<=> ! [X2] : c_div(X2,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X2,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f8822,plain,
( ! [X2] : c_uminus(X2,tc_IntDef_Oint) = c_div(X2,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1009
| ~ spl0_1081 ),
inference(forward_demodulation,[],[f8820,f8621]) ).
fof(f8820,plain,
( ! [X2] : c_div(X2,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X2,tc_IntDef_Oint)
| ~ spl0_1081 ),
inference(avatar_component_clause,[],[f8819]) ).
fof(f9095,plain,
( spl0_1132
| spl0_671
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f9068,f8759,f6738,f9092]) ).
fof(f9092,plain,
( spl0_1132
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f6738,plain,
( spl0_671
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f9068,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_671
| ~ spl0_1066 ),
inference(resolution,[],[f8760,f6740]) ).
fof(f6740,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_671 ),
inference(avatar_component_clause,[],[f6738]) ).
fof(f9035,plain,
( spl0_1131
| ~ spl0_116
| ~ spl0_1113
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f9004,f8999,f8949,f3744,f9032]) ).
fof(f9032,plain,
( spl0_1131
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f3744,plain,
( spl0_116
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f8949,plain,
( spl0_1113
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f8999,plain,
( spl0_1125
<=> ! [X19] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X19),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f9004,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_1113
| ~ spl0_1125 ),
inference(forward_demodulation,[],[f9003,f8950]) ).
fof(f8950,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1113 ),
inference(avatar_component_clause,[],[f8949]) ).
fof(f9003,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_1125 ),
inference(superposition,[],[f9000,f3746]) ).
fof(f3746,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f3744]) ).
fof(f9000,plain,
( ! [X19] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X19),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1125 ),
inference(avatar_component_clause,[],[f8999]) ).
fof(f9024,plain,
spl0_1130,
inference(avatar_split_clause,[],[f3121,f9022]) ).
fof(f9022,plain,
( spl0_1130
<=> ! [X4,X5] :
( c_IntDef_Oiszero(c_0,X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f3121,plain,
! [X4,X5] :
( c_IntDef_Oiszero(c_0,X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X4,X5) ),
inference(inner_rewriting,[],[f3120]) ).
fof(f3120,plain,
! [X4,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X4,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X4,X5) ),
inference(forward_demodulation,[],[f3119,f980]) ).
fof(f3119,plain,
! [X4,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X4,X5) ),
inference(forward_demodulation,[],[f2928,f2762]) ).
fof(f2928,plain,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X4,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f202,f994]) ).
fof(f202,axiom,
! [X4,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X4,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X4,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f9020,plain,
spl0_1129,
inference(avatar_split_clause,[],[f3006,f9018]) ).
fof(f9018,plain,
( spl0_1129
<=> ! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f3006,plain,
! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23),
inference(forward_demodulation,[],[f2808,f2763]) ).
fof(f2808,plain,
! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23),
inference(definition_unfolding,[],[f74,f1409]) ).
fof(f74,axiom,
! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f9016,plain,
spl0_1128,
inference(avatar_split_clause,[],[f3005,f9014]) ).
fof(f9014,plain,
( spl0_1128
<=> ! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f3005,plain,
! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23),
inference(forward_demodulation,[],[f2807,f2763]) ).
fof(f2807,plain,
! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23),
inference(definition_unfolding,[],[f75,f1409]) ).
fof(f75,axiom,
! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f9012,plain,
spl0_1127,
inference(avatar_split_clause,[],[f2879,f9010]) ).
fof(f9010,plain,
( spl0_1127
<=> ! [X4] :
( c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X4,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f2879,plain,
! [X4] :
( c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X4,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1144,f1409]) ).
fof(f1144,axiom,
! [X4] :
( c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f9008,plain,
spl0_1126,
inference(avatar_split_clause,[],[f2869,f9006]) ).
fof(f9006,plain,
( spl0_1126
<=> ! [X4] :
( ~ c_Parity_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X4,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f2869,plain,
! [X4] :
( ~ c_Parity_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X4,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1143,f1409]) ).
fof(f1143,axiom,
! [X4] :
( ~ c_Parity_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f9001,plain,
( spl0_1125
| ~ spl0_1124 ),
inference(avatar_split_clause,[],[f8997,f8994,f8999]) ).
fof(f8994,plain,
( spl0_1124
<=> ! [X19] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f8997,plain,
( ! [X19] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X19),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1124 ),
inference(forward_demodulation,[],[f8995,f2799]) ).
fof(f8995,plain,
( ! [X19] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1124 ),
inference(avatar_component_clause,[],[f8994]) ).
fof(f8996,plain,
spl0_1124,
inference(avatar_split_clause,[],[f2790,f8994]) ).
fof(f2790,plain,
! [X19] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f253,f1409]) ).
fof(f253,axiom,
! [X19] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X19)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f8992,plain,
( spl0_1123
| ~ spl0_10
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8091,f7841,f3220,f8990]) ).
fof(f8990,plain,
( spl0_1123
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f3220,plain,
( spl0_10
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f7841,plain,
( spl0_917
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f8091,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_10
| ~ spl0_917 ),
inference(resolution,[],[f7842,f3222]) ).
fof(f3222,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f3220]) ).
fof(f7842,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X8,X5) = X8 )
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f7841]) ).
fof(f8988,plain,
( spl0_1122
| ~ spl0_799
| ~ spl0_1121 ),
inference(avatar_split_clause,[],[f8984,f8981,f7290,f8986]) ).
fof(f8986,plain,
( spl0_1122
<=> ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f8981,plain,
( spl0_1121
<=> ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f8984,plain,
( ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X5)
| ~ spl0_799
| ~ spl0_1121 ),
inference(forward_demodulation,[],[f8982,f7291]) ).
fof(f8982,plain,
( ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X5,X5)),X5)
| ~ spl0_1121 ),
inference(avatar_component_clause,[],[f8981]) ).
fof(f8983,plain,
spl0_1121,
inference(avatar_split_clause,[],[f2764,f8981]) ).
fof(f2764,plain,
! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1574,f1581]) ).
fof(f1574,axiom,
! [X5] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f8979,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1697,f8977]) ).
fof(f8977,plain,
( spl0_1120
<=> ! [X2,X5,X7] :
( X2 = X7
| ~ c_in(X7,c_insert(X2,c_emptyset,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1697,axiom,
! [X2,X7,X5] :
( X2 = X7
| ~ c_in(X7,c_insert(X2,c_emptyset,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f8975,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1695,f8973]) ).
fof(f8973,plain,
( spl0_1119
<=> ! [X5,X1,X35] :
( ~ c_less(X1,X35,tc_set(X5))
| c_lessequals(X1,X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1695,axiom,
! [X1,X35,X5] :
( ~ c_less(X1,X35,tc_set(X5))
| c_lessequals(X1,X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f8971,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1694,f8969]) ).
fof(f1694,axiom,
! [X1,X35,X5] :
( ~ c_lessequals(X35,X1,tc_set(X5))
| ~ c_less(X1,X35,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f8967,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1536,f8965]) ).
fof(f8965,plain,
( spl0_1117
<=> ! [X5,X1] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X1,X5)
| c_emptyset = c_Union(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1536,axiom,
! [X1,X5] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X1,X5)
| c_emptyset = c_Union(X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f8963,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1519,f8961]) ).
fof(f8961,plain,
( spl0_1116
<=> ! [X5,X1] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X1,X5)
| c_emptyset = c_Union(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1519,axiom,
! [X1,X5] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X1,X5)
| c_emptyset = c_Union(X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f8959,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1483,f8957]) ).
fof(f8957,plain,
( spl0_1115
<=> ! [X5,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X1,X5)
| c_UNIV = c_Inter(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f1483,axiom,
! [X1,X5] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X1,X5)
| c_UNIV = c_Inter(X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f8955,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1480,f8953]) ).
fof(f8953,plain,
( spl0_1114
<=> ! [X5,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X1,X5)
| c_UNIV = c_Inter(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f1480,axiom,
! [X1,X5] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X1,X5)
| c_UNIV = c_Inter(X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f8951,plain,
( spl0_1113
| ~ spl0_10
| ~ spl0_916 ),
inference(avatar_split_clause,[],[f8089,f7837,f3220,f8949]) ).
fof(f7837,plain,
( spl0_916
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X8,c_0,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f8089,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_10
| ~ spl0_916 ),
inference(resolution,[],[f7838,f3222]) ).
fof(f7838,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X8,c_0,X5) = X8 )
| ~ spl0_916 ),
inference(avatar_component_clause,[],[f7837]) ).
fof(f8947,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1253,f8945]) ).
fof(f1253,axiom,
! [X4,X5] : c_in(c_Pair(X4,X4,X5,X5),c_Relation_OId,tc_prod(X5,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f8943,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1248,f8941]) ).
fof(f1248,axiom,
! [X1,X5] : c_Relation_Odiag(X1,X5) = c_Relation_Oconverse(c_Relation_Odiag(X1,X5),X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f8939,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1231,f8937]) ).
fof(f8937,plain,
( spl0_1110
<=> ! [X2,X5,X8,X23] : c_snd(c_Pair(X2,X8,X23,X5),X23,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f1231,axiom,
! [X2,X8,X5,X23] : c_snd(c_Pair(X2,X8,X23,X5),X23,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f8935,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1229,f8933]) ).
fof(f8933,plain,
( spl0_1109
<=> ! [X23,X7,X5,X8] : c_fst(c_Pair(X8,X7,X5,X23),X5,X23) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f1229,axiom,
! [X8,X7,X5,X23] : c_fst(c_Pair(X8,X7,X5,X23),X5,X23) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f8931,plain,
spl0_1108,
inference(avatar_split_clause,[],[f1207,f8929]) ).
fof(f8929,plain,
( spl0_1108
<=> ! [X4,X19] :
( c_0 = X4
| c_less(c_0,c_Nat_Opower(X4,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f1207,axiom,
! [X19,X4] :
( c_0 = X4
| c_less(c_0,c_Nat_Opower(X4,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f8927,plain,
spl0_1107,
inference(avatar_split_clause,[],[f1206,f8925]) ).
fof(f8925,plain,
( spl0_1107
<=> ! [X19] :
( c_0 = X19
| ~ c_less(c_0,c_Nat_Opower(c_0,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1206,axiom,
! [X19] :
( c_0 = X19
| ~ c_less(c_0,c_Nat_Opower(c_0,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f8923,plain,
spl0_1106,
inference(avatar_split_clause,[],[f1159,f8921]) ).
fof(f8921,plain,
( spl0_1106
<=> ! [X4,X19] :
( c_less(c_0,X19,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X19,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f1159,axiom,
! [X19,X4] :
( c_less(c_0,X19,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X19,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f8919,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1146,f8917]) ).
fof(f8917,plain,
( spl0_1105
<=> ! [X4,X8] :
( c_less(c_0,X8,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1146,axiom,
! [X8,X4] :
( c_less(c_0,X8,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f8915,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1112,f8913]) ).
fof(f8913,plain,
( spl0_1104
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(X2,c_uminus(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f1112,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(X2,c_uminus(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f8911,plain,
spl0_1103,
inference(avatar_split_clause,[],[f1090,f8909]) ).
fof(f8909,plain,
( spl0_1103
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = X2
| c_0 != c_uminus(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1090,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = X2
| c_0 != c_uminus(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
fof(f8907,plain,
( spl0_1102
| ~ spl0_702
| ~ spl0_869
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f8078,f7821,f7574,f6880,f8904]) ).
fof(f8904,plain,
( spl0_1102
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f7574,plain,
( spl0_869
<=> 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_869])]) ).
fof(f7821,plain,
( spl0_912
<=> ! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X39,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f8078,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_702
| ~ spl0_869
| ~ spl0_912 ),
inference(forward_demodulation,[],[f8076,f6882]) ).
fof(f8076,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_869
| ~ spl0_912 ),
inference(superposition,[],[f7822,f7576]) ).
fof(f7576,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f7574]) ).
fof(f7822,plain,
( ! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X39,c_Numeral_Obit_OB0))
| ~ spl0_912 ),
inference(avatar_component_clause,[],[f7821]) ).
fof(f8902,plain,
spl0_1101,
inference(avatar_split_clause,[],[f1078,f8900]) ).
fof(f8900,plain,
( spl0_1101
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f1078,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f8898,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1076,f8896]) ).
fof(f8896,plain,
( spl0_1100
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1076,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f8894,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1062,f8892]) ).
fof(f8892,plain,
( spl0_1099
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(X2,X5) = c_minus(c_0,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1062,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(X2,X5) = c_minus(c_0,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f8890,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1037,f8888]) ).
fof(f8888,plain,
( spl0_1098
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X2
| c_0 != c_HOL_Oabs(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1037,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X2
| c_0 != c_HOL_Oabs(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
fof(f8886,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1036,f8884]) ).
fof(f8884,plain,
( spl0_1097
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(c_uminus(X2,X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1036,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(c_uminus(X2,X5),X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f8882,plain,
spl0_1096,
inference(avatar_split_clause,[],[f904,f8880]) ).
fof(f8880,plain,
( spl0_1096
<=> ! [X30,X19] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_0 = c_minus(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f904,axiom,
! [X19,X30] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_0 = c_minus(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f8878,plain,
spl0_1095,
inference(avatar_split_clause,[],[f903,f8876]) ).
fof(f8876,plain,
( spl0_1095
<=> ! [X30,X19] :
( c_lessequals(X30,X19,tc_nat)
| c_0 != c_minus(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f903,axiom,
! [X19,X30] :
( c_lessequals(X30,X19,tc_nat)
| c_0 != c_minus(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f8874,plain,
spl0_1094,
inference(avatar_split_clause,[],[f698,f8872]) ).
fof(f8872,plain,
( spl0_1094
<=> ! [X40] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X40,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f698,axiom,
! [X40] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X40,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_2) ).
fof(f8870,plain,
spl0_1093,
inference(avatar_split_clause,[],[f697,f8868]) ).
fof(f8868,plain,
( spl0_1093
<=> ! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X40,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f697,axiom,
! [X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X40,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f8866,plain,
spl0_1092,
inference(avatar_split_clause,[],[f676,f8864]) ).
fof(f8864,plain,
( spl0_1092
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X30
| c_0 != c_NatArith_Oof__nat(X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f676,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X30
| c_0 != c_NatArith_Oof__nat(X30,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).
fof(f8862,plain,
( spl0_1091
| ~ spl0_88
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f8056,f7744,f3610,f8860]) ).
fof(f8860,plain,
( spl0_1091
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f3610,plain,
( spl0_88
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f7744,plain,
( spl0_893
<=> ! [X5,X8] :
( ~ class_LOrder_Omeet__semilorder(X5)
| c_LOrder_Omeet(X8,X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f8056,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_88
| ~ spl0_893 ),
inference(resolution,[],[f7745,f3612]) ).
fof(f3612,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f3610]) ).
fof(f7745,plain,
( ! [X8,X5] :
( ~ class_LOrder_Omeet__semilorder(X5)
| c_LOrder_Omeet(X8,X8,X5) = X8 )
| ~ spl0_893 ),
inference(avatar_component_clause,[],[f7744]) ).
fof(f8858,plain,
spl0_1090,
inference(avatar_split_clause,[],[f624,f8856]) ).
fof(f8856,plain,
( spl0_1090
<=> ! [X5,X44,X19] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Orotate(X19,X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f624,axiom,
! [X44,X19,X5] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Orotate(X19,X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f8854,plain,
spl0_1089,
inference(avatar_split_clause,[],[f595,f8852]) ).
fof(f8852,plain,
( spl0_1089
<=> ! [X45,X5,X44] :
( X44 = X45
| c_List_Orev(X44,X5) != c_List_Orev(X45,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f595,axiom,
! [X44,X45,X5] :
( X44 = X45
| c_List_Orev(X44,X5) != c_List_Orev(X45,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f8850,plain,
spl0_1088,
inference(avatar_split_clause,[],[f468,f8848]) ).
fof(f8848,plain,
( spl0_1088
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_less(c_0,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f468,axiom,
! [X44,X5] :
( c_List_Olist_ONil = X44
| c_less(c_0,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f8846,plain,
spl0_1087,
inference(avatar_split_clause,[],[f413,f8844]) ).
fof(f8844,plain,
( spl0_1087
<=> ! [X5,X46] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X46,X5)
| c_List_Olist_ONil = c_List_Oconcat(X46,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f413,axiom,
! [X46,X5] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X46,X5)
| c_List_Olist_ONil = c_List_Oconcat(X46,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f8842,plain,
spl0_1086,
inference(avatar_split_clause,[],[f406,f8840]) ).
fof(f8840,plain,
( spl0_1086
<=> ! [X52,X53,X50,X51] :
( X51 = X53
| c_List_Ochar_OChar(X50,X51) != c_List_Ochar_OChar(X52,X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f406,axiom,
! [X50,X51,X52,X53] :
( X51 = X53
| c_List_Ochar_OChar(X50,X51) != c_List_Ochar_OChar(X52,X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f8838,plain,
spl0_1085,
inference(avatar_split_clause,[],[f405,f8836]) ).
fof(f8836,plain,
( spl0_1085
<=> ! [X51,X53,X50,X52] :
( X50 = X52
| c_List_Ochar_OChar(X50,X51) != c_List_Ochar_OChar(X52,X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f405,axiom,
! [X50,X51,X52,X53] :
( X50 = X52
| c_List_Ochar_OChar(X50,X51) != c_List_Ochar_OChar(X52,X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f8834,plain,
spl0_1084,
inference(avatar_split_clause,[],[f374,f8832]) ).
fof(f8832,plain,
( spl0_1084
<=> ! [X5,X46] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X46,X5)
| c_List_Olist_ONil = c_List_Oconcat(X46,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f374,axiom,
! [X46,X5] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X46,X5)
| c_List_Olist_ONil = c_List_Oconcat(X46,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f8830,plain,
spl0_1083,
inference(avatar_split_clause,[],[f353,f8828]) ).
fof(f8828,plain,
( spl0_1083
<=> ! [X9,X39] :
( ~ c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X9,tc_IntDef_Oint),X39,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f353,axiom,
! [X39,X9] :
( ~ c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X9,tc_IntDef_Oint),X39,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f8826,plain,
spl0_1082,
inference(avatar_split_clause,[],[f352,f8824]) ).
fof(f352,axiom,
! [X39,X9] :
( c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X9,tc_IntDef_Oint),X39,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f8821,plain,
spl0_1081,
inference(avatar_split_clause,[],[f332,f8819]) ).
fof(f332,axiom,
! [X2] : c_div(X2,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X2,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f8817,plain,
( spl0_1080
| ~ spl0_30
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f8055,f7744,f3320,f8815]) ).
fof(f8815,plain,
( spl0_1080
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f3320,plain,
( spl0_30
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f8055,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_30
| ~ spl0_893 ),
inference(resolution,[],[f7745,f3322]) ).
fof(f3322,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f3320]) ).
fof(f8813,plain,
spl0_1079,
inference(avatar_split_clause,[],[f305,f8811]) ).
fof(f8811,plain,
( spl0_1079
<=> ! [X9,X39] :
( ~ c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X9,c_uminus(X39,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f305,axiom,
! [X39,X9] :
( ~ c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X9,c_uminus(X39,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f8809,plain,
spl0_1078,
inference(avatar_split_clause,[],[f304,f8807]) ).
fof(f304,axiom,
! [X39,X9] :
( c_Divides_Oop_Advd(X9,X39,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X9,c_uminus(X39,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f8805,plain,
spl0_1077,
inference(avatar_split_clause,[],[f295,f8803]) ).
fof(f8803,plain,
( spl0_1077
<=> ! [X9,X39] :
( c_less(X39,X9,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X39),c_IntDef_Onat(X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f295,axiom,
! [X39,X9] :
( c_less(X39,X9,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X39),c_IntDef_Onat(X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f8801,plain,
spl0_1076,
inference(avatar_split_clause,[],[f294,f8799]) ).
fof(f8799,plain,
( spl0_1076
<=> ! [X9,X39] :
( c_less(c_0,X9,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X39),c_IntDef_Onat(X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f294,axiom,
! [X39,X9] :
( c_less(c_0,X9,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X39),c_IntDef_Onat(X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f8797,plain,
spl0_1075,
inference(avatar_split_clause,[],[f293,f8795]) ).
fof(f8795,plain,
( spl0_1075
<=> ! [X30,X19] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f293,axiom,
! [X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| c_less(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f8793,plain,
spl0_1074,
inference(avatar_split_clause,[],[f292,f8791]) ).
fof(f8791,plain,
( spl0_1074
<=> ! [X30,X19] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f292,axiom,
! [X19,X30] :
( c_less(X30,X19,tc_nat)
| ~ c_less(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f8789,plain,
spl0_1073,
inference(avatar_split_clause,[],[f291,f8787]) ).
fof(f8787,plain,
( spl0_1073
<=> ! [X30,X19] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f291,axiom,
! [X19,X30] :
( ~ c_lessequals(X30,X19,tc_nat)
| c_lessequals(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f8785,plain,
spl0_1072,
inference(avatar_split_clause,[],[f290,f8783]) ).
fof(f8783,plain,
( spl0_1072
<=> ! [X30,X19] :
( c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f290,axiom,
! [X19,X30] :
( c_lessequals(X30,X19,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X30),c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f8781,plain,
spl0_1071,
inference(avatar_split_clause,[],[f272,f8779]) ).
fof(f8779,plain,
( spl0_1071
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_IntDef_Oint(X19),X5) = c_NatArith_Oof__nat(X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f272,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_IntDef_Oint(X19),X5) = c_NatArith_Oof__nat(X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f8777,plain,
spl0_1070,
inference(avatar_split_clause,[],[f260,f8775]) ).
fof(f8775,plain,
( spl0_1070
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X9
| c_0 != c_IntDef_Oof__int(X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f260,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X9
| c_0 != c_IntDef_Oof__int(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
fof(f8773,plain,
( spl0_1069
| ~ spl0_95
| ~ spl0_892 ),
inference(avatar_split_clause,[],[f8054,f7740,f3645,f8771]) ).
fof(f8771,plain,
( spl0_1069
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f3645,plain,
( spl0_95
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f7740,plain,
( spl0_892
<=> ! [X5,X8] :
( ~ class_LOrder_Ojoin__semilorder(X5)
| c_LOrder_Ojoin(X8,X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f8054,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_95
| ~ spl0_892 ),
inference(resolution,[],[f7741,f3647]) ).
fof(f3647,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f3645]) ).
fof(f7741,plain,
( ! [X8,X5] :
( ~ class_LOrder_Ojoin__semilorder(X5)
| c_LOrder_Ojoin(X8,X8,X5) = X8 )
| ~ spl0_892 ),
inference(avatar_component_clause,[],[f7740]) ).
fof(f8769,plain,
spl0_1068,
inference(avatar_split_clause,[],[f255,f8767]) ).
fof(f8767,plain,
( spl0_1068
<=> ! [X19,X30] :
( c_0 = X30
| c_IntDef_Oint(X30) != c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f255,axiom,
! [X19,X30] :
( c_0 = X30
| c_IntDef_Oint(X30) != c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f8765,plain,
spl0_1067,
inference(avatar_split_clause,[],[f254,f8763]) ).
fof(f8763,plain,
( spl0_1067
<=> ! [X30,X19] :
( c_0 = X19
| c_IntDef_Oint(X30) != c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f254,axiom,
! [X19,X30] :
( c_0 = X19
| c_IntDef_Oint(X30) != c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f8761,plain,
spl0_1066,
inference(avatar_split_clause,[],[f144,f8759]) ).
fof(f144,axiom,
! [X1,X5] :
( c_0 = c_Finite__Set_Ocard(X1,X5)
| c_in(X1,c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f8757,plain,
spl0_1065,
inference(avatar_split_clause,[],[f140,f8755]) ).
fof(f8755,plain,
( spl0_1065
<=> ! [X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMin(c_insert(X8,c_emptyset,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f140,axiom,
! [X8,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMin(c_insert(X8,c_emptyset,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f8753,plain,
spl0_1064,
inference(avatar_split_clause,[],[f130,f8751]) ).
fof(f8751,plain,
( spl0_1064
<=> ! [X5,X8] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMax(c_insert(X8,c_emptyset,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f130,axiom,
! [X8,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMax(c_insert(X8,c_emptyset,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f8749,plain,
spl0_1063,
inference(avatar_split_clause,[],[f100,f8747]) ).
fof(f8747,plain,
( spl0_1063
<=> ! [X8,X19] :
( ~ c_less(X8,X19,tc_nat)
| c_Divides_Oop_Amod(X8,X19,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f100,axiom,
! [X8,X19] :
( ~ c_less(X8,X19,tc_nat)
| c_Divides_Oop_Amod(X8,X19,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f8745,plain,
spl0_1062,
inference(avatar_split_clause,[],[f89,f8743]) ).
fof(f8743,plain,
( spl0_1062
<=> ! [X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_1 = c_div(X19,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f89,axiom,
! [X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_1 = c_div(X19,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f8741,plain,
spl0_1061,
inference(avatar_split_clause,[],[f81,f8739]) ).
fof(f8739,plain,
( spl0_1061
<=> ! [X30,X19] :
( ~ c_less(X30,X19,tc_nat)
| c_0 = c_div(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f81,axiom,
! [X19,X30] :
( ~ c_less(X30,X19,tc_nat)
| c_0 = c_div(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f8737,plain,
spl0_1060,
inference(avatar_split_clause,[],[f66,f8735]) ).
fof(f8735,plain,
( spl0_1060
<=> ! [X18,X23,X5,X25,X24] : c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_ONumb(X18,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f66,axiom,
! [X18,X24,X5,X25,X23] : c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_ONumb(X18,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb_0) ).
fof(f8733,plain,
spl0_1059,
inference(avatar_split_clause,[],[f65,f8731]) ).
fof(f8731,plain,
( spl0_1059
<=> ! [X24,X23,X5,X25,X2] : c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_OLeaf(X2,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f65,axiom,
! [X2,X24,X5,X25,X23] : c_Datatype__Universe_OScons(X24,X25,X5,X23) != c_Datatype__Universe_OLeaf(X2,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf_0) ).
fof(f8728,plain,
spl0_1058,
inference(avatar_split_clause,[],[f64,f8726]) ).
fof(f8726,plain,
( spl0_1058
<=> ! [X2,X24,X23,X5,X25] : c_Datatype__Universe_OAtom(X2,X5,X23) != c_Datatype__Universe_OScons(X24,X25,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f64,axiom,
! [X2,X24,X5,X25,X23] : c_Datatype__Universe_OAtom(X2,X5,X23) != c_Datatype__Universe_OScons(X24,X25,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom_0) ).
fof(f8724,plain,
spl0_1057,
inference(avatar_split_clause,[],[f45,f8722]) ).
fof(f8722,plain,
( spl0_1057
<=> ! [X5,X23,X7] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X7,X23,X5),tc_sum(X5,X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f45,axiom,
! [X7,X5,X23] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X7,X23,X5),tc_sum(X5,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f8720,plain,
spl0_1056,
inference(avatar_split_clause,[],[f44,f8718]) ).
fof(f8718,plain,
( spl0_1056
<=> ! [X2,X5,X23] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X2,X5,X23),tc_sum(X5,X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f44,axiom,
! [X2,X5,X23] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X2,X5,X23),tc_sum(X5,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f8716,plain,
spl0_1055,
inference(avatar_split_clause,[],[f40,f8714]) ).
fof(f8714,plain,
( spl0_1055
<=> ! [X22,X2,X5] :
( X2 = X22
| c_Datatype_Ooption_OSome(X22,X5) != c_Datatype_Ooption_OSome(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f40,axiom,
! [X2,X22,X5] :
( X2 = X22
| c_Datatype_Ooption_OSome(X22,X5) != c_Datatype_Ooption_OSome(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f8712,plain,
spl0_1054,
inference(avatar_split_clause,[],[f35,f8710]) ).
fof(f8710,plain,
( spl0_1054
<=> ! [X4,X21] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X4,X21),X21) = c_insert(X4,c_emptyset,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f35,axiom,
! [X21,X4] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X4,X21),X21) = c_insert(X4,c_emptyset,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f8708,plain,
spl0_1053,
inference(avatar_split_clause,[],[f34,f8706]) ).
fof(f8706,plain,
( spl0_1053
<=> ! [X4,X5] :
( c_Datatype_Ooption_ONone = X4
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X4,X5),X5) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f34,axiom,
! [X4,X5] :
( c_Datatype_Ooption_ONone = X4
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X4,X5),X5) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f8704,plain,
spl0_1052,
inference(avatar_split_clause,[],[f33,f8702]) ).
fof(f8702,plain,
( spl0_1052
<=> ! [X4,X5] :
( c_Datatype_Ooption_ONone = X4
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X4,X5),X5) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f33,axiom,
! [X4,X5] :
( c_Datatype_Ooption_ONone = X4
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X4,X5),X5) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f8665,plain,
( spl0_1051
| ~ spl0_801
| ~ spl0_1024 ),
inference(avatar_split_clause,[],[f8643,f8392,f7298,f8663]) ).
fof(f8663,plain,
( spl0_1051
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f8392,plain,
( spl0_1024
<=> ! [X5] : c_Pow(c_emptyset,X5) = c_insert(c_emptyset,c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f8643,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_801
| ~ spl0_1024 ),
inference(superposition,[],[f7299,f8393]) ).
fof(f8393,plain,
( ! [X5] : c_Pow(c_emptyset,X5) = c_insert(c_emptyset,c_emptyset,tc_set(X5))
| ~ spl0_1024 ),
inference(avatar_component_clause,[],[f8392]) ).
fof(f8640,plain,
( spl0_1050
| ~ spl0_873
| ~ spl0_1006 ),
inference(avatar_split_clause,[],[f8604,f8319,f7596,f8638]) ).
fof(f8638,plain,
( spl0_1050
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f7596,plain,
( spl0_873
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f8319,plain,
( spl0_1006
<=> ! [X29,X55] :
( ~ c_lessequals(X55,X29,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X29,X55) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f8604,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_873
| ~ spl0_1006 ),
inference(resolution,[],[f8320,f7597]) ).
fof(f7597,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f7596]) ).
fof(f8320,plain,
( ! [X29,X55] :
( ~ c_lessequals(X55,X29,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X29,X55) )
| ~ spl0_1006 ),
inference(avatar_component_clause,[],[f8319]) ).
fof(f8593,plain,
( spl0_1049
| ~ spl0_801
| ~ spl0_998 ),
inference(avatar_split_clause,[],[f8588,f8287,f7298,f8591]) ).
fof(f8591,plain,
( spl0_1049
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f8287,plain,
( spl0_998
<=> ! [X21] : c_List_Olistset(c_List_Olist_ONil,X21) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f8588,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_801
| ~ spl0_998 ),
inference(superposition,[],[f7299,f8288]) ).
fof(f8288,plain,
( ! [X21] : c_List_Olistset(c_List_Olist_ONil,X21) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X21))
| ~ spl0_998 ),
inference(avatar_component_clause,[],[f8287]) ).
fof(f8574,plain,
( spl0_1048
| ~ spl0_31
| ~ spl0_892 ),
inference(avatar_split_clause,[],[f8053,f7740,f3325,f8572]) ).
fof(f8572,plain,
( spl0_1048
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f3325,plain,
( spl0_31
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f8053,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_31
| ~ spl0_892 ),
inference(resolution,[],[f7741,f3327]) ).
fof(f3327,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f3325]) ).
fof(f8494,plain,
( ~ spl0_80
| spl0_1047
| ~ spl0_669
| ~ spl0_890 ),
inference(avatar_split_clause,[],[f8047,f7732,f6730,f8492,f3570]) ).
fof(f3570,plain,
( spl0_80
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f6730,plain,
( spl0_669
<=> ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f7732,plain,
( spl0_890
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_NatArith_Oof__nat(X19,X5),c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f8047,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_669
| ~ spl0_890 ),
inference(superposition,[],[f7733,f6731]) ).
fof(f6731,plain,
( ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8
| ~ spl0_669 ),
inference(avatar_component_clause,[],[f6730]) ).
fof(f7733,plain,
( ! [X19,X5] :
( c_in(c_NatArith_Oof__nat(X19,X5),c_IntDef_ONats,X5)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5) )
| ~ spl0_890 ),
inference(avatar_component_clause,[],[f7732]) ).
fof(f8482,plain,
spl0_1046,
inference(avatar_split_clause,[],[f3074,f8480]) ).
fof(f8480,plain,
( spl0_1046
<=> ! [X9] :
( ~ c_less(c_1,c_IntDef_Onat(X9),tc_nat)
| c_less(c_1,X9,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f3074,plain,
! [X9] :
( ~ c_less(c_1,c_IntDef_Onat(X9),tc_nat)
| c_less(c_1,X9,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2900,f2763]) ).
fof(f2900,plain,
! [X9] :
( c_less(c_1,X9,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X9),tc_nat) ),
inference(definition_unfolding,[],[f211,f1409]) ).
fof(f211,axiom,
! [X9] :
( c_less(c_1,X9,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f8478,plain,
spl0_1045,
inference(avatar_split_clause,[],[f3063,f8476]) ).
fof(f8476,plain,
( spl0_1045
<=> ! [X9] :
( c_less(c_1,c_IntDef_Onat(X9),tc_nat)
| ~ c_less(c_1,X9,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f3063,plain,
! [X9] :
( c_less(c_1,c_IntDef_Onat(X9),tc_nat)
| ~ c_less(c_1,X9,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2883,f2763]) ).
fof(f2883,plain,
! [X9] :
( ~ c_less(c_1,X9,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X9),tc_nat) ),
inference(definition_unfolding,[],[f212,f1409]) ).
fof(f212,axiom,
! [X9] :
( ~ c_less(c_1,X9,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f8474,plain,
spl0_1044,
inference(avatar_split_clause,[],[f3058,f8472]) ).
fof(f8472,plain,
( spl0_1044
<=> ! [X30,X19] :
( c_1 != c_times(X30,X19,tc_nat)
| c_1 = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f3058,plain,
! [X19,X30] :
( c_1 != c_times(X30,X19,tc_nat)
| c_1 = X30 ),
inference(forward_demodulation,[],[f2875,f2763]) ).
fof(f2875,plain,
! [X19,X30] :
( c_1 = X30
| c_times(X30,X19,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f957,f1409]) ).
fof(f957,axiom,
! [X19,X30] :
( c_1 = X30
| c_Suc(c_0) != c_times(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
fof(f8470,plain,
spl0_1043,
inference(avatar_split_clause,[],[f3057,f8468]) ).
fof(f8468,plain,
( spl0_1043
<=> ! [X30,X19] :
( c_1 != c_times(X30,X19,tc_nat)
| c_1 = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f3057,plain,
! [X19,X30] :
( c_1 != c_times(X30,X19,tc_nat)
| c_1 = X19 ),
inference(forward_demodulation,[],[f2874,f2763]) ).
fof(f2874,plain,
! [X19,X30] :
( c_1 = X19
| c_times(X30,X19,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f928,f1409]) ).
fof(f928,axiom,
! [X19,X30] :
( c_1 = X19
| c_Suc(c_0) != c_times(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
fof(f8466,plain,
spl0_1042,
inference(avatar_split_clause,[],[f2794,f8464]) ).
fof(f2794,plain,
! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X39,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f997,f978]) ).
fof(f997,axiom,
! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X39,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f8462,plain,
spl0_1041,
inference(avatar_split_clause,[],[f2783,f8460]) ).
fof(f8460,plain,
( spl0_1041
<=> ! [X5,X8] : c_Relation_OImage(c_Relation_Odiag(X8,X5),X8,X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f2783,plain,
! [X8,X5] : c_Relation_OImage(c_Relation_Odiag(X8,X5),X8,X5,X5) = X8,
inference(definition_unfolding,[],[f1468,f1238]) ).
fof(f1468,axiom,
! [X8,X5] : c_inter(X8,X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f8458,plain,
( spl0_1040
| ~ spl0_822
| ~ spl0_862 ),
inference(avatar_split_clause,[],[f7666,f7545,f7385,f8456]) ).
fof(f8456,plain,
( spl0_1040
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f7385,plain,
( spl0_822
<=> ! [X30] :
( c_0 = X30
| ~ c_Divides_Oop_Advd(c_0,X30,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f7545,plain,
( spl0_862
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f7666,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_822
| ~ spl0_862 ),
inference(resolution,[],[f7546,f7386]) ).
fof(f7386,plain,
( ! [X30] :
( ~ c_Divides_Oop_Advd(c_0,X30,tc_IntDef_Oint)
| c_0 = X30 )
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f7385]) ).
fof(f7546,plain,
( ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_862 ),
inference(avatar_component_clause,[],[f7545]) ).
fof(f8454,plain,
spl0_1039,
inference(avatar_split_clause,[],[f2782,f8452]) ).
fof(f8452,plain,
( spl0_1039
<=> ! [X5,X8] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X5),X8,X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f2782,plain,
! [X8,X5] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X5),X8,X5,X5) = X8,
inference(definition_unfolding,[],[f1466,f1238]) ).
fof(f1466,axiom,
! [X8,X5] : c_inter(c_UNIV,X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f8450,plain,
spl0_1038,
inference(avatar_split_clause,[],[f2781,f8448]) ).
fof(f8448,plain,
( spl0_1038
<=> ! [X5,X8] : c_Relation_OImage(c_Relation_Odiag(X8,X5),c_UNIV,X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f2781,plain,
! [X8,X5] : c_Relation_OImage(c_Relation_Odiag(X8,X5),c_UNIV,X5,X5) = X8,
inference(definition_unfolding,[],[f1467,f1238]) ).
fof(f1467,axiom,
! [X8,X5] : c_inter(X8,c_UNIV,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f8446,plain,
spl0_1037,
inference(avatar_split_clause,[],[f2775,f8444]) ).
fof(f8444,plain,
( spl0_1037
<=> ! [X18] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f2775,plain,
! [X18] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f25,f1409]) ).
fof(f25,axiom,
! [X18] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8442,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1655,f8440]) ).
fof(f8440,plain,
( spl0_1036
<=> ! [X6,X5] :
( ~ c_Wellfounded__Recursion_Owf(X6,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X6,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f1655,axiom,
! [X6,X5] :
( ~ c_Wellfounded__Recursion_Owf(X6,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X6,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8438,plain,
spl0_1035,
inference(avatar_split_clause,[],[f1654,f8436]) ).
fof(f8436,plain,
( spl0_1035
<=> ! [X6,X5] :
( ~ c_Wellfounded__Recursion_Owf(X6,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X6,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f1654,axiom,
! [X6,X5] :
( ~ c_Wellfounded__Recursion_Owf(X6,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X6,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8434,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1627,f8432]) ).
fof(f8432,plain,
( spl0_1034
<=> ! [X30,X19] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1627,axiom,
! [X19,X30] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8430,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1626,f8428]) ).
fof(f8428,plain,
( spl0_1033
<=> ! [X19,X30] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f1626,axiom,
! [X19,X30] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X30,X19,tc_nat,tc_nat)),X30,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8426,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1583,f8424]) ).
fof(f8424,plain,
( spl0_1032
<=> ! [X6,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X6,X5)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f1583,axiom,
! [X6,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X6,X5)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X5,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8422,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1582,f8420]) ).
fof(f8420,plain,
( spl0_1031
<=> ! [X6,X5] :
( c_Wellfounded__Recursion_Oacyclic(X6,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1582,axiom,
! [X6,X5] :
( c_Wellfounded__Recursion_Oacyclic(X6,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X6,X5,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8418,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1567,f8416]) ).
fof(f8416,plain,
( spl0_1030
<=> ! [X2,X5,X23,X7] : c_Sum__Type_OInl(X2,X5,X23) != c_Sum__Type_OInr(X7,X23,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1567,axiom,
! [X2,X7,X5,X23] : c_Sum__Type_OInl(X2,X5,X23) != c_Sum__Type_OInr(X7,X23,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr_0) ).
fof(f8414,plain,
( spl0_1029
| ~ spl0_822
| ~ spl0_861 ),
inference(avatar_split_clause,[],[f7665,f7541,f7385,f8412]) ).
fof(f8412,plain,
( spl0_1029
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f7541,plain,
( spl0_861
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f7665,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_822
| ~ spl0_861 ),
inference(resolution,[],[f7542,f7386]) ).
fof(f7542,plain,
( ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_861 ),
inference(avatar_component_clause,[],[f7541]) ).
fof(f8410,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1532,f8408]) ).
fof(f8408,plain,
( spl0_1028
<=> ! [X5,X8] : c_uminus(c_uminus(X8,tc_set(X5)),tc_set(X5)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f1532,axiom,
! [X8,X5] : c_uminus(c_uminus(X8,tc_set(X5)),tc_set(X5)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8406,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1524,f8404]) ).
fof(f8404,plain,
( spl0_1027
<=> ! [X5,X1] :
( c_emptyset = X1
| c_in(c_Main_Oall__not__in__conv__1(X1,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1524,axiom,
! [X1,X5] :
( c_emptyset = X1
| c_in(c_Main_Oall__not__in__conv__1(X1,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8402,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1501,f8400]) ).
fof(f1501,axiom,
! [X1,X35,X5] :
( c_emptyset = X35
| c_emptyset != c_union(X1,X35,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8398,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1500,f8396]) ).
fof(f1500,axiom,
! [X1,X35,X5] :
( c_emptyset = X1
| c_emptyset != c_union(X1,X35,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8394,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1491,f8392]) ).
fof(f1491,axiom,
! [X5] : c_Pow(c_emptyset,X5) = c_insert(c_emptyset,c_emptyset,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8390,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1255,f8388]) ).
fof(f8388,plain,
( spl0_1023
<=> ! [X82,X21] : c_Relation_OId = c_Nat_Opower(X82,c_0,tc_set(tc_prod(X21,X21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1255,axiom,
! [X82,X21] : c_Relation_OId = c_Nat_Opower(X82,c_0,tc_set(tc_prod(X21,X21))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8386,plain,
spl0_1022,
inference(avatar_split_clause,[],[f1254,f8384]) ).
fof(f8384,plain,
( spl0_1022
<=> ! [X5,X8] : c_Nat_Opower(X8,c_1,tc_set(tc_prod(X5,X5))) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f1254,axiom,
! [X8,X5] : c_Nat_Opower(X8,c_1,tc_set(tc_prod(X5,X5))) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8382,plain,
spl0_1021,
inference(avatar_split_clause,[],[f1247,f8380]) ).
fof(f8380,plain,
( spl0_1021
<=> ! [X5,X8,X23] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X5,X23),X23,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1247,axiom,
! [X8,X5,X23] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X5,X23),X23,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8378,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1163,f8376]) ).
fof(f8376,plain,
( spl0_1020
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f1163,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8374,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1162,f8372]) ).
fof(f8372,plain,
( spl0_1019
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1162,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X4,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8370,plain,
( spl0_1018
| ~ spl0_115
| ~ spl0_819 ),
inference(avatar_split_clause,[],[f7603,f7373,f3739,f8367]) ).
fof(f8367,plain,
( spl0_1018
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f7373,plain,
( spl0_819
<=> ! [X19] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f7603,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_115
| ~ spl0_819 ),
inference(superposition,[],[f7374,f3741]) ).
fof(f7374,plain,
( ! [X19] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint))
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7373]) ).
fof(f8365,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1158,f8363]) ).
fof(f8363,plain,
( spl0_1017
<=> ! [X4,X19] :
( c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X19,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1158,axiom,
! [X19,X4] :
( c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X19,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8361,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1150,f8359]) ).
fof(f8359,plain,
( spl0_1016
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(c_times(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1150,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(c_times(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8357,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1149,f8355]) ).
fof(f8355,plain,
( spl0_1015
<=> ! [X4,X8] :
( ~ c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_times(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1149,axiom,
! [X8,X4] :
( ~ c_Parity_Oeven(X4,tc_nat)
| c_Parity_Oeven(c_times(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8353,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1145,f8351]) ).
fof(f1145,axiom,
! [X8,X4] :
( c_Parity_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8349,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1081,f8347]) ).
fof(f8347,plain,
( spl0_1013
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_uminus(X8,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1081,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_uminus(X8,X5),X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8345,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1019,f8343]) ).
fof(f8343,plain,
( spl0_1012
<=> ! [X39] : c_Numeral_Obin__succ(c_Numeral_OBit(X39,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X39),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f8341,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1015,f8339]) ).
fof(f8339,plain,
( spl0_1011
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1015,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8337,plain,
spl0_1010,
inference(avatar_split_clause,[],[f1001,f8335]) ).
fof(f8335,plain,
( spl0_1010
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f1001,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8333,plain,
spl0_1009,
inference(avatar_split_clause,[],[f983,f8331]) ).
fof(f983,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_uminus(c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8329,plain,
spl0_1008,
inference(avatar_split_clause,[],[f897,f8327]) ).
fof(f8327,plain,
( spl0_1008
<=> ! [X30,X19] :
( c_0 = X19
| c_0 != c_plus(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f897,axiom,
! [X19,X30] :
( c_0 = X19
| c_0 != c_plus(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8325,plain,
spl0_1007,
inference(avatar_split_clause,[],[f896,f8323]) ).
fof(f8323,plain,
( spl0_1007
<=> ! [X19,X30] :
( c_0 = X30
| c_0 != c_plus(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f896,axiom,
! [X19,X30] :
( c_0 = X30
| c_0 != c_plus(X30,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8321,plain,
spl0_1006,
inference(avatar_split_clause,[],[f651,f8319]) ).
fof(f651,axiom,
! [X29,X55] :
( ~ c_lessequals(X55,X29,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X29,X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8317,plain,
spl0_1005,
inference(avatar_split_clause,[],[f623,f8315]) ).
fof(f8315,plain,
( spl0_1005
<=> ! [X5,X44] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Orotate1(X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f623,axiom,
! [X44,X5] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Orotate1(X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8313,plain,
spl0_1004,
inference(avatar_split_clause,[],[f622,f8311]) ).
fof(f8311,plain,
( spl0_1004
<=> ! [X5,X44] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Orev(X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f622,axiom,
! [X44,X5] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Orev(X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8309,plain,
spl0_1003,
inference(avatar_split_clause,[],[f619,f8307]) ).
fof(f8307,plain,
( spl0_1003
<=> ! [X5,X44] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Oremdups(X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f619,axiom,
! [X44,X5] : c_List_Oset(X44,X5) = c_List_Oset(c_List_Oremdups(X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8305,plain,
spl0_1002,
inference(avatar_split_clause,[],[f609,f8303]) ).
fof(f8303,plain,
( spl0_1002
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X44
| c_append(X44,X45,X5) != X45 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f609,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X44
| c_append(X44,X45,X5) != X45 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f8301,plain,
spl0_1001,
inference(avatar_split_clause,[],[f605,f8299]) ).
fof(f8299,plain,
( spl0_1001
<=> ! [X5,X44,X19] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_List_Orotate(X19,X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f605,axiom,
! [X44,X19,X5] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_List_Orotate(X19,X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8297,plain,
spl0_1000,
inference(avatar_split_clause,[],[f585,f8295]) ).
fof(f8295,plain,
( spl0_1000
<=> ! [X4,X5,X44] : c_List_Oremove1(X4,c_List_Olist_OCons(X4,X44,X5),X5) = X44 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f585,axiom,
! [X44,X4,X5] : c_List_Oremove1(X4,c_List_Olist_OCons(X4,X44,X5),X5) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8293,plain,
spl0_999,
inference(avatar_split_clause,[],[f557,f8291]) ).
fof(f8291,plain,
( spl0_999
<=> ! [X5,X44,X8] : c_List_Onth(c_List_Olist_OCons(X8,X44,X5),c_0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f557,axiom,
! [X8,X44,X5] : c_List_Onth(c_List_Olist_OCons(X8,X44,X5),c_0,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8289,plain,
spl0_998,
inference(avatar_split_clause,[],[f504,f8287]) ).
fof(f8285,plain,
( ~ spl0_58
| spl0_997
| ~ spl0_837
| ~ spl0_952 ),
inference(avatar_split_clause,[],[f8136,f7983,f7445,f8282,f3460]) ).
fof(f8282,plain,
( spl0_997
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f7445,plain,
( spl0_837
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f7983,plain,
( spl0_952
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f8136,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_837
| ~ spl0_952 ),
inference(superposition,[],[f7446,f7985]) ).
fof(f7985,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_952 ),
inference(avatar_component_clause,[],[f7983]) ).
fof(f7446,plain,
( ! [X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_837 ),
inference(avatar_component_clause,[],[f7445]) ).
fof(f8280,plain,
spl0_996,
inference(avatar_split_clause,[],[f472,f8278]) ).
fof(f8278,plain,
( spl0_996
<=> ! [X4,X5,X8] : c_Nat_Osize(c_List_Oreplicate(X8,X4,X5),tc_List_Olist(X5)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f472,axiom,
! [X8,X4,X5] : c_Nat_Osize(c_List_Oreplicate(X8,X4,X5),tc_List_Olist(X5)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8276,plain,
spl0_995,
inference(avatar_split_clause,[],[f462,f8274]) ).
fof(f8274,plain,
( spl0_995
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_0 != c_Nat_Osize(X44,tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f462,axiom,
! [X44,X5] :
( c_List_Olist_ONil = X44
| c_0 != c_Nat_Osize(X44,tc_List_Olist(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8272,plain,
spl0_994,
inference(avatar_split_clause,[],[f430,f8270]) ).
fof(f8270,plain,
( spl0_994
<=> ! [X54,X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Osublist(X44,X54,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f430,axiom,
! [X54,X44,X5] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Osublist(X44,X54,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8268,plain,
spl0_993,
inference(avatar_split_clause,[],[f429,f8266]) ).
fof(f8266,plain,
( spl0_993
<=> ! [X5,X44,X19] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Orotate(X19,X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f429,axiom,
! [X44,X19,X5] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Orotate(X19,X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8264,plain,
spl0_992,
inference(avatar_split_clause,[],[f428,f8262]) ).
fof(f8262,plain,
( spl0_992
<=> ! [X5,X44,X19] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_List_Orotate(X19,X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f428,axiom,
! [X44,X19,X5] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_List_Orotate(X19,X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8260,plain,
spl0_991,
inference(avatar_split_clause,[],[f425,f8258]) ).
fof(f8258,plain,
( spl0_991
<=> ! [X4,X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Oremove1(X4,X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f425,axiom,
! [X44,X4,X5] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Oremove1(X4,X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8256,plain,
spl0_990,
inference(avatar_split_clause,[],[f424,f8254]) ).
fof(f8254,plain,
( spl0_990
<=> ! [X29,X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Odrop(X29,X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f424,axiom,
! [X29,X44,X5] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Odrop(X29,X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8252,plain,
spl0_989,
inference(avatar_split_clause,[],[f421,f8250]) ).
fof(f8250,plain,
( spl0_989
<=> ! [X45,X5,X44] :
( c_List_Odistinct(X45,X5)
| ~ c_List_Odistinct(c_append(X44,X45,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f421,axiom,
! [X44,X45,X5] :
( c_List_Odistinct(X45,X5)
| ~ c_List_Odistinct(c_append(X44,X45,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8248,plain,
spl0_988,
inference(avatar_split_clause,[],[f420,f8246]) ).
fof(f8246,plain,
( spl0_988
<=> ! [X45,X5,X44] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_append(X44,X45,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f420,axiom,
! [X44,X45,X5] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_append(X44,X45,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8244,plain,
spl0_987,
inference(avatar_split_clause,[],[f418,f8242]) ).
fof(f8242,plain,
( spl0_987
<=> ! [X4,X21,X44] :
( c_List_Odistinct(X44,X21)
| ~ c_List_Odistinct(c_List_Olist_OCons(X4,X44,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f418,axiom,
! [X21,X44,X4] :
( c_List_Odistinct(X44,X21)
| ~ c_List_Odistinct(c_List_Olist_OCons(X4,X44,X21),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8240,plain,
spl0_986,
inference(avatar_split_clause,[],[f398,f8238]) ).
fof(f8238,plain,
( spl0_986
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X45
| c_append(X44,X45,X5) != X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f398,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X45
| c_append(X44,X45,X5) != X44 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f8236,plain,
spl0_985,
inference(avatar_split_clause,[],[f376,f8234]) ).
fof(f8234,plain,
( spl0_985
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X45
| c_List_Olist_ONil != c_append(X44,X45,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f376,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X45
| c_List_Olist_ONil != c_append(X44,X45,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).
fof(f8232,plain,
spl0_984,
inference(avatar_split_clause,[],[f375,f8230]) ).
fof(f8230,plain,
( spl0_984
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_append(X44,X45,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f375,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_append(X44,X45,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).
fof(f8228,plain,
spl0_983,
inference(avatar_split_clause,[],[f362,f8226]) ).
fof(f8226,plain,
( spl0_983
<=> ! [X2,X7] : c_0 = c_Divides_Oop_Amod(c_times(X7,X2,tc_IntDef_Oint),X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f362,axiom,
! [X2,X7] : c_0 = c_Divides_Oop_Amod(c_times(X7,X2,tc_IntDef_Oint),X7,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8224,plain,
spl0_982,
inference(avatar_split_clause,[],[f361,f8222]) ).
fof(f8222,plain,
( spl0_982
<=> ! [X2,X7] : c_0 = c_Divides_Oop_Amod(c_times(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f361,axiom,
! [X2,X7] : c_0 = c_Divides_Oop_Amod(c_times(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8220,plain,
spl0_981,
inference(avatar_split_clause,[],[f348,f8218]) ).
fof(f8218,plain,
( spl0_981
<=> ! [X4,X19] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X4,tc_IntDef_Oint),X19,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f348,axiom,
! [X19,X4] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X4,tc_IntDef_Oint),X19,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8216,plain,
spl0_980,
inference(avatar_split_clause,[],[f336,f8214]) ).
fof(f8214,plain,
( spl0_980
<=> ! [X2] :
( c_0 = X2
| c_1 = c_div(X2,X2,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f336,axiom,
! [X2] :
( c_0 = X2
| c_1 = c_div(X2,X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8212,plain,
spl0_979,
inference(avatar_split_clause,[],[f306,f8210]) ).
fof(f306,axiom,
! [X2,X7] : c_0 = c_div(c_Divides_Oop_Amod(X2,X7,tc_IntDef_Oint),X7,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8208,plain,
spl0_978,
inference(avatar_split_clause,[],[f288,f8206]) ).
fof(f8206,plain,
( spl0_978
<=> ! [X9] :
( ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f288,axiom,
! [X9] :
( ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8204,plain,
spl0_977,
inference(avatar_split_clause,[],[f287,f8202]) ).
fof(f8202,plain,
( spl0_977
<=> ! [X9] :
( c_less(c_0,X9,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f287,axiom,
! [X9] :
( c_less(c_0,X9,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8200,plain,
( ~ spl0_976
| ~ spl0_801
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8134,f7942,f7298,f8197]) ).
fof(f8197,plain,
( spl0_976
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f8134,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_801
| ~ spl0_942 ),
inference(superposition,[],[f7299,f7944]) ).
fof(f8195,plain,
spl0_975,
inference(avatar_split_clause,[],[f286,f8193]) ).
fof(f8193,plain,
( spl0_975
<=> ! [X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f286,axiom,
! [X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_less(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8191,plain,
spl0_974,
inference(avatar_split_clause,[],[f285,f8189]) ).
fof(f8189,plain,
( spl0_974
<=> ! [X19] :
( c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f285,axiom,
! [X19] :
( c_less(c_0,X19,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8187,plain,
spl0_973,
inference(avatar_split_clause,[],[f245,f8185]) ).
fof(f8185,plain,
( spl0_973
<=> ! [X9] :
( c_lessequals(c_0,X9,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f245,axiom,
! [X9] :
( c_lessequals(c_0,X9,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8183,plain,
spl0_972,
inference(avatar_split_clause,[],[f244,f8181]) ).
fof(f8181,plain,
( spl0_972
<=> ! [X9] :
( ~ c_lessequals(c_0,X9,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X9)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f244,axiom,
! [X9] :
( ~ c_lessequals(c_0,X9,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8179,plain,
spl0_971,
inference(avatar_split_clause,[],[f214,f8177]) ).
fof(f8177,plain,
( spl0_971
<=> ! [X9] :
( c_0 = X9
| ~ c_less(c_HOL_Oabs(X9,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f214,axiom,
! [X9] :
( c_0 = X9
| ~ c_less(c_HOL_Oabs(X9,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8175,plain,
spl0_970,
inference(avatar_split_clause,[],[f111,f8173]) ).
fof(f8173,plain,
( spl0_970
<=> ! [X6,X5,X1] :
( c_emptyset = X1
| c_emptyset != c_Equiv__Relations_Oquotient(X1,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f111,axiom,
! [X1,X6,X5] :
( c_emptyset = X1
| c_emptyset != c_Equiv__Relations_Oquotient(X1,X6,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
fof(f8171,plain,
spl0_969,
inference(avatar_split_clause,[],[f107,f8169]) ).
fof(f8169,plain,
( spl0_969
<=> ! [X30,X19] : c_0 = c_div(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f107,axiom,
! [X19,X30] : c_0 = c_div(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8167,plain,
spl0_968,
inference(avatar_split_clause,[],[f105,f8165]) ).
fof(f8165,plain,
( spl0_968
<=> ! [X30,X19] : c_0 = c_Divides_Oop_Amod(c_times(X30,X19,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f105,axiom,
! [X19,X30] : c_0 = c_Divides_Oop_Amod(c_times(X30,X19,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8163,plain,
spl0_967,
inference(avatar_split_clause,[],[f103,f8161]) ).
fof(f8161,plain,
( spl0_967
<=> ! [X30,X19] : c_0 = c_Divides_Oop_Amod(c_times(X19,X30,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f103,axiom,
! [X19,X30] : c_0 = c_Divides_Oop_Amod(c_times(X19,X30,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8159,plain,
spl0_966,
inference(avatar_split_clause,[],[f58,f8157]) ).
fof(f8157,plain,
( spl0_966
<=> ! [X18,X5,X2,X23] : c_Datatype__Universe_OLeaf(X2,X5,X23) != c_Datatype__Universe_ONumb(X18,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f58,axiom,
! [X2,X18,X5,X23] : c_Datatype__Universe_OLeaf(X2,X5,X23) != c_Datatype__Universe_ONumb(X18,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb_0) ).
fof(f8154,plain,
spl0_965,
inference(avatar_split_clause,[],[f57,f8152]) ).
fof(f8152,plain,
( spl0_965
<=> ! [X24,X25,X5,X23] : c_Datatype__Universe_OIn0(X24,X5,X23) != c_Datatype__Universe_OIn1(X25,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f57,axiom,
! [X24,X5,X25,X23] : c_Datatype__Universe_OIn0(X24,X5,X23) != c_Datatype__Universe_OIn1(X25,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0_0) ).
fof(f8052,plain,
( spl0_964
| ~ spl0_46
| ~ spl0_847 ),
inference(avatar_split_clause,[],[f7648,f7485,f3400,f8049]) ).
fof(f8049,plain,
( spl0_964
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f3400,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f7485,plain,
( spl0_847
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f7648,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_46
| ~ spl0_847 ),
inference(resolution,[],[f7486,f3402]) ).
fof(f3402,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f3400]) ).
fof(f7486,plain,
( ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) )
| ~ spl0_847 ),
inference(avatar_component_clause,[],[f7485]) ).
fof(f8031,plain,
( spl0_963
| ~ spl0_46
| ~ spl0_846 ),
inference(avatar_split_clause,[],[f7647,f7481,f3400,f8028]) ).
fof(f8028,plain,
( spl0_963
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f7481,plain,
( spl0_846
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f7647,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_46
| ~ spl0_846 ),
inference(resolution,[],[f7482,f3402]) ).
fof(f7482,plain,
( ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) )
| ~ spl0_846 ),
inference(avatar_component_clause,[],[f7481]) ).
fof(f8026,plain,
spl0_962,
inference(avatar_split_clause,[],[f3046,f8024]) ).
fof(f3046,plain,
! [X5] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f1035,f1021]) ).
fof(f1035,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f8022,plain,
spl0_961,
inference(avatar_split_clause,[],[f2998,f8020]) ).
fof(f8020,plain,
( spl0_961
<=> ! [X30] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X30,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2998,plain,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X30,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2798,f2763]) ).
fof(f2798,plain,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X30,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f165,f1409]) ).
fof(f165,axiom,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X30,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f8018,plain,
spl0_960,
inference(avatar_split_clause,[],[f2997,f8016]) ).
fof(f8016,plain,
( spl0_960
<=> ! [X30] : c_1 = c_GCD_Ogcd(c_Pair(X30,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2997,plain,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(X30,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2797,f2763]) ).
fof(f2797,plain,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f164,f1409]) ).
fof(f164,axiom,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(X30,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f8014,plain,
spl0_959,
inference(avatar_split_clause,[],[f2769,f8012]) ).
fof(f8012,plain,
( spl0_959
<=> ! [X19] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2769,plain,
! [X19] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1659,f1409]) ).
fof(f1659,axiom,
! [X19] : c_less(c_0,c_Suc(X19),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f8010,plain,
spl0_958,
inference(avatar_split_clause,[],[f2768,f8008]) ).
fof(f8008,plain,
( spl0_958
<=> ! [X19] : c_less(X19,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2768,plain,
! [X19] : c_less(X19,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1657,f1409]) ).
fof(f1657,axiom,
! [X19] : c_less(X19,c_Suc(X19),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f8006,plain,
spl0_957,
inference(avatar_split_clause,[],[f1844,f8004]) ).
fof(f8004,plain,
( spl0_957
<=> ! [X93,X92] :
( ~ class_Finite__Set_Ofinite(X93)
| ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_sum(X93,X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f1844,axiom,
! [X92,X93] :
( ~ class_Finite__Set_Ofinite(X93)
| ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_sum(X93,X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f8002,plain,
spl0_956,
inference(avatar_split_clause,[],[f1838,f8000]) ).
fof(f8000,plain,
( spl0_956
<=> ! [X93,X92] :
( ~ class_Finite__Set_Ofinite(X93)
| ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_prod(X93,X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f1838,axiom,
! [X92,X93] :
( ~ class_Finite__Set_Ofinite(X93)
| ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_prod(X93,X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f7998,plain,
spl0_955,
inference(avatar_split_clause,[],[f1788,f7996]) ).
fof(f7996,plain,
( spl0_955
<=> ! [X93,X92] :
( ~ class_Finite__Set_Ofinite(X93)
| ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_fun(X93,X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f1788,axiom,
! [X92,X93] :
( ~ class_Finite__Set_Ofinite(X93)
| ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_fun(X93,X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f7994,plain,
spl0_954,
inference(avatar_split_clause,[],[f1686,f7992]) ).
fof(f7992,plain,
( spl0_954
<=> ! [X77,X41] : c_in(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1686,axiom,
! [X41,X77] : c_in(c_SetInterval_OgreaterThanLessThan(X77,X41,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(f7990,plain,
spl0_953,
inference(avatar_split_clause,[],[f1685,f7988]) ).
fof(f7988,plain,
( spl0_953
<=> ! [X77,X41] : c_in(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1685,axiom,
! [X41,X77] : c_in(c_SetInterval_OgreaterThanLessThan(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f7986,plain,
( spl0_952
| ~ spl0_58
| ~ spl0_843 ),
inference(avatar_split_clause,[],[f7644,f7469,f3460,f7983]) ).
fof(f7469,plain,
( spl0_843
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f7644,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_843 ),
inference(resolution,[],[f7470,f3462]) ).
fof(f7470,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) )
| ~ spl0_843 ),
inference(avatar_component_clause,[],[f7469]) ).
fof(f7981,plain,
spl0_951,
inference(avatar_split_clause,[],[f1684,f7979]) ).
fof(f7979,plain,
( spl0_951
<=> ! [X77,X41] : c_in(c_SetInterval_OgreaterThanAtMost(X77,X41,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1684,axiom,
! [X41,X77] : c_in(c_SetInterval_OgreaterThanAtMost(X77,X41,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(f7977,plain,
spl0_950,
inference(avatar_split_clause,[],[f1683,f7975]) ).
fof(f7975,plain,
( spl0_950
<=> ! [X77,X41] : c_in(c_SetInterval_OgreaterThanAtMost(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f1683,axiom,
! [X41,X77] : c_in(c_SetInterval_OgreaterThanAtMost(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f7973,plain,
spl0_949,
inference(avatar_split_clause,[],[f1681,f7971]) ).
fof(f7971,plain,
( spl0_949
<=> ! [X77,X41] : c_in(c_SetInterval_OatLeastLessThan(X77,X41,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1681,axiom,
! [X41,X77] : c_in(c_SetInterval_OatLeastLessThan(X77,X41,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(f7969,plain,
spl0_948,
inference(avatar_split_clause,[],[f1680,f7967]) ).
fof(f7967,plain,
( spl0_948
<=> ! [X77,X41] : c_in(c_SetInterval_OatLeastLessThan(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1680,axiom,
! [X41,X77] : c_in(c_SetInterval_OatLeastLessThan(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f7965,plain,
spl0_947,
inference(avatar_split_clause,[],[f1679,f7963]) ).
fof(f7963,plain,
( spl0_947
<=> ! [X77,X41] : c_in(c_SetInterval_OatLeastAtMost(X77,X41,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f1679,axiom,
! [X41,X77] : c_in(c_SetInterval_OatLeastAtMost(X77,X41,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(f7961,plain,
spl0_946,
inference(avatar_split_clause,[],[f1678,f7959]) ).
fof(f7959,plain,
( spl0_946
<=> ! [X77,X41] : c_in(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1678,axiom,
! [X41,X77] : c_in(c_SetInterval_OatLeastAtMost(X77,X41,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f7957,plain,
spl0_945,
inference(avatar_split_clause,[],[f1629,f7955]) ).
fof(f7955,plain,
( spl0_945
<=> ! [X19,X30] : c_lessequals(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint),c_IntDef_Oint(X30),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1629,axiom,
! [X19,X30] : c_lessequals(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint),c_IntDef_Oint(X30),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f7953,plain,
spl0_944,
inference(avatar_split_clause,[],[f1564,f7951]) ).
fof(f7951,plain,
( spl0_944
<=> ! [X5,X1] :
( c_emptyset = X1
| ~ c_lessequals(X1,c_emptyset,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1564,axiom,
! [X1,X5] :
( c_emptyset = X1
| ~ c_lessequals(X1,c_emptyset,tc_set(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f7949,plain,
spl0_943,
inference(avatar_split_clause,[],[f1525,f7947]) ).
fof(f7947,plain,
( spl0_943
<=> ! [X5,X8] : c_Set_Ocontents(c_insert(X8,c_emptyset,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1525,axiom,
! [X8,X5] : c_Set_Ocontents(c_insert(X8,c_emptyset,X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f7945,plain,
spl0_942,
inference(avatar_split_clause,[],[f1399,f7942]) ).
fof(f1399,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(f7939,plain,
spl0_941,
inference(avatar_split_clause,[],[f1357,f7937]) ).
fof(f7937,plain,
( spl0_941
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(X2,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1357,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(X2,c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f7935,plain,
spl0_940,
inference(avatar_split_clause,[],[f1356,f7933]) ).
fof(f7933,plain,
( spl0_940
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(c_0,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1356,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(c_0,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f7931,plain,
spl0_939,
inference(avatar_split_clause,[],[f1339,f7929]) ).
fof(f7929,plain,
( spl0_939
<=> ! [X5,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(c_1,X31,X5) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1339,axiom,
! [X31,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(c_1,X31,X5) = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f7927,plain,
spl0_938,
inference(avatar_split_clause,[],[f1338,f7925]) ).
fof(f7925,plain,
( spl0_938
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(X7,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1338,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(X7,c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f7923,plain,
spl0_937,
inference(avatar_split_clause,[],[f1335,f7921]) ).
fof(f7921,plain,
( spl0_937
<=> ! [X5,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(X31,c_1,X5) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1335,axiom,
! [X31,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(X31,c_1,X5) = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f7919,plain,
spl0_936,
inference(avatar_split_clause,[],[f1334,f7917]) ).
fof(f7917,plain,
( spl0_936
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(c_0,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1334,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(c_0,X7,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f7915,plain,
spl0_935,
inference(avatar_split_clause,[],[f1244,f7913]) ).
fof(f7913,plain,
( spl0_935
<=> ! [X5,X8] : c_Relation_ORange(c_Relation_Odiag(X8,X5),X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1244,axiom,
! [X8,X5] : c_Relation_ORange(c_Relation_Odiag(X8,X5),X5,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f7911,plain,
spl0_934,
inference(avatar_split_clause,[],[f1242,f7909]) ).
fof(f7909,plain,
( spl0_934
<=> ! [X5,X8,X23] : c_Relation_Orel__comp(X8,c_Relation_OId,X5,X23,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1242,axiom,
! [X8,X5,X23] : c_Relation_Orel__comp(X8,c_Relation_OId,X5,X23,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f7907,plain,
spl0_933,
inference(avatar_split_clause,[],[f1236,f7905]) ).
fof(f7905,plain,
( spl0_933
<=> ! [X5,X8,X23] : c_Relation_Orel__comp(c_Relation_OId,X8,X23,X23,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1236,axiom,
! [X8,X5,X23] : c_Relation_Orel__comp(c_Relation_OId,X8,X23,X23,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f7903,plain,
spl0_932,
inference(avatar_split_clause,[],[f1234,f7901]) ).
fof(f7901,plain,
( spl0_932
<=> ! [X5,X8] : c_Relation_ODomain(c_Relation_Odiag(X8,X5),X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1234,axiom,
! [X8,X5] : c_Relation_ODomain(c_Relation_Odiag(X8,X5),X5,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f7899,plain,
spl0_931,
inference(avatar_split_clause,[],[f1222,f7897]) ).
fof(f7897,plain,
( spl0_931
<=> ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(X2,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1222,axiom,
! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(X2,c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f7895,plain,
spl0_930,
inference(avatar_split_clause,[],[f1219,f7893]) ).
fof(f1219,axiom,
! [X8,X5] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X8,c_1,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f7891,plain,
spl0_929,
inference(avatar_split_clause,[],[f1218,f7889]) ).
fof(f1218,axiom,
! [X19,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X19,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f7887,plain,
spl0_928,
inference(avatar_split_clause,[],[f1157,f7885]) ).
fof(f7885,plain,
( spl0_928
<=> ! [X4] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X4,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1157,axiom,
! [X4] :
( ~ c_Parity_Oeven(X4,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X4,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f7883,plain,
spl0_927,
inference(avatar_split_clause,[],[f1156,f7881]) ).
fof(f7881,plain,
( spl0_927
<=> ! [X4] :
( c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X4,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1156,axiom,
! [X4] :
( c_Parity_Oeven(X4,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X4,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f7879,plain,
spl0_926,
inference(avatar_split_clause,[],[f1132,f7877]) ).
fof(f1132,axiom,
! [X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omax(X8,X8,X23) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f7875,plain,
spl0_925,
inference(avatar_split_clause,[],[f1127,f7873]) ).
fof(f1127,axiom,
! [X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omin(X8,X8,X23) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f7871,plain,
spl0_924,
inference(avatar_split_clause,[],[f1116,f7869]) ).
fof(f7869,plain,
( spl0_924
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f1116,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f7867,plain,
spl0_923,
inference(avatar_split_clause,[],[f1115,f7865]) ).
fof(f7865,plain,
( spl0_923
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1115,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f7863,plain,
spl0_922,
inference(avatar_split_clause,[],[f1106,f7861]) ).
fof(f7861,plain,
( spl0_922
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_OrderedGroup_Onprt(X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f1106,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_OrderedGroup_Onprt(X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f7859,plain,
spl0_921,
inference(avatar_split_clause,[],[f1083,f7857]) ).
fof(f1083,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X8,c_1,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f7855,plain,
spl0_920,
inference(avatar_split_clause,[],[f1082,f7853]) ).
fof(f1082,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X8,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f7851,plain,
spl0_919,
inference(avatar_split_clause,[],[f1070,f7849]) ).
fof(f1070,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X2,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f7847,plain,
spl0_918,
inference(avatar_split_clause,[],[f1063,f7845]) ).
fof(f1063,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X8,c_0,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f7843,plain,
spl0_917,
inference(avatar_split_clause,[],[f1061,f7841]) ).
fof(f1061,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X8,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f7839,plain,
spl0_916,
inference(avatar_split_clause,[],[f1050,f7837]) ).
fof(f1050,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X8,c_0,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f7835,plain,
spl0_915,
inference(avatar_split_clause,[],[f1047,f7833]) ).
fof(f7833,plain,
( spl0_915
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_HOL_Oabs(X2,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1047,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_HOL_Oabs(X2,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f7831,plain,
spl0_914,
inference(avatar_split_clause,[],[f1045,f7829]) ).
fof(f7829,plain,
( spl0_914
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_HOL_Oabs(c_0,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f1045,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_HOL_Oabs(c_0,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f7827,plain,
spl0_913,
inference(avatar_split_clause,[],[f1042,f7825]) ).
fof(f7825,plain,
( spl0_913
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_0,c_HOL_Oabs(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f1042,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_0,c_HOL_Oabs(X2,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f7823,plain,
spl0_912,
inference(avatar_split_clause,[],[f1018,f7821]) ).
fof(f1018,axiom,
! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X39,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f7819,plain,
( ~ spl0_910
| spl0_911
| ~ spl0_701
| ~ spl0_837 ),
inference(avatar_split_clause,[],[f7638,f7445,f6875,f7816,f7812]) ).
fof(f7812,plain,
( spl0_910
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f7816,plain,
( spl0_911
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f7638,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_701
| ~ spl0_837 ),
inference(superposition,[],[f7446,f6877]) ).
fof(f7810,plain,
spl0_909,
inference(avatar_split_clause,[],[f730,f7808]) ).
fof(f7808,plain,
( spl0_909
<=> ! [X39] : c_IntDef_Onat(c_Numeral_Onumber__of(X39,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X39,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f730,axiom,
! [X39] : c_IntDef_Onat(c_Numeral_Onumber__of(X39,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X39,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f7806,plain,
spl0_908,
inference(avatar_split_clause,[],[f683,f7804]) ).
fof(f7804,plain,
( spl0_908
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_NatArith_Oof__nat(X30,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f683,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_NatArith_Oof__nat(X30,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f7802,plain,
spl0_907,
inference(avatar_split_clause,[],[f680,f7800]) ).
fof(f7800,plain,
( spl0_907
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_NatArith_Oof__nat(c_0,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f680,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_NatArith_Oof__nat(c_0,X5),c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f7798,plain,
spl0_906,
inference(avatar_split_clause,[],[f670,f7796]) ).
fof(f7796,plain,
( spl0_906
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_NatArith_Oof__nat(X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f670,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_NatArith_Oof__nat(X19,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f7794,plain,
spl0_905,
inference(avatar_split_clause,[],[f644,f7792]) ).
fof(f7792,plain,
( spl0_905
<=> ! [X4,X21,X8] : c_List_Otl(c_List_Olist_OCons(X4,X8,X21),X21) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f644,axiom,
! [X21,X8,X4] : c_List_Otl(c_List_Olist_OCons(X4,X8,X21),X21) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f7790,plain,
spl0_904,
inference(avatar_split_clause,[],[f615,f7788]) ).
fof(f7788,plain,
( spl0_904
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_emptyset != c_List_Oset(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f615,axiom,
! [X44,X5] :
( c_List_Olist_ONil = X44
| c_emptyset != c_List_Oset(X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
fof(f7786,plain,
spl0_903,
inference(avatar_split_clause,[],[f600,f7784]) ).
fof(f7784,plain,
( spl0_903
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_List_Orotate1(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f600,axiom,
! [X44,X5] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_List_Orotate1(X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f7782,plain,
spl0_902,
inference(avatar_split_clause,[],[f582,f7780]) ).
fof(f7780,plain,
( spl0_902
<=> ! [X4,X5] :
( c_List_Olist_ONil = X4
| c_List_Olist_ONil != c_List_Oremdups(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f582,axiom,
! [X4,X5] :
( c_List_Olist_ONil = X4
| c_List_Olist_ONil != c_List_Oremdups(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
fof(f7778,plain,
spl0_901,
inference(avatar_split_clause,[],[f453,f7776]) ).
fof(f7776,plain,
( spl0_901
<=> ! [X4,X5] : c_List_Olast(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f453,axiom,
! [X4,X5] : c_List_Olast(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f7774,plain,
spl0_900,
inference(avatar_split_clause,[],[f444,f7772]) ).
fof(f7772,plain,
( spl0_900
<=> ! [X5,X44,X8] : c_List_Ohd(c_List_Olist_OCons(X8,X44,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f444,axiom,
! [X8,X44,X5] : c_List_Ohd(c_List_Olist_OCons(X8,X44,X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f7770,plain,
spl0_899,
inference(avatar_split_clause,[],[f427,f7768]) ).
fof(f7768,plain,
( spl0_899
<=> ! [X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Orev(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f427,axiom,
! [X44,X5] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Orev(X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f7766,plain,
spl0_898,
inference(avatar_split_clause,[],[f426,f7764]) ).
fof(f7764,plain,
( spl0_898
<=> ! [X5,X44] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_List_Orev(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f426,axiom,
! [X44,X5] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_List_Orev(X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f7762,plain,
spl0_897,
inference(avatar_split_clause,[],[f415,f7760]) ).
fof(f7760,plain,
( spl0_897
<=> ! [X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Orotate1(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f415,axiom,
! [X44,X5] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Orotate1(X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f7758,plain,
spl0_896,
inference(avatar_split_clause,[],[f414,f7756]) ).
fof(f7756,plain,
( spl0_896
<=> ! [X5,X44] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_List_Orotate1(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f414,axiom,
! [X44,X5] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_List_Orotate1(X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f7754,plain,
spl0_895,
inference(avatar_split_clause,[],[f402,f7752]) ).
fof(f7752,plain,
( spl0_895
<=> ! [X4,X21] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X4,c_List_Olist_ONil,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f402,axiom,
! [X21,X4] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X4,c_List_Olist_ONil,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f7750,plain,
spl0_894,
inference(avatar_split_clause,[],[f378,f7748]) ).
fof(f7748,plain,
( spl0_894
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_List_Orev(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f378,axiom,
! [X44,X5] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_List_Orev(X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f7746,plain,
spl0_893,
inference(avatar_split_clause,[],[f364,f7744]) ).
fof(f364,axiom,
! [X8,X5] :
( ~ class_LOrder_Omeet__semilorder(X5)
| c_LOrder_Omeet(X8,X8,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f7742,plain,
spl0_892,
inference(avatar_split_clause,[],[f363,f7740]) ).
fof(f363,axiom,
! [X8,X5] :
( ~ class_LOrder_Ojoin__semilorder(X5)
| c_LOrder_Ojoin(X8,X8,X5) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f7738,plain,
spl0_891,
inference(avatar_split_clause,[],[f355,f7736]) ).
fof(f7736,plain,
( spl0_891
<=> ! [X2] : c_0 = c_Divides_Oop_Amod(X2,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f355,axiom,
! [X2] : c_0 = c_Divides_Oop_Amod(X2,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(f7734,plain,
spl0_890,
inference(avatar_split_clause,[],[f284,f7732]) ).
fof(f284,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_NatArith_Oof__nat(X19,X5),c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f7730,plain,
( spl0_889
| ~ spl0_27
| ~ spl0_830 ),
inference(avatar_split_clause,[],[f7613,f7417,f3305,f7727]) ).
fof(f7727,plain,
( spl0_889
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f3305,plain,
( spl0_27
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f7417,plain,
( spl0_830
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_1 = c_NatArith_Oof__nat(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f7613,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_27
| ~ spl0_830 ),
inference(resolution,[],[f7418,f3307]) ).
fof(f3307,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f3305]) ).
fof(f7418,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_1 = c_NatArith_Oof__nat(c_1,X5) )
| ~ spl0_830 ),
inference(avatar_component_clause,[],[f7417]) ).
fof(f7725,plain,
spl0_888,
inference(avatar_split_clause,[],[f257,f7723]) ).
fof(f7723,plain,
( spl0_888
<=> ! [X19,X30] : ~ c_less(c_IntDef_Oint(X19),c_uminus(c_IntDef_Oint(X30),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f257,axiom,
! [X19,X30] : ~ c_less(c_IntDef_Oint(X19),c_uminus(c_IntDef_Oint(X30),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f7721,plain,
spl0_887,
inference(avatar_split_clause,[],[f250,f7719]) ).
fof(f7719,plain,
( spl0_887
<=> ! [X9] :
( ~ c_lessequals(X9,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f250,axiom,
! [X9] :
( ~ c_lessequals(X9,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f7717,plain,
spl0_886,
inference(avatar_split_clause,[],[f241,f7715]) ).
fof(f7715,plain,
( spl0_886
<=> ! [X19] :
( c_0 = X19
| ~ c_lessequals(c_IntDef_Oint(X19),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f241,axiom,
! [X19] :
( c_0 = X19
| ~ c_lessequals(c_IntDef_Oint(X19),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f7713,plain,
spl0_885,
inference(avatar_split_clause,[],[f240,f7711]) ).
fof(f7711,plain,
( spl0_885
<=> ! [X19,X30] :
( X19 = X30
| c_IntDef_Oint(X30) != c_IntDef_Oint(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f240,axiom,
! [X19,X30] :
( X19 = X30
| c_IntDef_Oint(X30) != c_IntDef_Oint(X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f7709,plain,
spl0_884,
inference(avatar_split_clause,[],[f173,f7707]) ).
fof(f7707,plain,
( spl0_884
<=> ! [X8] : c_GCD_Ogcd(c_Pair(X8,X8,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f173,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(X8,X8,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f7705,plain,
spl0_883,
inference(avatar_split_clause,[],[f163,f7703]) ).
fof(f7703,plain,
( spl0_883
<=> ! [X8] : c_GCD_Ogcd(c_Pair(c_0,X8,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f163,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(c_0,X8,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f7701,plain,
spl0_882,
inference(avatar_split_clause,[],[f162,f7699]) ).
fof(f7699,plain,
( spl0_882
<=> ! [X8] : c_GCD_Ogcd(c_Pair(X8,c_0,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f162,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(X8,c_0,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f7697,plain,
spl0_881,
inference(avatar_split_clause,[],[f42,f7695]) ).
fof(f7695,plain,
( spl0_881
<=> ! [X2,X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X2,X5),tc_Datatype_Ooption(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f42,axiom,
! [X2,X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X2,X5),tc_Datatype_Ooption(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f7693,plain,
spl0_880,
inference(avatar_split_clause,[],[f36,f7691]) ).
fof(f7691,plain,
( spl0_880
<=> ! [X20,X5] :
( c_Datatype_Ooption_ONone = X20
| c_emptyset != c_Datatype_Oo2s(X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f36,axiom,
! [X5,X20] :
( c_Datatype_Ooption_ONone = X20
| c_emptyset != c_Datatype_Oo2s(X20,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f7688,plain,
spl0_879,
inference(avatar_split_clause,[],[f32,f7686]) ).
fof(f7686,plain,
( spl0_879
<=> ! [X4,X5] : c_in(X4,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X4,X5),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f32,axiom,
! [X4,X5] : c_in(X4,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X4,X5),X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f7684,plain,
( spl0_878
| ~ spl0_54
| ~ spl0_829 ),
inference(avatar_split_clause,[],[f7611,f7413,f3440,f7681]) ).
fof(f7681,plain,
( spl0_878
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f3440,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f7413,plain,
( spl0_829
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f7611,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_829 ),
inference(resolution,[],[f7414,f3442]) ).
fof(f3442,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f7414,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) )
| ~ spl0_829 ),
inference(avatar_component_clause,[],[f7413]) ).
fof(f7671,plain,
( spl0_877
| ~ spl0_56
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f7607,f7381,f3450,f7668]) ).
fof(f7668,plain,
( spl0_877
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f3450,plain,
( spl0_56
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f7381,plain,
( spl0_821
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f7607,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_821 ),
inference(resolution,[],[f7382,f3452]) ).
fof(f3452,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f3450]) ).
fof(f7382,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) )
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f7381]) ).
fof(f7655,plain,
( spl0_876
| ~ spl0_28
| ~ spl0_820 ),
inference(avatar_split_clause,[],[f7606,f7377,f3310,f7652]) ).
fof(f7652,plain,
( spl0_876
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f3310,plain,
( spl0_28
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f7377,plain,
( spl0_820
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_1 = c_IntDef_Oof__int(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f7606,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_28
| ~ spl0_820 ),
inference(resolution,[],[f7378,f3312]) ).
fof(f3312,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3310]) ).
fof(f7378,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_1 = c_IntDef_Oof__int(c_1,X5) )
| ~ spl0_820 ),
inference(avatar_component_clause,[],[f7377]) ).
fof(f7643,plain,
( spl0_875
| ~ spl0_116
| ~ spl0_817 ),
inference(avatar_split_clause,[],[f7600,f7365,f3744,f7640]) ).
fof(f7365,plain,
( spl0_817
<=> ! [X30] : c_IntDef_Oint(X30) = c_HOL_Oabs(c_IntDef_Oint(X30),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f7600,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_817 ),
inference(superposition,[],[f7366,f3746]) ).
fof(f7366,plain,
( ! [X30] : c_IntDef_Oint(X30) = c_HOL_Oabs(c_IntDef_Oint(X30),tc_IntDef_Oint)
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f7365]) ).
fof(f7627,plain,
( spl0_874
| ~ spl0_115
| ~ spl0_817 ),
inference(avatar_split_clause,[],[f7599,f7365,f3739,f7624]) ).
fof(f7624,plain,
( spl0_874
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f7599,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_115
| ~ spl0_817 ),
inference(superposition,[],[f7366,f3741]) ).
fof(f7598,plain,
( spl0_873
| ~ spl0_808
| ~ spl0_811 ),
inference(avatar_split_clause,[],[f7591,f7341,f7329,f7596]) ).
fof(f7329,plain,
( spl0_808
<=> ! [X8] : c_div(X8,c_1,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f7341,plain,
( spl0_811
<=> ! [X19,X30] : c_lessequals(c_div(X30,X19,tc_nat),X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f7591,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_808
| ~ spl0_811 ),
inference(superposition,[],[f7342,f7330]) ).
fof(f7330,plain,
( ! [X8] : c_div(X8,c_1,tc_nat) = X8
| ~ spl0_808 ),
inference(avatar_component_clause,[],[f7329]) ).
fof(f7342,plain,
( ! [X19,X30] : c_lessequals(c_div(X30,X19,tc_nat),X30,tc_nat)
| ~ spl0_811 ),
inference(avatar_component_clause,[],[f7341]) ).
fof(f7589,plain,
spl0_872,
inference(avatar_split_clause,[],[f3071,f7587]) ).
fof(f7587,plain,
( spl0_872
<=> ! [X30] :
( ~ c_Divides_Oop_Advd(X30,c_1,tc_nat)
| c_1 = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f3071,plain,
! [X30] :
( ~ c_Divides_Oop_Advd(X30,c_1,tc_nat)
| c_1 = X30 ),
inference(forward_demodulation,[],[f3070,f2763]) ).
fof(f3070,plain,
! [X30] :
( c_1 = X30
| ~ c_Divides_Oop_Advd(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2894,f2763]) ).
fof(f2894,plain,
! [X30] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X30
| ~ c_Divides_Oop_Advd(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f92,f1409,f1409]) ).
fof(f92,axiom,
! [X30] :
( c_Suc(c_0) = X30
| ~ c_Divides_Oop_Advd(X30,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f7585,plain,
spl0_871,
inference(avatar_split_clause,[],[f2985,f7583]) ).
fof(f7583,plain,
( spl0_871
<=> ! [X5,X35] : c_emptyset = c_Relation_OImage(c_emptyset,X35,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2985,plain,
! [X35,X5] : c_emptyset = c_Relation_OImage(c_emptyset,X35,X5,X5),
inference(forward_demodulation,[],[f2774,f1251]) ).
fof(f1251,axiom,
! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2774,plain,
! [X5,X35] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X5),X35,X5,X5),
inference(definition_unfolding,[],[f1469,f1238]) ).
fof(f1469,axiom,
! [X35,X5] : c_emptyset = c_inter(c_emptyset,X35,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f7581,plain,
spl0_870,
inference(avatar_split_clause,[],[f2778,f7579]) ).
fof(f7577,plain,
spl0_869,
inference(avatar_split_clause,[],[f2776,f7574]) ).
fof(f2776,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f998,f978]) ).
fof(f998,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(f7572,plain,
spl0_868,
inference(avatar_split_clause,[],[f2763,f7569]) ).
fof(f7569,plain,
( spl0_868
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f7567,plain,
spl0_867,
inference(avatar_split_clause,[],[f2759,f7565]) ).
fof(f7565,plain,
( spl0_867
<=> ! [X30] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2759,plain,
! [X30] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),
inference(definition_unfolding,[],[f890,f1409]) ).
fof(f890,axiom,
! [X30] : c_0 != c_Suc(X30),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
fof(f7563,plain,
spl0_866,
inference(avatar_split_clause,[],[f1687,f7561]) ).
fof(f7561,plain,
( spl0_866
<=> ! [X18] : c_in(c_SetInterval_OlessThan(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f1687,axiom,
! [X18] : c_in(c_SetInterval_OlessThan(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7559,plain,
spl0_865,
inference(avatar_split_clause,[],[f1682,f7557]) ).
fof(f7557,plain,
( spl0_865
<=> ! [X18] : c_in(c_SetInterval_OatMost(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1682,axiom,
! [X18] : c_in(c_SetInterval_OatMost(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7555,plain,
spl0_864,
inference(avatar_split_clause,[],[f1653,f7553]) ).
fof(f7553,plain,
( spl0_864
<=> ! [X5,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f1653,axiom,
! [X1,X5] : c_in(c_List_Olist_ONil,c_List_Olists(X1,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7551,plain,
spl0_863,
inference(avatar_split_clause,[],[f1637,f7549]) ).
fof(f7549,plain,
( spl0_863
<=> ! [X5,X44] : c_in(c_List_Oset(X44,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f1637,axiom,
! [X44,X5] : c_in(c_List_Oset(X44,X5),c_Finite__Set_OFinites,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7547,plain,
spl0_862,
inference(avatar_split_clause,[],[f1634,f7545]) ).
fof(f1634,axiom,
! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7543,plain,
spl0_861,
inference(avatar_split_clause,[],[f1633,f7541]) ).
fof(f1633,axiom,
! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7539,plain,
spl0_860,
inference(avatar_split_clause,[],[f1618,f7537]) ).
fof(f7537,plain,
( spl0_860
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1618,axiom,
! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7535,plain,
spl0_859,
inference(avatar_split_clause,[],[f1617,f7533]) ).
fof(f7533,plain,
( spl0_859
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1617,axiom,
! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7531,plain,
spl0_858,
inference(avatar_split_clause,[],[f1570,f7529]) ).
fof(f7529,plain,
( spl0_858
<=> ! [X5,X23] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1570,axiom,
! [X5,X23] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7527,plain,
spl0_857,
inference(avatar_split_clause,[],[f1549,f7525]) ).
fof(f1549,axiom,
! [X1,X4,X5] : c_in(X4,c_insert(X4,X1,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7523,plain,
spl0_856,
inference(avatar_split_clause,[],[f1533,f7521]) ).
fof(f7521,plain,
( spl0_856
<=> ! [X5,X1] : c_emptyset = c_minus(c_emptyset,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1533,axiom,
! [X1,X5] : c_emptyset = c_minus(c_emptyset,X1,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7519,plain,
spl0_855,
inference(avatar_split_clause,[],[f1513,f7517]) ).
fof(f7517,plain,
( spl0_855
<=> ! [X5,X8] : c_Union(c_Pow(X8,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f1513,axiom,
! [X8,X5] : c_Union(c_Pow(X8,X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7515,plain,
spl0_854,
inference(avatar_split_clause,[],[f1455,f7513]) ).
fof(f7513,plain,
( spl0_854
<=> ! [X5,X8] : c_minus(X8,c_emptyset,tc_set(X5)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f1455,axiom,
! [X8,X5] : c_minus(X8,c_emptyset,tc_set(X5)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7511,plain,
spl0_853,
inference(avatar_split_clause,[],[f1453,f7509]) ).
fof(f7509,plain,
( spl0_853
<=> ! [X5,X1] : c_emptyset = c_minus(X1,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f1453,axiom,
! [X1,X5] : c_emptyset = c_minus(X1,X1,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7507,plain,
spl0_852,
inference(avatar_split_clause,[],[f1452,f7505]) ).
fof(f7505,plain,
( spl0_852
<=> ! [X5,X1] : c_emptyset = c_minus(X1,c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1452,axiom,
! [X1,X5] : c_emptyset = c_minus(X1,c_UNIV,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7503,plain,
spl0_851,
inference(avatar_split_clause,[],[f1414,f7501]) ).
fof(f7501,plain,
( spl0_851
<=> ! [X8] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X8,tc_nat),tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1414,axiom,
! [X8] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X8,tc_nat),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7499,plain,
spl0_850,
inference(avatar_split_clause,[],[f1259,f7497]) ).
fof(f7497,plain,
( spl0_850
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1259,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7495,plain,
spl0_849,
inference(avatar_split_clause,[],[f1239,f7493]) ).
fof(f7493,plain,
( spl0_849
<=> ! [X82,X5,X23] : c_emptyset = c_Relation_OImage(X82,c_emptyset,X23,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1239,axiom,
! [X82,X5,X23] : c_emptyset = c_Relation_OImage(X82,c_emptyset,X23,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7491,plain,
spl0_848,
inference(avatar_split_clause,[],[f1237,f7489]) ).
fof(f7489,plain,
( spl0_848
<=> ! [X5,X8] : c_Relation_OImage(c_Relation_OId,X8,X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1237,axiom,
! [X8,X5] : c_Relation_OImage(c_Relation_OId,X8,X5,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7487,plain,
spl0_847,
inference(avatar_split_clause,[],[f1108,f7485]) ).
fof(f1108,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7483,plain,
spl0_846,
inference(avatar_split_clause,[],[f1103,f7481]) ).
fof(f1103,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7479,plain,
spl0_845,
inference(avatar_split_clause,[],[f1085,f7477]) ).
fof(f7477,plain,
( spl0_845
<=> ! [X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_uminus(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1085,axiom,
! [X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_uminus(c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
fof(f7475,plain,
spl0_844,
inference(avatar_split_clause,[],[f1038,f7473]) ).
fof(f7473,plain,
( spl0_844
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = c_HOL_Oabs(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1038,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = c_HOL_Oabs(c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
fof(f7471,plain,
spl0_843,
inference(avatar_split_clause,[],[f1034,f7469]) ).
fof(f1034,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7467,plain,
spl0_842,
inference(avatar_split_clause,[],[f1027,f7465]) ).
fof(f7465,plain,
( spl0_842
<=> ! [X5,X8,X33] : c_Numeral_Obit_Obit__rec(X33,X8,c_Numeral_Obit_OB1,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f1027,axiom,
! [X8,X5,X33] : c_Numeral_Obit_Obit__rec(X33,X8,c_Numeral_Obit_OB1,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7463,plain,
spl0_841,
inference(avatar_split_clause,[],[f1026,f7461]) ).
fof(f7461,plain,
( spl0_841
<=> ! [X5,X8,X32] : c_Numeral_Obit_Obit__rec(X8,X32,c_Numeral_Obit_OB0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1026,axiom,
! [X8,X5,X32] : c_Numeral_Obit_Obit__rec(X8,X32,c_Numeral_Obit_OB0,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7459,plain,
spl0_840,
inference(avatar_split_clause,[],[f1023,f7457]) ).
fof(f7457,plain,
( spl0_840
<=> ! [X5,X8,X33] : c_Numeral_Obit_Obit__case(X33,X8,c_Numeral_Obit_OB1,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f1023,axiom,
! [X8,X5,X33] : c_Numeral_Obit_Obit__case(X33,X8,c_Numeral_Obit_OB1,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7455,plain,
spl0_839,
inference(avatar_split_clause,[],[f1022,f7453]) ).
fof(f7453,plain,
( spl0_839
<=> ! [X5,X8,X32] : c_Numeral_Obit_Obit__case(X8,X32,c_Numeral_Obit_OB0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f1022,axiom,
! [X8,X5,X32] : c_Numeral_Obit_Obit__case(X8,X32,c_Numeral_Obit_OB0,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7451,plain,
spl0_838,
inference(avatar_split_clause,[],[f1009,f7449]) ).
fof(f7449,plain,
( spl0_838
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f1009,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7447,plain,
spl0_837,
inference(avatar_split_clause,[],[f1008,f7445]) ).
fof(f1008,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7443,plain,
spl0_836,
inference(avatar_split_clause,[],[f954,f7441]) ).
fof(f7441,plain,
( spl0_836
<=> ! [X19] :
( c_0 = X19
| c_less(c_0,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f954,axiom,
! [X19] :
( c_0 = X19
| c_less(c_0,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7439,plain,
spl0_835,
inference(avatar_split_clause,[],[f953,f7437]) ).
fof(f7437,plain,
( spl0_835
<=> ! [X29,X55] : ~ c_less(c_plus(X55,X29,tc_nat),X29,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f953,axiom,
! [X29,X55] : ~ c_less(c_plus(X55,X29,tc_nat),X29,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7435,plain,
spl0_834,
inference(avatar_split_clause,[],[f952,f7433]) ).
fof(f7433,plain,
( spl0_834
<=> ! [X29,X55] : ~ c_less(c_plus(X29,X55,tc_nat),X29,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f952,axiom,
! [X29,X55] : ~ c_less(c_plus(X29,X55,tc_nat),X29,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7431,plain,
spl0_833,
inference(avatar_split_clause,[],[f913,f7429]) ).
fof(f7429,plain,
( spl0_833
<=> ! [X19] :
( c_0 = X19
| ~ c_less(X19,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f913,axiom,
! [X19] :
( c_0 = X19
| ~ c_less(X19,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7427,plain,
spl0_832,
inference(avatar_split_clause,[],[f907,f7425]) ).
fof(f7425,plain,
( spl0_832
<=> ! [X29] :
( c_0 = X29
| ~ c_lessequals(X29,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f907,axiom,
! [X29] :
( c_0 = X29
| ~ c_lessequals(X29,c_0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7423,plain,
spl0_831,
inference(avatar_split_clause,[],[f905,f7421]) ).
fof(f7421,plain,
( spl0_831
<=> ! [X19,X30] : c_lessequals(c_minus(X30,X19,tc_nat),X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f905,axiom,
! [X19,X30] : c_lessequals(c_minus(X30,X19,tc_nat),X30,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7419,plain,
spl0_830,
inference(avatar_split_clause,[],[f673,f7417]) ).
fof(f673,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_1 = c_NatArith_Oof__nat(c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7415,plain,
spl0_829,
inference(avatar_split_clause,[],[f669,f7413]) ).
fof(f669,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).
fof(f7411,plain,
spl0_828,
inference(avatar_split_clause,[],[f655,f7409]) ).
fof(f7409,plain,
( spl0_828
<=> ! [X45,X5,X23] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X45,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f655,axiom,
! [X45,X5,X23] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X45,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7407,plain,
spl0_827,
inference(avatar_split_clause,[],[f653,f7405]) ).
fof(f7405,plain,
( spl0_827
<=> ! [X21,X44,X79] : c_List_Olist_ONil = c_List_Ozip(X44,c_List_Olist_ONil,X21,X79) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f653,axiom,
! [X21,X44,X79] : c_List_Olist_ONil = c_List_Ozip(X44,c_List_Olist_ONil,X21,X79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7403,plain,
spl0_826,
inference(avatar_split_clause,[],[f597,f7401]) ).
fof(f7401,plain,
( spl0_826
<=> ! [X5,X8] : c_List_Orev(c_List_Orev(X8,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f597,axiom,
! [X8,X5] : c_List_Orev(c_List_Orev(X8,X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7399,plain,
spl0_825,
inference(avatar_split_clause,[],[f576,f7397]) ).
fof(f7397,plain,
( spl0_825
<=> ! [X45,X4,X5] : c_List_Oop_Amem(X4,c_List_Olist_OCons(X4,X45,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f576,axiom,
! [X45,X4,X5] : c_List_Oop_Amem(X4,c_List_Olist_OCons(X4,X45,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7395,plain,
spl0_824,
inference(avatar_split_clause,[],[f496,f7393]) ).
fof(f7393,plain,
( spl0_824
<=> ! [X29,X21,X40] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X29,X40,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f496,axiom,
! [X40,X21,X29] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X29,X40,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7391,plain,
spl0_823,
inference(avatar_split_clause,[],[f407,f7389]) ).
fof(f7389,plain,
( spl0_823
<=> ! [X50,X51] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X50,X51),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f407,axiom,
! [X50,X51] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X50,X51),tc_List_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7387,plain,
spl0_822,
inference(avatar_split_clause,[],[f343,f7385]) ).
fof(f343,axiom,
! [X30] :
( c_0 = X30
| ~ c_Divides_Oop_Advd(c_0,X30,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7383,plain,
spl0_821,
inference(avatar_split_clause,[],[f270,f7381]) ).
fof(f270,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
fof(f7379,plain,
spl0_820,
inference(avatar_split_clause,[],[f266,f7377]) ).
fof(f266,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_1 = c_IntDef_Oof__int(c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7375,plain,
spl0_819,
inference(avatar_split_clause,[],[f252,f7373]) ).
fof(f252,axiom,
! [X19] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7371,plain,
spl0_818,
inference(avatar_split_clause,[],[f238,f7369]) ).
fof(f7369,plain,
( spl0_818
<=> ! [X19] :
( c_0 = X19
| c_0 != c_IntDef_Oint(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f238,axiom,
! [X19] :
( c_0 = X19
| c_0 != c_IntDef_Oint(X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7367,plain,
spl0_817,
inference(avatar_split_clause,[],[f232,f7365]) ).
fof(f232,axiom,
! [X30] : c_IntDef_Oint(X30) = c_HOL_Oabs(c_IntDef_Oint(X30),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7363,plain,
spl0_816,
inference(avatar_split_clause,[],[f118,f7361]) ).
fof(f7361,plain,
( spl0_816
<=> ! [X5,X8,X33] : c_Extraction_Osumbool_Osumbool__rec(X33,X8,c_Extraction_Osumbool_ORight,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f118,axiom,
! [X8,X5,X33] : c_Extraction_Osumbool_Osumbool__rec(X33,X8,c_Extraction_Osumbool_ORight,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7359,plain,
spl0_815,
inference(avatar_split_clause,[],[f117,f7357]) ).
fof(f7357,plain,
( spl0_815
<=> ! [X5,X8,X32] : c_Extraction_Osumbool_Osumbool__rec(X8,X32,c_Extraction_Osumbool_OLeft,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f117,axiom,
! [X8,X5,X32] : c_Extraction_Osumbool_Osumbool__rec(X8,X32,c_Extraction_Osumbool_OLeft,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7355,plain,
spl0_814,
inference(avatar_split_clause,[],[f114,f7353]) ).
fof(f7353,plain,
( spl0_814
<=> ! [X5,X8,X33] : c_Extraction_Osumbool_Osumbool__case(X33,X8,c_Extraction_Osumbool_ORight,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f114,axiom,
! [X8,X5,X33] : c_Extraction_Osumbool_Osumbool__case(X33,X8,c_Extraction_Osumbool_ORight,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7351,plain,
spl0_813,
inference(avatar_split_clause,[],[f113,f7349]) ).
fof(f7349,plain,
( spl0_813
<=> ! [X5,X8,X32] : c_Extraction_Osumbool_Osumbool__case(X8,X32,c_Extraction_Osumbool_OLeft,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f113,axiom,
! [X8,X5,X32] : c_Extraction_Osumbool_Osumbool__case(X8,X32,c_Extraction_Osumbool_OLeft,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7347,plain,
spl0_812,
inference(avatar_split_clause,[],[f90,f7345]) ).
fof(f7345,plain,
( spl0_812
<=> ! [X30] :
( c_0 = X30
| ~ c_Divides_Oop_Advd(c_0,X30,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f90,axiom,
! [X30] :
( c_0 = X30
| ~ c_Divides_Oop_Advd(c_0,X30,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7343,plain,
spl0_811,
inference(avatar_split_clause,[],[f80,f7341]) ).
fof(f80,axiom,
! [X19,X30] : c_lessequals(c_div(X30,X19,tc_nat),X30,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7339,plain,
spl0_810,
inference(avatar_split_clause,[],[f67,f7337]) ).
fof(f7337,plain,
( spl0_810
<=> ! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X24,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f67,axiom,
! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X24,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7335,plain,
spl0_809,
inference(avatar_split_clause,[],[f46,f7333]) ).
fof(f7333,plain,
( spl0_809
<=> ! [X5,X8] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f46,axiom,
! [X8,X5] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X5),X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7331,plain,
spl0_808,
inference(avatar_split_clause,[],[f2995,f7329]) ).
fof(f2995,plain,
! [X8] : c_div(X8,c_1,tc_nat) = X8,
inference(forward_demodulation,[],[f2789,f2763]) ).
fof(f2789,plain,
! [X8] : c_div(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X8,
inference(definition_unfolding,[],[f79,f1409]) ).
fof(f79,axiom,
! [X8] : c_div(X8,c_Suc(c_0),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7327,plain,
spl0_807,
inference(avatar_split_clause,[],[f2993,f7324]) ).
fof(f7324,plain,
( spl0_807
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2993,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2786,f2763]) ).
fof(f2786,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,[],[f959,f1409]) ).
fof(f959,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(f7322,plain,
spl0_806,
inference(avatar_split_clause,[],[f2991,f7320]) ).
fof(f7320,plain,
( spl0_806
<=> ! [X30] : c_0 = c_Divides_Oop_Amod(X30,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2991,plain,
! [X30] : c_0 = c_Divides_Oop_Amod(X30,c_1,tc_nat),
inference(forward_demodulation,[],[f2785,f2763]) ).
fof(f2785,plain,
! [X30] : c_0 = c_Divides_Oop_Amod(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f96,f1409]) ).
fof(f96,axiom,
! [X30] : c_0 = c_Divides_Oop_Amod(X30,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7318,plain,
spl0_805,
inference(avatar_split_clause,[],[f2990,f7315]) ).
fof(f7315,plain,
( spl0_805
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2990,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f732,f1021]) ).
fof(f732,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(f7313,plain,
spl0_804,
inference(avatar_split_clause,[],[f2988,f7311]) ).
fof(f7311,plain,
( spl0_804
<=> ! [X21,X8] : c_append(c_List_Olist_ONil,X8,X21) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2988,plain,
! [X21,X8] : c_append(c_List_Olist_ONil,X8,X21) = X8,
inference(forward_demodulation,[],[f2780,f379]) ).
fof(f379,axiom,
! [X5] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).
fof(f2780,plain,
! [X21,X8] : c_append(c_List_Orev(c_List_Olist_ONil,X21),X8,X21) = X8,
inference(definition_unfolding,[],[f451,f450]) ).
fof(f451,axiom,
! [X21,X8] : c_List_Oitrev(c_List_Olist_ONil,X8,X21) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7309,plain,
spl0_803,
inference(avatar_split_clause,[],[f2986,f7306]) ).
fof(f7306,plain,
( spl0_803
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2986,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2777,f1021]) ).
fof(f2777,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f990,f994]) ).
fof(f990,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(f7304,plain,
spl0_802,
inference(avatar_split_clause,[],[f1660,f7302]) ).
fof(f7302,plain,
( spl0_802
<=> ! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f1660,axiom,
! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X4,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7300,plain,
spl0_801,
inference(avatar_split_clause,[],[f1538,f7298]) ).
fof(f1538,axiom,
! [X2,X1,X5] : c_emptyset != c_insert(X2,X1,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
fof(f7296,plain,
spl0_800,
inference(avatar_split_clause,[],[f1504,f7294]) ).
fof(f1504,axiom,
! [X8,X5] : c_union(X8,c_emptyset,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7292,plain,
spl0_799,
inference(avatar_split_clause,[],[f1503,f7290]) ).
fof(f1503,axiom,
! [X8,X5] : c_union(c_emptyset,X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7288,plain,
spl0_798,
inference(avatar_split_clause,[],[f1499,f7286]) ).
fof(f1499,axiom,
! [X8,X5] : c_union(X8,X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7284,plain,
spl0_797,
inference(avatar_split_clause,[],[f1498,f7282]) ).
fof(f7282,plain,
( spl0_797
<=> ! [X5,X1] : c_UNIV = c_union(X1,c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f1498,axiom,
! [X1,X5] : c_UNIV = c_union(X1,c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7280,plain,
spl0_796,
inference(avatar_split_clause,[],[f1497,f7278]) ).
fof(f1497,axiom,
! [X35,X5] : c_UNIV = c_union(c_UNIV,X35,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7276,plain,
spl0_795,
inference(avatar_split_clause,[],[f1445,f7274]) ).
fof(f1445,axiom,
! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7272,plain,
spl0_794,
inference(avatar_split_clause,[],[f1441,f7270]) ).
fof(f7270,plain,
( spl0_794
<=> ! [X5] : c_emptyset = c_uminus(c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f1441,axiom,
! [X5] : c_emptyset = c_uminus(c_UNIV,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7268,plain,
spl0_793,
inference(avatar_split_clause,[],[f1376,f7266]) ).
fof(f7266,plain,
( spl0_793
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1376,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7264,plain,
spl0_792,
inference(avatar_split_clause,[],[f1364,f7262]) ).
fof(f7262,plain,
( spl0_792
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f1364,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7260,plain,
spl0_791,
inference(avatar_split_clause,[],[f1359,f7258]) ).
fof(f7258,plain,
( spl0_791
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f1359,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7256,plain,
spl0_790,
inference(avatar_split_clause,[],[f1358,f7254]) ).
fof(f7254,plain,
( spl0_790
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(c_1,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1358,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(c_1,c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7252,plain,
spl0_789,
inference(avatar_split_clause,[],[f1246,f7250]) ).
fof(f7250,plain,
( spl0_789
<=> ! [X5] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f1246,axiom,
! [X5] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7248,plain,
spl0_788,
inference(avatar_split_clause,[],[f1245,f7246]) ).
fof(f7246,plain,
( spl0_788
<=> ! [X5,X23] : c_emptyset = c_Relation_ORange(c_emptyset,X23,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f1245,axiom,
! [X5,X23] : c_emptyset = c_Relation_ORange(c_emptyset,X23,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7244,plain,
spl0_787,
inference(avatar_split_clause,[],[f1243,f7242]) ).
fof(f7242,plain,
( spl0_787
<=> ! [X5] : c_UNIV = c_Relation_ORange(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f1243,axiom,
! [X5] : c_UNIV = c_Relation_ORange(c_Relation_OId,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7240,plain,
spl0_786,
inference(avatar_split_clause,[],[f1235,f7238]) ).
fof(f7238,plain,
( spl0_786
<=> ! [X5,X23] : c_emptyset = c_Relation_ODomain(c_emptyset,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1235,axiom,
! [X5,X23] : c_emptyset = c_Relation_ODomain(c_emptyset,X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7236,plain,
spl0_785,
inference(avatar_split_clause,[],[f1233,f7234]) ).
fof(f7234,plain,
( spl0_785
<=> ! [X5] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1233,axiom,
! [X5] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7232,plain,
spl0_784,
inference(avatar_split_clause,[],[f1209,f7230]) ).
fof(f1209,axiom,
! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7228,plain,
spl0_783,
inference(avatar_split_clause,[],[f1134,f7226]) ).
fof(f7226,plain,
( spl0_783
<=> ! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f1134,axiom,
! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X4,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7224,plain,
spl0_782,
inference(avatar_split_clause,[],[f1021,f7221]) ).
fof(f7219,plain,
spl0_781,
inference(avatar_split_clause,[],[f967,f7217]) ).
fof(f7217,plain,
( spl0_781
<=> ! [X8] : c_minus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f967,axiom,
! [X8] : c_minus(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7215,plain,
spl0_780,
inference(avatar_split_clause,[],[f965,f7213]) ).
fof(f965,axiom,
! [X8] : c_plus(c_0,X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7211,plain,
spl0_779,
inference(avatar_split_clause,[],[f963,f7209]) ).
fof(f7209,plain,
( spl0_779
<=> ! [X19] : c_0 = c_times(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f963,axiom,
! [X19] : c_0 = c_times(c_0,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7207,plain,
spl0_778,
inference(avatar_split_clause,[],[f921,f7205]) ).
fof(f7205,plain,
( spl0_778
<=> ! [X30] : c_0 = c_times(X30,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f921,axiom,
! [X30] : c_0 = c_times(X30,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7203,plain,
spl0_777,
inference(avatar_split_clause,[],[f919,f7201]) ).
fof(f7201,plain,
( spl0_777
<=> ! [X19] : c_0 = c_Orderings_Omin(X19,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f919,axiom,
! [X19] : c_0 = c_Orderings_Omin(X19,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7199,plain,
spl0_776,
inference(avatar_split_clause,[],[f918,f7197]) ).
fof(f7197,plain,
( spl0_776
<=> ! [X19] : c_0 = c_Orderings_Omin(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f918,axiom,
! [X19] : c_0 = c_Orderings_Omin(c_0,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7195,plain,
spl0_775,
inference(avatar_split_clause,[],[f916,f7193]) ).
fof(f7193,plain,
( spl0_775
<=> ! [X8] : c_Orderings_Omax(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f916,axiom,
! [X8] : c_Orderings_Omax(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7191,plain,
spl0_774,
inference(avatar_split_clause,[],[f915,f7189]) ).
fof(f7189,plain,
( spl0_774
<=> ! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f915,axiom,
! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7187,plain,
spl0_773,
inference(avatar_split_clause,[],[f906,f7185]) ).
fof(f7185,plain,
( spl0_773
<=> ! [X30] : c_0 = c_minus(X30,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f906,axiom,
! [X30] : c_0 = c_minus(X30,X30,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7183,plain,
spl0_772,
inference(avatar_split_clause,[],[f899,f7181]) ).
fof(f899,axiom,
! [X19] : c_0 = c_minus(c_0,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7179,plain,
spl0_771,
inference(avatar_split_clause,[],[f891,f7177]) ).
fof(f891,axiom,
! [X8] : c_plus(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7175,plain,
spl0_770,
inference(avatar_split_clause,[],[f652,f7173]) ).
fof(f7173,plain,
( spl0_770
<=> ! [X4,X5,X78] : c_List_Olist_OCons(X4,X78,X5) != X78 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f652,axiom,
! [X78,X4,X5] : c_List_Olist_OCons(X4,X78,X5) != X78,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
fof(f7171,plain,
spl0_769,
inference(avatar_split_clause,[],[f628,f7169]) ).
fof(f7169,plain,
( spl0_769
<=> ! [X5,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X1,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f628,axiom,
! [X1,X5] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X1,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7167,plain,
spl0_768,
inference(avatar_split_clause,[],[f627,f7165]) ).
fof(f7165,plain,
( spl0_768
<=> ! [X5,X44] : c_List_Olist_ONil = c_List_Osublist(X44,c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f627,axiom,
! [X44,X5] : c_List_Olist_ONil = c_List_Osublist(X44,c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7163,plain,
spl0_767,
inference(avatar_split_clause,[],[f612,f7161]) ).
fof(f7161,plain,
( spl0_767
<=> ! [X5,X44] : c_append(X44,c_List_Olist_ONil,X5) = X44 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f612,axiom,
! [X44,X5] : c_append(X44,c_List_Olist_ONil,X5) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
fof(f7159,plain,
spl0_766,
inference(avatar_split_clause,[],[f606,f7157]) ).
fof(f7157,plain,
( spl0_766
<=> ! [X5,X19] : c_List_Olist_ONil = c_List_Orotate(X19,c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f606,axiom,
! [X19,X5] : c_List_Olist_ONil = c_List_Orotate(X19,c_List_Olist_ONil,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7155,plain,
spl0_765,
inference(avatar_split_clause,[],[f587,f7153]) ).
fof(f587,axiom,
! [X21,X4] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X4,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7151,plain,
spl0_764,
inference(avatar_split_clause,[],[f584,f7149]) ).
fof(f7149,plain,
( spl0_764
<=> ! [X4,X21] : c_List_Olist_ONil = c_List_Oremove1(X4,c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f584,axiom,
! [X21,X4] : c_List_Olist_ONil = c_List_Oremove1(X4,c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7147,plain,
spl0_763,
inference(avatar_split_clause,[],[f572,f7145]) ).
fof(f7145,plain,
( spl0_763
<=> ! [X4,X21,X44] : ~ c_List_Onull(c_List_Olist_OCons(X4,X44,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f572,axiom,
! [X21,X44,X4] : ~ c_List_Onull(c_List_Olist_OCons(X4,X44,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7143,plain,
spl0_762,
inference(avatar_split_clause,[],[f493,f7141]) ).
fof(f7141,plain,
( spl0_762
<=> ! [X61,X21] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X61,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f493,axiom,
! [X21,X61] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X61,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7139,plain,
spl0_761,
inference(avatar_split_clause,[],[f488,f7137]) ).
fof(f7137,plain,
( spl0_761
<=> ! [X22,X5,X59] : c_List_Olist_ONil != c_List_Olist_OCons(X22,X59,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f488,axiom,
! [X59,X22,X5] : c_List_Olist_ONil != c_List_Olist_OCons(X22,X59,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
fof(f7135,plain,
spl0_760,
inference(avatar_split_clause,[],[f480,f7133]) ).
fof(f7133,plain,
( spl0_760
<=> ! [X6,X21] : c_emptyset = c_List_Olexn(X6,c_0,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f480,axiom,
! [X21,X6] : c_emptyset = c_List_Olexn(X6,c_0,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7131,plain,
spl0_759,
inference(avatar_split_clause,[],[f463,f7129]) ).
fof(f7129,plain,
( spl0_759
<=> ! [X5] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f463,axiom,
! [X5] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7127,plain,
spl0_758,
inference(avatar_split_clause,[],[f434,f7125]) ).
fof(f7125,plain,
( spl0_758
<=> ! [X5,X8] : c_List_Odrop(c_0,X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f434,axiom,
! [X8,X5] : c_List_Odrop(c_0,X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7123,plain,
spl0_757,
inference(avatar_split_clause,[],[f433,f7121]) ).
fof(f7121,plain,
( spl0_757
<=> ! [X21,X19] : c_List_Olist_ONil = c_List_Odrop(X19,c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f433,axiom,
! [X21,X19] : c_List_Olist_ONil = c_List_Odrop(X19,c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7119,plain,
spl0_756,
inference(avatar_split_clause,[],[f359,f7117]) ).
fof(f7117,plain,
( spl0_756
<=> ! [X7] : c_0 = c_Divides_Oop_Amod(c_0,X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f359,axiom,
! [X7] : c_0 = c_Divides_Oop_Amod(c_0,X7,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7115,plain,
spl0_755,
inference(avatar_split_clause,[],[f356,f7113]) ).
fof(f7113,plain,
( spl0_755
<=> ! [X2] : c_0 = c_Divides_Oop_Amod(X2,X2,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f356,axiom,
! [X2] : c_0 = c_Divides_Oop_Amod(X2,X2,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7111,plain,
spl0_754,
inference(avatar_split_clause,[],[f354,f7109]) ).
fof(f7109,plain,
( spl0_754
<=> ! [X2] : c_0 = c_Divides_Oop_Amod(X2,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f354,axiom,
! [X2] : c_0 = c_Divides_Oop_Amod(X2,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7107,plain,
spl0_753,
inference(avatar_split_clause,[],[f339,f7105]) ).
fof(f7105,plain,
( spl0_753
<=> ! [X7] : c_0 = c_div(c_0,X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f339,axiom,
! [X7] : c_0 = c_div(c_0,X7,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7103,plain,
spl0_752,
inference(avatar_split_clause,[],[f331,f7101]) ).
fof(f7101,plain,
( spl0_752
<=> ! [X8] : c_div(X8,c_1,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f331,axiom,
! [X8] : c_div(X8,c_1,tc_IntDef_Oint) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7099,plain,
spl0_751,
inference(avatar_split_clause,[],[f329,f7097]) ).
fof(f7097,plain,
( spl0_751
<=> ! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f329,axiom,
! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7095,plain,
spl0_750,
inference(avatar_split_clause,[],[f297,f7093]) ).
fof(f297,axiom,
! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7091,plain,
spl0_749,
inference(avatar_split_clause,[],[f229,f7089]) ).
fof(f7089,plain,
( spl0_749
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_1,c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f229,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_1,c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7087,plain,
spl0_748,
inference(avatar_split_clause,[],[f228,f7085]) ).
fof(f7085,plain,
( spl0_748
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_0,c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f228,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_0,c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7083,plain,
spl0_747,
inference(avatar_split_clause,[],[f223,f7081]) ).
fof(f7081,plain,
( spl0_747
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_1,c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f223,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_1,c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7079,plain,
spl0_746,
inference(avatar_split_clause,[],[f222,f7077]) ).
fof(f7077,plain,
( spl0_746
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_0,c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f222,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_0,c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7075,plain,
spl0_745,
inference(avatar_split_clause,[],[f215,f7072]) ).
fof(f7072,plain,
( spl0_745
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f215,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(f7070,plain,
spl0_744,
inference(avatar_split_clause,[],[f110,f7068]) ).
fof(f7068,plain,
( spl0_744
<=> ! [X6,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X6,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f110,axiom,
! [X6,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X6,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
fof(f7066,plain,
spl0_743,
inference(avatar_split_clause,[],[f106,f7064]) ).
fof(f7064,plain,
( spl0_743
<=> ! [X19] : c_0 = c_Divides_Oop_Amod(X19,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f106,axiom,
! [X19] : c_0 = c_Divides_Oop_Amod(X19,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7062,plain,
spl0_742,
inference(avatar_split_clause,[],[f95,f7060]) ).
fof(f7060,plain,
( spl0_742
<=> ! [X30] : c_0 = c_Divides_Oop_Amod(c_0,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f95,axiom,
! [X30] : c_0 = c_Divides_Oop_Amod(c_0,X30,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7058,plain,
spl0_741,
inference(avatar_split_clause,[],[f78,f7056]) ).
fof(f7056,plain,
( spl0_741
<=> ! [X30] : c_0 = c_div(c_0,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f78,axiom,
! [X30] : c_0 = c_div(c_0,X30,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7054,plain,
spl0_740,
inference(avatar_split_clause,[],[f77,f7052]) ).
fof(f7052,plain,
( spl0_740
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f77,axiom,
! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7050,plain,
spl0_739,
inference(avatar_split_clause,[],[f76,f7048]) ).
fof(f7048,plain,
( spl0_739
<=> ! [X2] : c_0 = c_div(X2,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f76,axiom,
! [X2] : c_0 = c_div(X2,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f7046,plain,
spl0_738,
inference(avatar_split_clause,[],[f48,f7044]) ).
fof(f7044,plain,
( spl0_738
<=> ! [X5,X8] : c_Datatype_Ounit_Ounit__rec(X8,c_Product__Type_OUnity,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f48,axiom,
! [X8,X5] : c_Datatype_Ounit_Ounit__rec(X8,c_Product__Type_OUnity,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f7042,plain,
spl0_737,
inference(avatar_split_clause,[],[f47,f7040]) ).
fof(f7040,plain,
( spl0_737
<=> ! [X5,X8] : c_Datatype_Ounit_Ounit__case(X8,c_Product__Type_OUnity,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f47,axiom,
! [X8,X5] : c_Datatype_Ounit_Ounit__case(X8,c_Product__Type_OUnity,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f7038,plain,
spl0_736,
inference(avatar_split_clause,[],[f41,f7036]) ).
fof(f7036,plain,
( spl0_736
<=> ! [X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f41,axiom,
! [X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f7034,plain,
spl0_735,
inference(avatar_split_clause,[],[f15,f7031]) ).
fof(f7031,plain,
( spl0_735
<=> c_in(v_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f15,axiom,
c_in(v_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
fof(f7027,plain,
( spl0_734
| ~ spl0_115
| ~ spl0_674 ),
inference(avatar_split_clause,[],[f7011,f6751,f3739,f7024]) ).
fof(f7024,plain,
( spl0_734
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f6751,plain,
( spl0_674
<=> ! [X19] : c_lessequals(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f7011,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_115
| ~ spl0_674 ),
inference(superposition,[],[f6752,f3741]) ).
fof(f6752,plain,
( ! [X19] : c_lessequals(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint)
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f6751]) ).
fof(f7022,plain,
( ~ spl0_733
| ~ spl0_116
| ~ spl0_672 ),
inference(avatar_split_clause,[],[f7008,f6743,f3744,f7019]) ).
fof(f7019,plain,
( spl0_733
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f6743,plain,
( spl0_672
<=> ! [X18] : ~ c_less(c_IntDef_Oint(X18),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f7008,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_672 ),
inference(superposition,[],[f6744,f3746]) ).
fof(f6744,plain,
( ! [X18] : ~ c_less(c_IntDef_Oint(X18),c_0,tc_IntDef_Oint)
| ~ spl0_672 ),
inference(avatar_component_clause,[],[f6743]) ).
fof(f7017,plain,
( ~ spl0_732
| ~ spl0_115
| ~ spl0_672 ),
inference(avatar_split_clause,[],[f7007,f6743,f3739,f7014]) ).
fof(f7014,plain,
( spl0_732
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f7007,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_115
| ~ spl0_672 ),
inference(superposition,[],[f6744,f3741]) ).
fof(f7006,plain,
spl0_731,
inference(avatar_split_clause,[],[f2992,f7003]) ).
fof(f7003,plain,
( spl0_731
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2992,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f256,f239]) ).
fof(f239,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f256,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(f7001,plain,
spl0_730,
inference(avatar_split_clause,[],[f2987,f6999]) ).
fof(f6999,plain,
( spl0_730
<=> ! [X8] : c_Binomial_Obinomial(X8,c_1) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2987,plain,
! [X8] : c_Binomial_Obinomial(X8,c_1) = X8,
inference(forward_demodulation,[],[f2779,f2763]) ).
fof(f2779,plain,
! [X8] : c_Binomial_Obinomial(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X8,
inference(definition_unfolding,[],[f26,f1409]) ).
fof(f26,axiom,
! [X8] : c_Binomial_Obinomial(X8,c_Suc(c_0)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f6997,plain,
spl0_729,
inference(avatar_split_clause,[],[f2762,f6994]) ).
fof(f6992,plain,
spl0_728,
inference(avatar_split_clause,[],[f1842,f6990]) ).
fof(f6990,plain,
( spl0_728
<=> ! [X92] :
( ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_set(X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f1842,axiom,
! [X92] :
( ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_set(X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6988,plain,
spl0_727,
inference(avatar_split_clause,[],[f1720,f6986]) ).
fof(f6986,plain,
( spl0_727
<=> ! [X92] :
( ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1720,axiom,
! [X92] :
( ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6984,plain,
spl0_726,
inference(avatar_split_clause,[],[f1704,f6982]) ).
fof(f1704,axiom,
! [X1,X5] : c_lessequals(X1,X1,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6980,plain,
spl0_725,
inference(avatar_split_clause,[],[f1693,f6978]) ).
fof(f6978,plain,
( spl0_725
<=> ! [X5,X1] : c_lessequals(c_emptyset,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1693,axiom,
! [X1,X5] : c_lessequals(c_emptyset,X1,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6976,plain,
spl0_724,
inference(avatar_split_clause,[],[f1636,f6974]) ).
fof(f6974,plain,
( spl0_724
<=> ! [X5,X44] : c_List_Odistinct(c_List_Oremdups(X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1636,axiom,
! [X44,X5] : c_List_Odistinct(c_List_Oremdups(X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6972,plain,
spl0_723,
inference(avatar_split_clause,[],[f1620,f6970]) ).
fof(f6970,plain,
( spl0_723
<=> ! [X5] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f1620,axiom,
! [X5] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6968,plain,
spl0_722,
inference(avatar_split_clause,[],[f1579,f6966]) ).
fof(f6966,plain,
( spl0_722
<=> ! [X5] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1579,axiom,
! [X5] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f6964,plain,
spl0_721,
inference(avatar_split_clause,[],[f1563,f6962]) ).
fof(f6962,plain,
( spl0_721
<=> ! [X5,X1] : c_lessequals(X1,c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1563,axiom,
! [X1,X5] : c_lessequals(X1,c_UNIV,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f6960,plain,
spl0_720,
inference(avatar_split_clause,[],[f1556,f6958]) ).
fof(f6958,plain,
( spl0_720
<=> ! [X5,X1] : ~ c_less(X1,c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1556,axiom,
! [X1,X5] : ~ c_less(X1,c_emptyset,tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f6956,plain,
spl0_719,
inference(avatar_split_clause,[],[f1516,f6954]) ).
fof(f6954,plain,
( spl0_719
<=> ! [X5] : c_emptyset = c_Union(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f1516,axiom,
! [X5] : c_emptyset = c_Union(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f6952,plain,
spl0_718,
inference(avatar_split_clause,[],[f1514,f6950]) ).
fof(f6950,plain,
( spl0_718
<=> ! [X5] : c_UNIV = c_Union(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1514,axiom,
! [X5] : c_UNIV = c_Union(c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f6948,plain,
spl0_717,
inference(avatar_split_clause,[],[f1490,f6946]) ).
fof(f6946,plain,
( spl0_717
<=> ! [X5] : c_UNIV = c_Pow(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1490,axiom,
! [X5] : c_UNIV = c_Pow(c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f6944,plain,
spl0_716,
inference(avatar_split_clause,[],[f1484,f6942]) ).
fof(f6942,plain,
( spl0_716
<=> ! [X5] : c_UNIV = c_Inter(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1484,axiom,
! [X5] : c_UNIV = c_Inter(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f6940,plain,
spl0_715,
inference(avatar_split_clause,[],[f1477,f6938]) ).
fof(f6938,plain,
( spl0_715
<=> ! [X5] : c_emptyset = c_Inter(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f1477,axiom,
! [X5] : c_emptyset = c_Inter(c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f6936,plain,
spl0_714,
inference(avatar_split_clause,[],[f1432,f6933]) ).
fof(f6933,plain,
( spl0_714
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1432,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f6931,plain,
spl0_713,
inference(avatar_split_clause,[],[f1393,f6928]) ).
fof(f6928,plain,
( spl0_713
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1393,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f6926,plain,
spl0_712,
inference(avatar_split_clause,[],[f1251,f6924]) ).
fof(f6922,plain,
spl0_711,
inference(avatar_split_clause,[],[f1029,f6919]) ).
fof(f6919,plain,
( spl0_711
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f1029,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(f6917,plain,
spl0_710,
inference(avatar_split_clause,[],[f1028,f6914]) ).
fof(f6914,plain,
( spl0_710
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f1028,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(f6912,plain,
spl0_709,
inference(avatar_split_clause,[],[f1017,f6910]) ).
fof(f6910,plain,
( spl0_709
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f1017,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f6908,plain,
spl0_708,
inference(avatar_split_clause,[],[f1016,f6906]) ).
fof(f6906,plain,
( spl0_708
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f1016,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f6904,plain,
spl0_707,
inference(avatar_split_clause,[],[f1000,f6902]) ).
fof(f6902,plain,
( spl0_707
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_IntDef_Oiszero(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f1000,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_IntDef_Oiszero(c_1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f6900,plain,
spl0_706,
inference(avatar_split_clause,[],[f995,f6898]) ).
fof(f6898,plain,
( spl0_706
<=> ! [X39] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X39) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f995,axiom,
! [X39] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f6896,plain,
spl0_705,
inference(avatar_split_clause,[],[f980,f6894]) ).
fof(f6894,plain,
( spl0_705
<=> ! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f6892,plain,
spl0_704,
inference(avatar_split_clause,[],[f979,f6890]) ).
fof(f6888,plain,
spl0_703,
inference(avatar_split_clause,[],[f971,f6885]) ).
fof(f971,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(f6883,plain,
spl0_702,
inference(avatar_split_clause,[],[f970,f6880]) ).
fof(f970,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(f6878,plain,
spl0_701,
inference(avatar_split_clause,[],[f731,f6875]) ).
fof(f731,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(f6873,plain,
spl0_700,
inference(avatar_split_clause,[],[f650,f6871]) ).
fof(f6871,plain,
( spl0_700
<=> ! [X29] : c_List_Olist_ONil = c_List_Oupt(X29,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f650,axiom,
! [X29] : c_List_Olist_ONil = c_List_Oupt(X29,c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f6869,plain,
spl0_699,
inference(avatar_split_clause,[],[f643,f6867]) ).
fof(f6867,plain,
( spl0_699
<=> ! [X21] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f643,axiom,
! [X21] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f6865,plain,
spl0_698,
inference(avatar_split_clause,[],[f616,f6863]) ).
fof(f6863,plain,
( spl0_698
<=> ! [X5] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f616,axiom,
! [X5] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
fof(f6861,plain,
spl0_697,
inference(avatar_split_clause,[],[f601,f6859]) ).
fof(f6859,plain,
( spl0_697
<=> ! [X5] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f601,axiom,
! [X5] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f6857,plain,
spl0_696,
inference(avatar_split_clause,[],[f581,f6855]) ).
fof(f6855,plain,
( spl0_696
<=> ! [X5] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f581,axiom,
! [X5] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
fof(f6853,plain,
spl0_695,
inference(avatar_split_clause,[],[f553,f6850]) ).
fof(f6850,plain,
( spl0_695
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f553,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(f6848,plain,
spl0_694,
inference(avatar_split_clause,[],[f552,f6845]) ).
fof(f6845,plain,
( spl0_694
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f552,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(f6843,plain,
spl0_693,
inference(avatar_split_clause,[],[f551,f6840]) ).
fof(f6840,plain,
( spl0_693
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f551,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(f6838,plain,
spl0_692,
inference(avatar_split_clause,[],[f550,f6835]) ).
fof(f6835,plain,
( spl0_692
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f550,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(f6833,plain,
spl0_691,
inference(avatar_split_clause,[],[f549,f6830]) ).
fof(f6830,plain,
( spl0_691
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f549,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(f6828,plain,
spl0_690,
inference(avatar_split_clause,[],[f548,f6825]) ).
fof(f6825,plain,
( spl0_690
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f548,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(f6823,plain,
spl0_689,
inference(avatar_split_clause,[],[f547,f6820]) ).
fof(f6820,plain,
( spl0_689
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f547,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(f6818,plain,
spl0_688,
inference(avatar_split_clause,[],[f546,f6815]) ).
fof(f6815,plain,
( spl0_688
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f546,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(f6813,plain,
spl0_687,
inference(avatar_split_clause,[],[f545,f6810]) ).
fof(f6810,plain,
( spl0_687
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f545,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(f6808,plain,
spl0_686,
inference(avatar_split_clause,[],[f544,f6805]) ).
fof(f6805,plain,
( spl0_686
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f544,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(f6803,plain,
spl0_685,
inference(avatar_split_clause,[],[f543,f6800]) ).
fof(f6800,plain,
( spl0_685
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f543,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(f6798,plain,
spl0_684,
inference(avatar_split_clause,[],[f542,f6795]) ).
fof(f6795,plain,
( spl0_684
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f542,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(f6793,plain,
spl0_683,
inference(avatar_split_clause,[],[f541,f6790]) ).
fof(f6790,plain,
( spl0_683
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f541,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(f6788,plain,
spl0_682,
inference(avatar_split_clause,[],[f540,f6785]) ).
fof(f6785,plain,
( spl0_682
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f540,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(f6783,plain,
spl0_681,
inference(avatar_split_clause,[],[f539,f6780]) ).
fof(f6780,plain,
( spl0_681
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f539,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(f6778,plain,
spl0_680,
inference(avatar_split_clause,[],[f538,f6775]) ).
fof(f6775,plain,
( spl0_680
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f538,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(f6773,plain,
spl0_679,
inference(avatar_split_clause,[],[f503,f6771]) ).
fof(f6771,plain,
( spl0_679
<=> ! [X5] : c_UNIV = c_List_Olists(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f503,axiom,
! [X5] : c_UNIV = c_List_Olists(c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f6769,plain,
spl0_678,
inference(avatar_split_clause,[],[f432,f6767]) ).
fof(f6767,plain,
( spl0_678
<=> ! [X29,X55] : c_List_Odistinct(c_List_Oupt(X29,X55),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f432,axiom,
! [X29,X55] : c_List_Odistinct(c_List_Oupt(X29,X55),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f6765,plain,
spl0_677,
inference(avatar_split_clause,[],[f408,f6763]) ).
fof(f6763,plain,
( spl0_677
<=> ! [X21] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f408,axiom,
! [X21] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f6761,plain,
spl0_676,
inference(avatar_split_clause,[],[f401,f6759]) ).
fof(f6759,plain,
( spl0_676
<=> ! [X21] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f401,axiom,
! [X21] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f6757,plain,
spl0_675,
inference(avatar_split_clause,[],[f379,f6755]) ).
fof(f6755,plain,
( spl0_675
<=> ! [X5] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f6753,plain,
spl0_674,
inference(avatar_split_clause,[],[f289,f6751]) ).
fof(f289,axiom,
! [X19] : c_lessequals(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f6749,plain,
spl0_673,
inference(avatar_split_clause,[],[f249,f6747]) ).
fof(f249,axiom,
! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f6745,plain,
spl0_672,
inference(avatar_split_clause,[],[f243,f6743]) ).
fof(f243,axiom,
! [X18] : ~ c_less(c_IntDef_Oint(X18),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f6741,plain,
~ spl0_671,
inference(avatar_split_clause,[],[f174,f6738]) ).
fof(f174,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(f6736,plain,
spl0_670,
inference(avatar_split_clause,[],[f161,f6734]) ).
fof(f6734,plain,
( spl0_670
<=> ! [X5,X8] : c_Fun_Oid(X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f161,axiom,
! [X8,X5] : c_Fun_Oid(X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6732,plain,
spl0_669,
inference(avatar_split_clause,[],[f160,f6730]) ).
fof(f160,axiom,
! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f6728,plain,
spl0_668,
inference(avatar_split_clause,[],[f143,f6726]) ).
fof(f6726,plain,
( spl0_668
<=> ! [X5] : c_0 = c_Finite__Set_Ocard(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f143,axiom,
! [X5] : c_0 = c_Finite__Set_Ocard(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f6724,plain,
spl0_667,
inference(avatar_split_clause,[],[f120,f6721]) ).
fof(f6721,plain,
( spl0_667
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f120,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(f6719,plain,
spl0_666,
inference(avatar_split_clause,[],[f119,f6716]) ).
fof(f6716,plain,
( spl0_666
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f119,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(f6714,plain,
spl0_665,
inference(avatar_split_clause,[],[f49,f6711]) ).
fof(f6711,plain,
( spl0_665
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f49,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(f6709,plain,
spl0_664,
inference(avatar_split_clause,[],[f38,f6707]) ).
fof(f6707,plain,
( spl0_664
<=> ! [X22,X5] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X22,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f38,axiom,
! [X22,X5] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X22,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f6705,plain,
spl0_663,
inference(avatar_split_clause,[],[f37,f6703]) ).
fof(f6703,plain,
( spl0_663
<=> ! [X5] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f37,axiom,
! [X5] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f6701,plain,
spl0_662,
inference(avatar_split_clause,[],[f30,f6699]) ).
fof(f6699,plain,
( spl0_662
<=> ! [X19] : c_1 = c_Binomial_Obinomial(X19,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f30,axiom,
! [X19] : c_1 = c_Binomial_Obinomial(X19,X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6697,plain,
spl0_661,
inference(avatar_split_clause,[],[f29,f6695]) ).
fof(f6695,plain,
( spl0_661
<=> ! [X19] : c_Binomial_Obinomial(X19,c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f29,axiom,
! [X19] : c_Binomial_Obinomial(X19,c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f5941,plain,
( ~ spl0_660
| ~ spl0_116
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f5923,f3754,f3744,f5938]) ).
fof(f5938,plain,
( spl0_660
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f3754,plain,
( spl0_118
<=> ! [X19] : ~ c_IntDef_Oneg(c_IntDef_Oint(X19),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f5923,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_118 ),
inference(superposition,[],[f3755,f3746]) ).
fof(f3755,plain,
( ! [X19] : ~ c_IntDef_Oneg(c_IntDef_Oint(X19),tc_IntDef_Oint)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f3754]) ).
fof(f5928,plain,
( ~ spl0_659
| ~ spl0_115
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f5922,f3754,f3739,f5925]) ).
fof(f5925,plain,
( spl0_659
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f5922,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_115
| ~ spl0_118 ),
inference(superposition,[],[f3755,f3741]) ).
fof(f5921,plain,
spl0_658,
inference(avatar_split_clause,[],[f3002,f5918]) ).
fof(f5918,plain,
( spl0_658
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f3002,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f351,f329]) ).
fof(f351,axiom,
! [X4] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X4,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(f5916,plain,
spl0_657,
inference(avatar_split_clause,[],[f2983,f5913]) ).
fof(f5913,plain,
( spl0_657
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2983,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f242,f239]) ).
fof(f242,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(f5911,plain,
spl0_656,
inference(avatar_split_clause,[],[f2982,f5909]) ).
fof(f5909,plain,
( spl0_656
<=> ! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2982,plain,
! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_nat),
inference(forward_demodulation,[],[f2767,f2763]) ).
fof(f2767,plain,
! [X18] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X18,tc_nat),
inference(definition_unfolding,[],[f1616,f1409]) ).
fof(f1616,axiom,
! [X18] : c_Divides_Oop_Advd(c_Suc(c_0),X18,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f5907,plain,
spl0_655,
inference(avatar_split_clause,[],[f2980,f5904]) ).
fof(f5904,plain,
( spl0_655
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2980,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2765,f2763]) ).
fof(f2765,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f209,f1409]) ).
fof(f209,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f5902,plain,
spl0_654,
inference(avatar_split_clause,[],[f2751,f5900]) ).
fof(f5900,plain,
( spl0_654
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2751,axiom,
! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Olinorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f5898,plain,
spl0_653,
inference(avatar_split_clause,[],[f2750,f5896]) ).
fof(f5896,plain,
( spl0_653
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2750,axiom,
! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f5894,plain,
spl0_652,
inference(avatar_split_clause,[],[f2749,f5892]) ).
fof(f5892,plain,
( spl0_652
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2749,axiom,
! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f5890,plain,
spl0_651,
inference(avatar_split_clause,[],[f2748,f5888]) ).
fof(f5888,plain,
( spl0_651
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2748,axiom,
! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f5886,plain,
spl0_650,
inference(avatar_split_clause,[],[f2747,f5884]) ).
fof(f5884,plain,
( spl0_650
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2747,axiom,
! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f5882,plain,
spl0_649,
inference(avatar_split_clause,[],[f2746,f5880]) ).
fof(f5880,plain,
( spl0_649
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2746,axiom,
! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f5878,plain,
spl0_648,
inference(avatar_split_clause,[],[f2745,f5876]) ).
fof(f5876,plain,
( spl0_648
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2745,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f5874,plain,
spl0_647,
inference(avatar_split_clause,[],[f2740,f5872]) ).
fof(f5872,plain,
( spl0_647
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2740,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f5870,plain,
spl0_646,
inference(avatar_split_clause,[],[f2739,f5868]) ).
fof(f5868,plain,
( spl0_646
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f2739,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f5866,plain,
spl0_645,
inference(avatar_split_clause,[],[f2738,f5864]) ).
fof(f5864,plain,
( spl0_645
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f2738,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f5862,plain,
spl0_644,
inference(avatar_split_clause,[],[f2737,f5860]) ).
fof(f5860,plain,
( spl0_644
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f2737,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f5858,plain,
spl0_643,
inference(avatar_split_clause,[],[f2736,f5856]) ).
fof(f5856,plain,
( spl0_643
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2736,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f5854,plain,
spl0_642,
inference(avatar_split_clause,[],[f2735,f5852]) ).
fof(f5852,plain,
( spl0_642
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f2735,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f5850,plain,
spl0_641,
inference(avatar_split_clause,[],[f2732,f5848]) ).
fof(f5848,plain,
( spl0_641
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f2732,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f5846,plain,
spl0_640,
inference(avatar_split_clause,[],[f2731,f5844]) ).
fof(f5844,plain,
( spl0_640
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f2731,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f5842,plain,
spl0_639,
inference(avatar_split_clause,[],[f2730,f5840]) ).
fof(f5840,plain,
( spl0_639
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f2730,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f5838,plain,
spl0_638,
inference(avatar_split_clause,[],[f2727,f5836]) ).
fof(f5836,plain,
( spl0_638
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f2727,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f5834,plain,
spl0_637,
inference(avatar_split_clause,[],[f2724,f5832]) ).
fof(f5832,plain,
( spl0_637
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f2724,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f5830,plain,
spl0_636,
inference(avatar_split_clause,[],[f2723,f5828]) ).
fof(f5828,plain,
( spl0_636
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f2723,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f5826,plain,
spl0_635,
inference(avatar_split_clause,[],[f2722,f5824]) ).
fof(f5824,plain,
( spl0_635
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f2722,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f5822,plain,
spl0_634,
inference(avatar_split_clause,[],[f2721,f5820]) ).
fof(f5820,plain,
( spl0_634
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f2721,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f5818,plain,
spl0_633,
inference(avatar_split_clause,[],[f2718,f5816]) ).
fof(f5816,plain,
( spl0_633
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f2718,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f5814,plain,
spl0_632,
inference(avatar_split_clause,[],[f2717,f5812]) ).
fof(f5812,plain,
( spl0_632
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f2717,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f5810,plain,
spl0_631,
inference(avatar_split_clause,[],[f2712,f5808]) ).
fof(f5808,plain,
( spl0_631
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f2712,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5806,plain,
spl0_630,
inference(avatar_split_clause,[],[f2709,f5804]) ).
fof(f5804,plain,
( spl0_630
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f2709,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5802,plain,
spl0_629,
inference(avatar_split_clause,[],[f2708,f5800]) ).
fof(f5800,plain,
( spl0_629
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f2708,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5798,plain,
spl0_628,
inference(avatar_split_clause,[],[f2707,f5796]) ).
fof(f5796,plain,
( spl0_628
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2707,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5794,plain,
spl0_627,
inference(avatar_split_clause,[],[f2705,f5792]) ).
fof(f5792,plain,
( spl0_627
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2705,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__0(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5790,plain,
spl0_626,
inference(avatar_split_clause,[],[f2699,f5788]) ).
fof(f5788,plain,
( spl0_626
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2699,axiom,
! [X94] :
( ~ class_Ring__and__Field_Osemiring__0(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5786,plain,
spl0_625,
inference(avatar_split_clause,[],[f2691,f5784]) ).
fof(f5784,plain,
( spl0_625
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2691,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5782,plain,
spl0_624,
inference(avatar_split_clause,[],[f2690,f5780]) ).
fof(f5780,plain,
( spl0_624
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2690,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5778,plain,
spl0_623,
inference(avatar_split_clause,[],[f2689,f5776]) ).
fof(f5776,plain,
( spl0_623
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f2689,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5774,plain,
spl0_622,
inference(avatar_split_clause,[],[f2688,f5772]) ).
fof(f5772,plain,
( spl0_622
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2688,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5770,plain,
spl0_621,
inference(avatar_split_clause,[],[f2687,f5768]) ).
fof(f5768,plain,
( spl0_621
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2687,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5766,plain,
spl0_620,
inference(avatar_split_clause,[],[f2685,f5764]) ).
fof(f5764,plain,
( spl0_620
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f2685,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5762,plain,
spl0_619,
inference(avatar_split_clause,[],[f2684,f5760]) ).
fof(f5760,plain,
( spl0_619
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f2684,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5758,plain,
spl0_618,
inference(avatar_split_clause,[],[f2683,f5756]) ).
fof(f5756,plain,
( spl0_618
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f2683,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5754,plain,
spl0_617,
inference(avatar_split_clause,[],[f2682,f5752]) ).
fof(f5752,plain,
( spl0_617
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f2682,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5750,plain,
spl0_616,
inference(avatar_split_clause,[],[f2681,f5748]) ).
fof(f5748,plain,
( spl0_616
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2681,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5746,plain,
spl0_615,
inference(avatar_split_clause,[],[f2676,f5744]) ).
fof(f5744,plain,
( spl0_615
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2676,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5742,plain,
spl0_614,
inference(avatar_split_clause,[],[f2675,f5740]) ).
fof(f5740,plain,
( spl0_614
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2675,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5738,plain,
spl0_613,
inference(avatar_split_clause,[],[f2674,f5736]) ).
fof(f5736,plain,
( spl0_613
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2674,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5734,plain,
spl0_612,
inference(avatar_split_clause,[],[f2672,f5732]) ).
fof(f5732,plain,
( spl0_612
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2672,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5730,plain,
spl0_611,
inference(avatar_split_clause,[],[f2670,f5728]) ).
fof(f5728,plain,
( spl0_611
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2670,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5726,plain,
spl0_610,
inference(avatar_split_clause,[],[f2665,f5724]) ).
fof(f5724,plain,
( spl0_610
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2665,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5722,plain,
spl0_609,
inference(avatar_split_clause,[],[f2664,f5720]) ).
fof(f5720,plain,
( spl0_609
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2664,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5718,plain,
spl0_608,
inference(avatar_split_clause,[],[f2663,f5716]) ).
fof(f5716,plain,
( spl0_608
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2663,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5714,plain,
spl0_607,
inference(avatar_split_clause,[],[f2662,f5712]) ).
fof(f5712,plain,
( spl0_607
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2662,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5710,plain,
spl0_606,
inference(avatar_split_clause,[],[f2660,f5708]) ).
fof(f5708,plain,
( spl0_606
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2660,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5706,plain,
spl0_605,
inference(avatar_split_clause,[],[f2659,f5704]) ).
fof(f5704,plain,
( spl0_605
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2659,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5702,plain,
spl0_604,
inference(avatar_split_clause,[],[f2654,f5700]) ).
fof(f5700,plain,
( spl0_604
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2654,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5698,plain,
spl0_603,
inference(avatar_split_clause,[],[f2651,f5696]) ).
fof(f5696,plain,
( spl0_603
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f2651,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5694,plain,
spl0_602,
inference(avatar_split_clause,[],[f2650,f5692]) ).
fof(f5692,plain,
( spl0_602
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f2650,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5690,plain,
spl0_601,
inference(avatar_split_clause,[],[f2649,f5688]) ).
fof(f5688,plain,
( spl0_601
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f2649,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5686,plain,
spl0_600,
inference(avatar_split_clause,[],[f2648,f5684]) ).
fof(f5684,plain,
( spl0_600
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f2648,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5682,plain,
spl0_599,
inference(avatar_split_clause,[],[f2645,f5680]) ).
fof(f5680,plain,
( spl0_599
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f2645,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5678,plain,
spl0_598,
inference(avatar_split_clause,[],[f2644,f5676]) ).
fof(f5676,plain,
( spl0_598
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f2644,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5674,plain,
spl0_597,
inference(avatar_split_clause,[],[f2643,f5672]) ).
fof(f5672,plain,
( spl0_597
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f2643,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5670,plain,
spl0_596,
inference(avatar_split_clause,[],[f2642,f5668]) ).
fof(f5668,plain,
( spl0_596
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2642,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5666,plain,
spl0_595,
inference(avatar_split_clause,[],[f2641,f5664]) ).
fof(f5664,plain,
( spl0_595
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2641,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5662,plain,
spl0_594,
inference(avatar_split_clause,[],[f2640,f5660]) ).
fof(f5660,plain,
( spl0_594
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2640,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5658,plain,
spl0_593,
inference(avatar_split_clause,[],[f2639,f5656]) ).
fof(f5656,plain,
( spl0_593
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2639,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5654,plain,
spl0_592,
inference(avatar_split_clause,[],[f2638,f5652]) ).
fof(f5652,plain,
( spl0_592
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2638,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5650,plain,
spl0_591,
inference(avatar_split_clause,[],[f2636,f5648]) ).
fof(f5648,plain,
( spl0_591
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2636,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5646,plain,
spl0_590,
inference(avatar_split_clause,[],[f2635,f5644]) ).
fof(f5644,plain,
( spl0_590
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2635,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5642,plain,
spl0_589,
inference(avatar_split_clause,[],[f2634,f5640]) ).
fof(f5640,plain,
( spl0_589
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2634,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5638,plain,
spl0_588,
inference(avatar_split_clause,[],[f2633,f5636]) ).
fof(f5636,plain,
( spl0_588
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2633,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5634,plain,
spl0_587,
inference(avatar_split_clause,[],[f2632,f5632]) ).
fof(f5632,plain,
( spl0_587
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2632,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5630,plain,
spl0_586,
inference(avatar_split_clause,[],[f2627,f5628]) ).
fof(f5628,plain,
( spl0_586
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2627,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5626,plain,
spl0_585,
inference(avatar_split_clause,[],[f2626,f5624]) ).
fof(f5624,plain,
( spl0_585
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2626,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5622,plain,
spl0_584,
inference(avatar_split_clause,[],[f2625,f5620]) ).
fof(f5620,plain,
( spl0_584
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2625,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5618,plain,
spl0_583,
inference(avatar_split_clause,[],[f2622,f5616]) ).
fof(f5616,plain,
( spl0_583
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2622,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5614,plain,
spl0_582,
inference(avatar_split_clause,[],[f2619,f5612]) ).
fof(f5612,plain,
( spl0_582
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2619,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5610,plain,
spl0_581,
inference(avatar_split_clause,[],[f2618,f5608]) ).
fof(f5608,plain,
( spl0_581
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2618,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5606,plain,
spl0_580,
inference(avatar_split_clause,[],[f2616,f5604]) ).
fof(f5604,plain,
( spl0_580
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2616,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5602,plain,
spl0_579,
inference(avatar_split_clause,[],[f2615,f5600]) ).
fof(f5600,plain,
( spl0_579
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2615,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5598,plain,
spl0_578,
inference(avatar_split_clause,[],[f2614,f5596]) ).
fof(f5596,plain,
( spl0_578
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2614,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5594,plain,
spl0_577,
inference(avatar_split_clause,[],[f2613,f5592]) ).
fof(f5592,plain,
( spl0_577
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2613,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5590,plain,
spl0_576,
inference(avatar_split_clause,[],[f2610,f5588]) ).
fof(f5588,plain,
( spl0_576
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2610,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5586,plain,
spl0_575,
inference(avatar_split_clause,[],[f2609,f5584]) ).
fof(f5584,plain,
( spl0_575
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2609,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5582,plain,
spl0_574,
inference(avatar_split_clause,[],[f2581,f5580]) ).
fof(f5580,plain,
( spl0_574
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2581,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5578,plain,
spl0_573,
inference(avatar_split_clause,[],[f2579,f5576]) ).
fof(f5576,plain,
( spl0_573
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2579,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5574,plain,
spl0_572,
inference(avatar_split_clause,[],[f2576,f5572]) ).
fof(f5572,plain,
( spl0_572
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2576,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5570,plain,
spl0_571,
inference(avatar_split_clause,[],[f2575,f5568]) ).
fof(f5568,plain,
( spl0_571
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2575,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5566,plain,
spl0_570,
inference(avatar_split_clause,[],[f2574,f5564]) ).
fof(f5564,plain,
( spl0_570
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2574,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5562,plain,
spl0_569,
inference(avatar_split_clause,[],[f2573,f5560]) ).
fof(f5560,plain,
( spl0_569
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2573,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5558,plain,
spl0_568,
inference(avatar_split_clause,[],[f2572,f5556]) ).
fof(f5556,plain,
( spl0_568
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2572,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5554,plain,
spl0_567,
inference(avatar_split_clause,[],[f2571,f5552]) ).
fof(f5552,plain,
( spl0_567
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2571,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5550,plain,
spl0_566,
inference(avatar_split_clause,[],[f2569,f5548]) ).
fof(f5548,plain,
( spl0_566
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2569,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5546,plain,
spl0_565,
inference(avatar_split_clause,[],[f2568,f5544]) ).
fof(f5544,plain,
( spl0_565
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2568,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5542,plain,
spl0_564,
inference(avatar_split_clause,[],[f2566,f5540]) ).
fof(f5540,plain,
( spl0_564
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2566,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5538,plain,
spl0_563,
inference(avatar_split_clause,[],[f2563,f5536]) ).
fof(f5536,plain,
( spl0_563
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2563,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5534,plain,
spl0_562,
inference(avatar_split_clause,[],[f2562,f5532]) ).
fof(f5532,plain,
( spl0_562
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2562,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5530,plain,
spl0_561,
inference(avatar_split_clause,[],[f2560,f5528]) ).
fof(f5528,plain,
( spl0_561
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2560,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5526,plain,
spl0_560,
inference(avatar_split_clause,[],[f2559,f5524]) ).
fof(f5524,plain,
( spl0_560
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2559,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5522,plain,
spl0_559,
inference(avatar_split_clause,[],[f2558,f5520]) ).
fof(f5520,plain,
( spl0_559
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2558,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5518,plain,
spl0_558,
inference(avatar_split_clause,[],[f2557,f5516]) ).
fof(f5516,plain,
( spl0_558
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2557,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5514,plain,
spl0_557,
inference(avatar_split_clause,[],[f2556,f5512]) ).
fof(f5512,plain,
( spl0_557
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2556,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5510,plain,
spl0_556,
inference(avatar_split_clause,[],[f2555,f5508]) ).
fof(f5508,plain,
( spl0_556
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f2555,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5506,plain,
spl0_555,
inference(avatar_split_clause,[],[f2554,f5504]) ).
fof(f5504,plain,
( spl0_555
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2554,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5502,plain,
spl0_554,
inference(avatar_split_clause,[],[f2553,f5500]) ).
fof(f5500,plain,
( spl0_554
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f2553,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5498,plain,
spl0_553,
inference(avatar_split_clause,[],[f2549,f5496]) ).
fof(f5496,plain,
( spl0_553
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2549,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5494,plain,
spl0_552,
inference(avatar_split_clause,[],[f2548,f5492]) ).
fof(f5492,plain,
( spl0_552
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2548,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5490,plain,
spl0_551,
inference(avatar_split_clause,[],[f2547,f5488]) ).
fof(f5488,plain,
( spl0_551
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f2547,axiom,
! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5486,plain,
spl0_550,
inference(avatar_split_clause,[],[f2546,f5484]) ).
fof(f5484,plain,
( spl0_550
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2546,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5482,plain,
spl0_549,
inference(avatar_split_clause,[],[f2541,f5480]) ).
fof(f5480,plain,
( spl0_549
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f2541,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5478,plain,
spl0_548,
inference(avatar_split_clause,[],[f2539,f5476]) ).
fof(f5476,plain,
( spl0_548
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2539,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5474,plain,
spl0_547,
inference(avatar_split_clause,[],[f2538,f5472]) ).
fof(f5472,plain,
( spl0_547
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f2538,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5470,plain,
spl0_546,
inference(avatar_split_clause,[],[f2537,f5468]) ).
fof(f5468,plain,
( spl0_546
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2537,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5466,plain,
spl0_545,
inference(avatar_split_clause,[],[f2536,f5464]) ).
fof(f5464,plain,
( spl0_545
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2536,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5462,plain,
spl0_544,
inference(avatar_split_clause,[],[f2534,f5460]) ).
fof(f5460,plain,
( spl0_544
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2534,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5458,plain,
spl0_543,
inference(avatar_split_clause,[],[f2533,f5456]) ).
fof(f5456,plain,
( spl0_543
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2533,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5454,plain,
spl0_542,
inference(avatar_split_clause,[],[f2532,f5452]) ).
fof(f5452,plain,
( spl0_542
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2532,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5450,plain,
spl0_541,
inference(avatar_split_clause,[],[f2531,f5448]) ).
fof(f5448,plain,
( spl0_541
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2531,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5446,plain,
spl0_540,
inference(avatar_split_clause,[],[f2530,f5444]) ).
fof(f5444,plain,
( spl0_540
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2530,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5442,plain,
spl0_539,
inference(avatar_split_clause,[],[f2529,f5440]) ).
fof(f5440,plain,
( spl0_539
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2529,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5438,plain,
spl0_538,
inference(avatar_split_clause,[],[f2528,f5436]) ).
fof(f5436,plain,
( spl0_538
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2528,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5434,plain,
spl0_537,
inference(avatar_split_clause,[],[f2527,f5432]) ).
fof(f5432,plain,
( spl0_537
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2527,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5430,plain,
spl0_536,
inference(avatar_split_clause,[],[f2526,f5428]) ).
fof(f5428,plain,
( spl0_536
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2526,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5426,plain,
spl0_535,
inference(avatar_split_clause,[],[f2525,f5424]) ).
fof(f5424,plain,
( spl0_535
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2525,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Olinorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5422,plain,
spl0_534,
inference(avatar_split_clause,[],[f2524,f5420]) ).
fof(f5420,plain,
( spl0_534
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f2524,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5418,plain,
spl0_533,
inference(avatar_split_clause,[],[f2523,f5416]) ).
fof(f5416,plain,
( spl0_533
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f2523,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5414,plain,
spl0_532,
inference(avatar_split_clause,[],[f2522,f5412]) ).
fof(f5412,plain,
( spl0_532
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f2522,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5410,plain,
spl0_531,
inference(avatar_split_clause,[],[f2521,f5408]) ).
fof(f5408,plain,
( spl0_531
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f2521,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5406,plain,
spl0_530,
inference(avatar_split_clause,[],[f2520,f5404]) ).
fof(f5404,plain,
( spl0_530
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2520,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5402,plain,
spl0_529,
inference(avatar_split_clause,[],[f2519,f5400]) ).
fof(f5400,plain,
( spl0_529
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f2519,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5398,plain,
spl0_528,
inference(avatar_split_clause,[],[f2518,f5396]) ).
fof(f5396,plain,
( spl0_528
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2518,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5394,plain,
spl0_527,
inference(avatar_split_clause,[],[f2517,f5392]) ).
fof(f5392,plain,
( spl0_527
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f2517,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5390,plain,
spl0_526,
inference(avatar_split_clause,[],[f2516,f5388]) ).
fof(f5388,plain,
( spl0_526
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f2516,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5386,plain,
spl0_525,
inference(avatar_split_clause,[],[f2515,f5384]) ).
fof(f5384,plain,
( spl0_525
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2515,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5382,plain,
spl0_524,
inference(avatar_split_clause,[],[f2514,f5380]) ).
fof(f5380,plain,
( spl0_524
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2514,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5378,plain,
spl0_523,
inference(avatar_split_clause,[],[f2513,f5376]) ).
fof(f5376,plain,
( spl0_523
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2513,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5374,plain,
spl0_522,
inference(avatar_split_clause,[],[f2512,f5372]) ).
fof(f5372,plain,
( spl0_522
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2512,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5370,plain,
spl0_521,
inference(avatar_split_clause,[],[f2511,f5368]) ).
fof(f5368,plain,
( spl0_521
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2511,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5366,plain,
spl0_520,
inference(avatar_split_clause,[],[f2510,f5364]) ).
fof(f5364,plain,
( spl0_520
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2510,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5362,plain,
spl0_519,
inference(avatar_split_clause,[],[f2509,f5360]) ).
fof(f5360,plain,
( spl0_519
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2509,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5358,plain,
spl0_518,
inference(avatar_split_clause,[],[f2508,f5356]) ).
fof(f5356,plain,
( spl0_518
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2508,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5354,plain,
spl0_517,
inference(avatar_split_clause,[],[f2507,f5352]) ).
fof(f5352,plain,
( spl0_517
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2507,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5350,plain,
spl0_516,
inference(avatar_split_clause,[],[f2506,f5348]) ).
fof(f5348,plain,
( spl0_516
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2506,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5346,plain,
spl0_515,
inference(avatar_split_clause,[],[f2505,f5344]) ).
fof(f5344,plain,
( spl0_515
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2505,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5342,plain,
spl0_514,
inference(avatar_split_clause,[],[f2504,f5340]) ).
fof(f5340,plain,
( spl0_514
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f2504,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5338,plain,
spl0_513,
inference(avatar_split_clause,[],[f2503,f5336]) ).
fof(f5336,plain,
( spl0_513
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2503,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Olinorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5334,plain,
spl0_512,
inference(avatar_split_clause,[],[f2502,f5332]) ).
fof(f5332,plain,
( spl0_512
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2502,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5330,plain,
spl0_511,
inference(avatar_split_clause,[],[f2501,f5328]) ).
fof(f5328,plain,
( spl0_511
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2501,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5326,plain,
spl0_510,
inference(avatar_split_clause,[],[f2500,f5324]) ).
fof(f5324,plain,
( spl0_510
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2500,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5322,plain,
spl0_509,
inference(avatar_split_clause,[],[f2497,f5320]) ).
fof(f5320,plain,
( spl0_509
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2497,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5318,plain,
spl0_508,
inference(avatar_split_clause,[],[f2495,f5316]) ).
fof(f5316,plain,
( spl0_508
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f2495,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5314,plain,
spl0_507,
inference(avatar_split_clause,[],[f2494,f5312]) ).
fof(f5312,plain,
( spl0_507
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2494,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5310,plain,
spl0_506,
inference(avatar_split_clause,[],[f2492,f5308]) ).
fof(f5308,plain,
( spl0_506
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2492,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5306,plain,
spl0_505,
inference(avatar_split_clause,[],[f2489,f5304]) ).
fof(f5304,plain,
( spl0_505
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2489,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5302,plain,
spl0_504,
inference(avatar_split_clause,[],[f2488,f5300]) ).
fof(f5300,plain,
( spl0_504
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2488,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5298,plain,
spl0_503,
inference(avatar_split_clause,[],[f2487,f5296]) ).
fof(f5296,plain,
( spl0_503
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2487,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5294,plain,
spl0_502,
inference(avatar_split_clause,[],[f2485,f5292]) ).
fof(f5292,plain,
( spl0_502
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2485,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5290,plain,
spl0_501,
inference(avatar_split_clause,[],[f2484,f5288]) ).
fof(f5288,plain,
( spl0_501
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2484,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5286,plain,
spl0_500,
inference(avatar_split_clause,[],[f2483,f5284]) ).
fof(f5284,plain,
( spl0_500
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2483,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5282,plain,
spl0_499,
inference(avatar_split_clause,[],[f2480,f5280]) ).
fof(f5280,plain,
( spl0_499
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2480,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5278,plain,
spl0_498,
inference(avatar_split_clause,[],[f2479,f5276]) ).
fof(f5276,plain,
( spl0_498
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2479,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5274,plain,
spl0_497,
inference(avatar_split_clause,[],[f2478,f5272]) ).
fof(f5272,plain,
( spl0_497
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2478,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5270,plain,
spl0_496,
inference(avatar_split_clause,[],[f2477,f5268]) ).
fof(f5268,plain,
( spl0_496
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2477,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5266,plain,
spl0_495,
inference(avatar_split_clause,[],[f2475,f5264]) ).
fof(f5264,plain,
( spl0_495
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2475,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5262,plain,
spl0_494,
inference(avatar_split_clause,[],[f2474,f5260]) ).
fof(f5260,plain,
( spl0_494
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2474,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5258,plain,
spl0_493,
inference(avatar_split_clause,[],[f2473,f5256]) ).
fof(f5256,plain,
( spl0_493
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2473,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5254,plain,
spl0_492,
inference(avatar_split_clause,[],[f2472,f5252]) ).
fof(f5252,plain,
( spl0_492
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2472,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5250,plain,
spl0_491,
inference(avatar_split_clause,[],[f2471,f5248]) ).
fof(f5248,plain,
( spl0_491
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Olordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2471,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Olordered__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5246,plain,
spl0_490,
inference(avatar_split_clause,[],[f2470,f5244]) ).
fof(f5244,plain,
( spl0_490
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2470,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5242,plain,
spl0_489,
inference(avatar_split_clause,[],[f2469,f5240]) ).
fof(f5240,plain,
( spl0_489
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2469,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5238,plain,
spl0_488,
inference(avatar_split_clause,[],[f2468,f5236]) ).
fof(f5236,plain,
( spl0_488
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f2468,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5234,plain,
spl0_487,
inference(avatar_split_clause,[],[f2467,f5232]) ).
fof(f5232,plain,
( spl0_487
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oaxclass__abs__if(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2467,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oaxclass__abs__if(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5230,plain,
spl0_486,
inference(avatar_split_clause,[],[f2466,f5228]) ).
fof(f5228,plain,
( spl0_486
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2466,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5226,plain,
spl0_485,
inference(avatar_split_clause,[],[f2465,f5224]) ).
fof(f5224,plain,
( spl0_485
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2465,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5222,plain,
spl0_484,
inference(avatar_split_clause,[],[f2464,f5220]) ).
fof(f5220,plain,
( spl0_484
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f2464,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5218,plain,
spl0_483,
inference(avatar_split_clause,[],[f2463,f5216]) ).
fof(f5216,plain,
( spl0_483
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2463,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5214,plain,
spl0_482,
inference(avatar_split_clause,[],[f2462,f5212]) ).
fof(f5212,plain,
( spl0_482
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2462,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5210,plain,
spl0_481,
inference(avatar_split_clause,[],[f2461,f5208]) ).
fof(f5208,plain,
( spl0_481
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2461,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5206,plain,
spl0_480,
inference(avatar_split_clause,[],[f2460,f5204]) ).
fof(f5204,plain,
( spl0_480
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2460,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5202,plain,
spl0_479,
inference(avatar_split_clause,[],[f2459,f5200]) ).
fof(f5200,plain,
( spl0_479
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2459,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5198,plain,
spl0_478,
inference(avatar_split_clause,[],[f2457,f5196]) ).
fof(f5196,plain,
( spl0_478
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2457,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5194,plain,
spl0_477,
inference(avatar_split_clause,[],[f2456,f5192]) ).
fof(f5192,plain,
( spl0_477
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2456,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5190,plain,
spl0_476,
inference(avatar_split_clause,[],[f2455,f5188]) ).
fof(f5188,plain,
( spl0_476
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f2455,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Olinorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5186,plain,
spl0_475,
inference(avatar_split_clause,[],[f2454,f5184]) ).
fof(f5184,plain,
( spl0_475
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2454,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5182,plain,
spl0_474,
inference(avatar_split_clause,[],[f2453,f5180]) ).
fof(f5180,plain,
( spl0_474
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2453,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5178,plain,
spl0_473,
inference(avatar_split_clause,[],[f2448,f5176]) ).
fof(f5176,plain,
( spl0_473
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2448,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5174,plain,
spl0_472,
inference(avatar_split_clause,[],[f2447,f5172]) ).
fof(f5172,plain,
( spl0_472
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2447,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5170,plain,
spl0_471,
inference(avatar_split_clause,[],[f2446,f5168]) ).
fof(f5168,plain,
( spl0_471
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2446,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5166,plain,
spl0_470,
inference(avatar_split_clause,[],[f2445,f5164]) ).
fof(f5164,plain,
( spl0_470
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f2445,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5162,plain,
spl0_469,
inference(avatar_split_clause,[],[f2444,f5160]) ).
fof(f5160,plain,
( spl0_469
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2444,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5158,plain,
spl0_468,
inference(avatar_split_clause,[],[f2443,f5156]) ).
fof(f5156,plain,
( spl0_468
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2443,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5154,plain,
spl0_467,
inference(avatar_split_clause,[],[f2442,f5152]) ).
fof(f5152,plain,
( spl0_467
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f2442,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5150,plain,
spl0_466,
inference(avatar_split_clause,[],[f2441,f5148]) ).
fof(f5148,plain,
( spl0_466
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oidom(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2441,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oidom(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5146,plain,
spl0_465,
inference(avatar_split_clause,[],[f2439,f5144]) ).
fof(f5144,plain,
( spl0_465
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__semidom(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2439,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__semidom(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5142,plain,
spl0_464,
inference(avatar_split_clause,[],[f2438,f5140]) ).
fof(f5140,plain,
( spl0_464
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2438,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5138,plain,
spl0_463,
inference(avatar_split_clause,[],[f2437,f5136]) ).
fof(f5136,plain,
( spl0_463
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2437,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5134,plain,
spl0_462,
inference(avatar_split_clause,[],[f2436,f5132]) ).
fof(f5132,plain,
( spl0_462
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2436,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5130,plain,
spl0_461,
inference(avatar_split_clause,[],[f2435,f5128]) ).
fof(f5128,plain,
( spl0_461
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2435,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5126,plain,
spl0_460,
inference(avatar_split_clause,[],[f2434,f5124]) ).
fof(f5124,plain,
( spl0_460
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2434,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5122,plain,
spl0_459,
inference(avatar_split_clause,[],[f2432,f5120]) ).
fof(f5120,plain,
( spl0_459
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2432,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5118,plain,
spl0_458,
inference(avatar_split_clause,[],[f2431,f5116]) ).
fof(f5116,plain,
( spl0_458
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Olordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2431,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Olordered__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5114,plain,
spl0_457,
inference(avatar_split_clause,[],[f2430,f5112]) ).
fof(f5112,plain,
( spl0_457
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__ring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2430,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__ring__strict(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5110,plain,
spl0_456,
inference(avatar_split_clause,[],[f2429,f5108]) ).
fof(f5108,plain,
( spl0_456
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oaxclass__abs__if(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2429,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oaxclass__abs__if(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5106,plain,
spl0_455,
inference(avatar_split_clause,[],[f2428,f5104]) ).
fof(f5104,plain,
( spl0_455
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f2428,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5102,plain,
spl0_454,
inference(avatar_split_clause,[],[f2427,f5100]) ).
fof(f5100,plain,
( spl0_454
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2427,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5098,plain,
spl0_453,
inference(avatar_split_clause,[],[f2426,f5096]) ).
fof(f5096,plain,
( spl0_453
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f2426,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5094,plain,
spl0_452,
inference(avatar_split_clause,[],[f2425,f5092]) ).
fof(f5092,plain,
( spl0_452
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2425,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5090,plain,
spl0_451,
inference(avatar_split_clause,[],[f2424,f5088]) ).
fof(f5088,plain,
( spl0_451
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f2424,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5086,plain,
spl0_450,
inference(avatar_split_clause,[],[f2423,f5084]) ).
fof(f5084,plain,
( spl0_450
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2423,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5082,plain,
spl0_449,
inference(avatar_split_clause,[],[f2422,f5080]) ).
fof(f5080,plain,
( spl0_449
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2422,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5078,plain,
spl0_448,
inference(avatar_split_clause,[],[f2421,f5076]) ).
fof(f5076,plain,
( spl0_448
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f2421,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5074,plain,
spl0_447,
inference(avatar_split_clause,[],[f2420,f5072]) ).
fof(f5072,plain,
( spl0_447
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2420,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5070,plain,
spl0_446,
inference(avatar_split_clause,[],[f2419,f5068]) ).
fof(f5068,plain,
( spl0_446
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2419,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5066,plain,
spl0_445,
inference(avatar_split_clause,[],[f2418,f5064]) ).
fof(f5064,plain,
( spl0_445
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f2418,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5062,plain,
spl0_444,
inference(avatar_split_clause,[],[f2417,f5060]) ).
fof(f5060,plain,
( spl0_444
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2417,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5058,plain,
spl0_443,
inference(avatar_split_clause,[],[f2416,f5056]) ).
fof(f5056,plain,
( spl0_443
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f2416,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5054,plain,
spl0_442,
inference(avatar_split_clause,[],[f2415,f5052]) ).
fof(f5052,plain,
( spl0_442
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f2415,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Olinorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5050,plain,
spl0_441,
inference(avatar_split_clause,[],[f2414,f5048]) ).
fof(f5048,plain,
( spl0_441
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2414,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5046,plain,
spl0_440,
inference(avatar_split_clause,[],[f2413,f5044]) ).
fof(f5044,plain,
( spl0_440
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2413,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5042,plain,
spl0_439,
inference(avatar_split_clause,[],[f2412,f5040]) ).
fof(f5040,plain,
( spl0_439
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2412,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5038,plain,
spl0_438,
inference(avatar_split_clause,[],[f2411,f5036]) ).
fof(f5036,plain,
( spl0_438
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2411,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5034,plain,
spl0_437,
inference(avatar_split_clause,[],[f2408,f5032]) ).
fof(f5032,plain,
( spl0_437
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2408,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5030,plain,
spl0_436,
inference(avatar_split_clause,[],[f2406,f5028]) ).
fof(f5028,plain,
( spl0_436
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2406,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5026,plain,
spl0_435,
inference(avatar_split_clause,[],[f2404,f5024]) ).
fof(f5024,plain,
( spl0_435
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2404,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5022,plain,
spl0_434,
inference(avatar_split_clause,[],[f2401,f5020]) ).
fof(f5020,plain,
( spl0_434
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2401,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5018,plain,
spl0_433,
inference(avatar_split_clause,[],[f2400,f5016]) ).
fof(f5016,plain,
( spl0_433
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2400,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f5014,plain,
spl0_432,
inference(avatar_split_clause,[],[f2399,f5012]) ).
fof(f5012,plain,
( spl0_432
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2399,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f5010,plain,
spl0_431,
inference(avatar_split_clause,[],[f2398,f5008]) ).
fof(f5008,plain,
( spl0_431
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f2398,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f5006,plain,
spl0_430,
inference(avatar_split_clause,[],[f2396,f5004]) ).
fof(f5004,plain,
( spl0_430
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2396,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f5002,plain,
spl0_429,
inference(avatar_split_clause,[],[f2395,f5000]) ).
fof(f5000,plain,
( spl0_429
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2395,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f4998,plain,
spl0_428,
inference(avatar_split_clause,[],[f2394,f4996]) ).
fof(f4996,plain,
( spl0_428
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f2394,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f4994,plain,
spl0_427,
inference(avatar_split_clause,[],[f2393,f4992]) ).
fof(f4992,plain,
( spl0_427
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2393,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f4990,plain,
spl0_426,
inference(avatar_split_clause,[],[f2392,f4988]) ).
fof(f4988,plain,
( spl0_426
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2392,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f4986,plain,
spl0_425,
inference(avatar_split_clause,[],[f2391,f4984]) ).
fof(f4984,plain,
( spl0_425
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2391,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f4982,plain,
spl0_424,
inference(avatar_split_clause,[],[f2390,f4980]) ).
fof(f4980,plain,
( spl0_424
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2390,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f4978,plain,
spl0_423,
inference(avatar_split_clause,[],[f2389,f4976]) ).
fof(f4976,plain,
( spl0_423
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f2389,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f4974,plain,
spl0_422,
inference(avatar_split_clause,[],[f2388,f4972]) ).
fof(f4972,plain,
( spl0_422
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2388,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f4970,plain,
spl0_421,
inference(avatar_split_clause,[],[f2324,f4968]) ).
fof(f4968,plain,
( spl0_421
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f2324,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f4966,plain,
spl0_420,
inference(avatar_split_clause,[],[f2321,f4964]) ).
fof(f4964,plain,
( spl0_420
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f2321,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f4962,plain,
spl0_419,
inference(avatar_split_clause,[],[f2320,f4960]) ).
fof(f4960,plain,
( spl0_419
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f2320,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f4958,plain,
spl0_418,
inference(avatar_split_clause,[],[f2319,f4956]) ).
fof(f4956,plain,
( spl0_418
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2319,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f4954,plain,
spl0_417,
inference(avatar_split_clause,[],[f2318,f4952]) ).
fof(f4952,plain,
( spl0_417
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2318,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f4950,plain,
spl0_416,
inference(avatar_split_clause,[],[f2317,f4948]) ).
fof(f4948,plain,
( spl0_416
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2317,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f4946,plain,
spl0_415,
inference(avatar_split_clause,[],[f2316,f4944]) ).
fof(f4944,plain,
( spl0_415
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2316,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f4942,plain,
spl0_414,
inference(avatar_split_clause,[],[f2315,f4940]) ).
fof(f4940,plain,
( spl0_414
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2315,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f4938,plain,
spl0_413,
inference(avatar_split_clause,[],[f2314,f4936]) ).
fof(f4936,plain,
( spl0_413
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2314,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f4934,plain,
spl0_412,
inference(avatar_split_clause,[],[f2313,f4932]) ).
fof(f4932,plain,
( spl0_412
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2313,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f4930,plain,
spl0_411,
inference(avatar_split_clause,[],[f2312,f4928]) ).
fof(f4928,plain,
( spl0_411
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2312,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f4926,plain,
spl0_410,
inference(avatar_split_clause,[],[f2311,f4924]) ).
fof(f4924,plain,
( spl0_410
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2311,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f4922,plain,
spl0_409,
inference(avatar_split_clause,[],[f2310,f4920]) ).
fof(f4920,plain,
( spl0_409
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f2310,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f4918,plain,
spl0_408,
inference(avatar_split_clause,[],[f2308,f4916]) ).
fof(f4916,plain,
( spl0_408
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f2308,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f4914,plain,
spl0_407,
inference(avatar_split_clause,[],[f2307,f4912]) ).
fof(f4912,plain,
( spl0_407
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2307,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f4910,plain,
spl0_406,
inference(avatar_split_clause,[],[f2306,f4908]) ).
fof(f4908,plain,
( spl0_406
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2306,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f4906,plain,
spl0_405,
inference(avatar_split_clause,[],[f2305,f4904]) ).
fof(f4904,plain,
( spl0_405
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f2305,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f4902,plain,
spl0_404,
inference(avatar_split_clause,[],[f2304,f4900]) ).
fof(f4900,plain,
( spl0_404
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f2304,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f4898,plain,
spl0_403,
inference(avatar_split_clause,[],[f2303,f4896]) ).
fof(f4896,plain,
( spl0_403
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2303,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f4894,plain,
spl0_402,
inference(avatar_split_clause,[],[f2302,f4892]) ).
fof(f4892,plain,
( spl0_402
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2302,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Olinorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f4890,plain,
spl0_401,
inference(avatar_split_clause,[],[f2301,f4888]) ).
fof(f4888,plain,
( spl0_401
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2301,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f4886,plain,
spl0_400,
inference(avatar_split_clause,[],[f2298,f4884]) ).
fof(f4884,plain,
( spl0_400
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f2298,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f4882,plain,
spl0_399,
inference(avatar_split_clause,[],[f2297,f4880]) ).
fof(f4880,plain,
( spl0_399
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2297,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f4878,plain,
spl0_398,
inference(avatar_split_clause,[],[f2296,f4876]) ).
fof(f4876,plain,
( spl0_398
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2296,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f4874,plain,
spl0_397,
inference(avatar_split_clause,[],[f2295,f4872]) ).
fof(f4872,plain,
( spl0_397
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2295,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f4870,plain,
spl0_396,
inference(avatar_split_clause,[],[f2294,f4868]) ).
fof(f4868,plain,
( spl0_396
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f2294,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f4866,plain,
spl0_395,
inference(avatar_split_clause,[],[f2293,f4864]) ).
fof(f4864,plain,
( spl0_395
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2293,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f4862,plain,
spl0_394,
inference(avatar_split_clause,[],[f2292,f4860]) ).
fof(f4860,plain,
( spl0_394
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2292,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f4858,plain,
spl0_393,
inference(avatar_split_clause,[],[f2290,f4856]) ).
fof(f4856,plain,
( spl0_393
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f2290,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f4854,plain,
spl0_392,
inference(avatar_split_clause,[],[f2289,f4852]) ).
fof(f4852,plain,
( spl0_392
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2289,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f4850,plain,
spl0_391,
inference(avatar_split_clause,[],[f2288,f4848]) ).
fof(f4848,plain,
( spl0_391
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2288,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f4846,plain,
spl0_390,
inference(avatar_split_clause,[],[f2287,f4844]) ).
fof(f4844,plain,
( spl0_390
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2287,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f4842,plain,
spl0_389,
inference(avatar_split_clause,[],[f2286,f4840]) ).
fof(f4840,plain,
( spl0_389
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2286,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f4838,plain,
spl0_388,
inference(avatar_split_clause,[],[f2285,f4836]) ).
fof(f4836,plain,
( spl0_388
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f2285,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f4834,plain,
spl0_387,
inference(avatar_split_clause,[],[f2284,f4832]) ).
fof(f4832,plain,
( spl0_387
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f2284,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f4830,plain,
spl0_386,
inference(avatar_split_clause,[],[f2283,f4828]) ).
fof(f4828,plain,
( spl0_386
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2283,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f4826,plain,
spl0_385,
inference(avatar_split_clause,[],[f2280,f4824]) ).
fof(f4824,plain,
( spl0_385
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2280,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f4822,plain,
spl0_384,
inference(avatar_split_clause,[],[f2278,f4820]) ).
fof(f4820,plain,
( spl0_384
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2278,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f4818,plain,
spl0_383,
inference(avatar_split_clause,[],[f2277,f4816]) ).
fof(f4816,plain,
( spl0_383
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2277,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f4814,plain,
spl0_382,
inference(avatar_split_clause,[],[f2275,f4812]) ).
fof(f4812,plain,
( spl0_382
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2275,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f4810,plain,
spl0_381,
inference(avatar_split_clause,[],[f2272,f4808]) ).
fof(f4808,plain,
( spl0_381
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2272,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4806,plain,
spl0_380,
inference(avatar_split_clause,[],[f2271,f4804]) ).
fof(f4804,plain,
( spl0_380
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2271,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4802,plain,
spl0_379,
inference(avatar_split_clause,[],[f2270,f4800]) ).
fof(f4800,plain,
( spl0_379
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2270,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4798,plain,
spl0_378,
inference(avatar_split_clause,[],[f2269,f4796]) ).
fof(f4796,plain,
( spl0_378
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f2269,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4794,plain,
spl0_377,
inference(avatar_split_clause,[],[f2268,f4792]) ).
fof(f4792,plain,
( spl0_377
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f2268,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4790,plain,
spl0_376,
inference(avatar_split_clause,[],[f2267,f4788]) ).
fof(f4788,plain,
( spl0_376
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f2267,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4786,plain,
spl0_375,
inference(avatar_split_clause,[],[f2266,f4784]) ).
fof(f4784,plain,
( spl0_375
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f2266,axiom,
! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4782,plain,
spl0_374,
inference(avatar_split_clause,[],[f2265,f4780]) ).
fof(f4780,plain,
( spl0_374
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f2265,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4778,plain,
spl0_373,
inference(avatar_split_clause,[],[f2264,f4776]) ).
fof(f4776,plain,
( spl0_373
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2264,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4774,plain,
spl0_372,
inference(avatar_split_clause,[],[f2263,f4772]) ).
fof(f4772,plain,
( spl0_372
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2263,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4770,plain,
spl0_371,
inference(avatar_split_clause,[],[f2262,f4768]) ).
fof(f4768,plain,
( spl0_371
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f2262,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4766,plain,
spl0_370,
inference(avatar_split_clause,[],[f2260,f4764]) ).
fof(f4764,plain,
( spl0_370
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2260,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4762,plain,
spl0_369,
inference(avatar_split_clause,[],[f2258,f4760]) ).
fof(f4760,plain,
( spl0_369
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2258,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4758,plain,
spl0_368,
inference(avatar_split_clause,[],[f2255,f4756]) ).
fof(f4756,plain,
( spl0_368
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f2255,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4754,plain,
spl0_367,
inference(avatar_split_clause,[],[f2253,f4752]) ).
fof(f4752,plain,
( spl0_367
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f2253,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4750,plain,
spl0_366,
inference(avatar_split_clause,[],[f2251,f4748]) ).
fof(f4748,plain,
( spl0_366
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f2251,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4746,plain,
spl0_365,
inference(avatar_split_clause,[],[f2248,f4744]) ).
fof(f4744,plain,
( spl0_365
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2248,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4742,plain,
spl0_364,
inference(avatar_split_clause,[],[f2247,f4740]) ).
fof(f4740,plain,
( spl0_364
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2247,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4738,plain,
spl0_363,
inference(avatar_split_clause,[],[f2246,f4736]) ).
fof(f4736,plain,
( spl0_363
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2246,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4734,plain,
spl0_362,
inference(avatar_split_clause,[],[f2245,f4732]) ).
fof(f4732,plain,
( spl0_362
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f2245,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4730,plain,
spl0_361,
inference(avatar_split_clause,[],[f2243,f4728]) ).
fof(f4728,plain,
( spl0_361
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f2243,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4726,plain,
spl0_360,
inference(avatar_split_clause,[],[f2242,f4724]) ).
fof(f4724,plain,
( spl0_360
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f2242,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4722,plain,
spl0_359,
inference(avatar_split_clause,[],[f2241,f4720]) ).
fof(f4720,plain,
( spl0_359
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2241,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4718,plain,
spl0_358,
inference(avatar_split_clause,[],[f2240,f4716]) ).
fof(f4716,plain,
( spl0_358
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f2240,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4714,plain,
spl0_357,
inference(avatar_split_clause,[],[f2239,f4712]) ).
fof(f4712,plain,
( spl0_357
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2239,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4710,plain,
spl0_356,
inference(avatar_split_clause,[],[f2238,f4708]) ).
fof(f4708,plain,
( spl0_356
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2238,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4706,plain,
spl0_355,
inference(avatar_split_clause,[],[f2237,f4704]) ).
fof(f4704,plain,
( spl0_355
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2237,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4702,plain,
spl0_354,
inference(avatar_split_clause,[],[f2236,f4700]) ).
fof(f4700,plain,
( spl0_354
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2236,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4698,plain,
spl0_353,
inference(avatar_split_clause,[],[f2235,f4696]) ).
fof(f4696,plain,
( spl0_353
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2235,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4694,plain,
spl0_352,
inference(avatar_split_clause,[],[f2199,f4692]) ).
fof(f4692,plain,
( spl0_352
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f2199,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4690,plain,
spl0_351,
inference(avatar_split_clause,[],[f2198,f4688]) ).
fof(f4688,plain,
( spl0_351
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f2198,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4686,plain,
spl0_350,
inference(avatar_split_clause,[],[f2197,f4684]) ).
fof(f4684,plain,
( spl0_350
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f2197,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4682,plain,
spl0_349,
inference(avatar_split_clause,[],[f2196,f4680]) ).
fof(f4680,plain,
( spl0_349
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f2196,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4678,plain,
spl0_348,
inference(avatar_split_clause,[],[f2195,f4676]) ).
fof(f4676,plain,
( spl0_348
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f2195,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4674,plain,
spl0_347,
inference(avatar_split_clause,[],[f2193,f4672]) ).
fof(f4672,plain,
( spl0_347
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2193,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4670,plain,
spl0_346,
inference(avatar_split_clause,[],[f2192,f4668]) ).
fof(f4668,plain,
( spl0_346
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2192,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4666,plain,
spl0_345,
inference(avatar_split_clause,[],[f2191,f4664]) ).
fof(f4664,plain,
( spl0_345
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f2191,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4662,plain,
spl0_344,
inference(avatar_split_clause,[],[f2190,f4660]) ).
fof(f4660,plain,
( spl0_344
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2190,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4658,plain,
spl0_343,
inference(avatar_split_clause,[],[f2189,f4656]) ).
fof(f4656,plain,
( spl0_343
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2189,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4654,plain,
spl0_342,
inference(avatar_split_clause,[],[f2188,f4652]) ).
fof(f4652,plain,
( spl0_342
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2188,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4650,plain,
spl0_341,
inference(avatar_split_clause,[],[f2187,f4648]) ).
fof(f4648,plain,
( spl0_341
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f2187,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4646,plain,
spl0_340,
inference(avatar_split_clause,[],[f2184,f4644]) ).
fof(f4644,plain,
( spl0_340
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f2184,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4642,plain,
spl0_339,
inference(avatar_split_clause,[],[f2183,f4640]) ).
fof(f4640,plain,
( spl0_339
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2183,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4638,plain,
spl0_338,
inference(avatar_split_clause,[],[f2178,f4636]) ).
fof(f4636,plain,
( spl0_338
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2178,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4634,plain,
spl0_337,
inference(avatar_split_clause,[],[f2177,f4632]) ).
fof(f4632,plain,
( spl0_337
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2177,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4630,plain,
spl0_336,
inference(avatar_split_clause,[],[f2174,f4628]) ).
fof(f4628,plain,
( spl0_336
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2174,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4626,plain,
spl0_335,
inference(avatar_split_clause,[],[f2173,f4624]) ).
fof(f4624,plain,
( spl0_335
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2173,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4622,plain,
spl0_334,
inference(avatar_split_clause,[],[f2171,f4620]) ).
fof(f4620,plain,
( spl0_334
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f2171,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4618,plain,
spl0_333,
inference(avatar_split_clause,[],[f2170,f4616]) ).
fof(f4616,plain,
( spl0_333
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2170,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4614,plain,
spl0_332,
inference(avatar_split_clause,[],[f2169,f4612]) ).
fof(f4612,plain,
( spl0_332
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2169,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4610,plain,
spl0_331,
inference(avatar_split_clause,[],[f2168,f4608]) ).
fof(f4608,plain,
( spl0_331
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2168,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4606,plain,
spl0_330,
inference(avatar_split_clause,[],[f2167,f4604]) ).
fof(f4604,plain,
( spl0_330
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2167,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4602,plain,
spl0_329,
inference(avatar_split_clause,[],[f2166,f4600]) ).
fof(f4600,plain,
( spl0_329
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2166,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4598,plain,
spl0_328,
inference(avatar_split_clause,[],[f2162,f4596]) ).
fof(f4596,plain,
( spl0_328
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2162,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4594,plain,
spl0_327,
inference(avatar_split_clause,[],[f2160,f4592]) ).
fof(f4592,plain,
( spl0_327
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2160,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4590,plain,
spl0_326,
inference(avatar_split_clause,[],[f2157,f4588]) ).
fof(f4588,plain,
( spl0_326
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2157,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4586,plain,
spl0_325,
inference(avatar_split_clause,[],[f2154,f4584]) ).
fof(f4584,plain,
( spl0_325
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2154,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4582,plain,
spl0_324,
inference(avatar_split_clause,[],[f2153,f4580]) ).
fof(f4580,plain,
( spl0_324
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2153,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4578,plain,
spl0_323,
inference(avatar_split_clause,[],[f2151,f4576]) ).
fof(f4576,plain,
( spl0_323
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2151,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4574,plain,
spl0_322,
inference(avatar_split_clause,[],[f2150,f4572]) ).
fof(f4572,plain,
( spl0_322
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2150,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4570,plain,
spl0_321,
inference(avatar_split_clause,[],[f2149,f4568]) ).
fof(f4568,plain,
( spl0_321
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2149,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4566,plain,
spl0_320,
inference(avatar_split_clause,[],[f2146,f4564]) ).
fof(f4564,plain,
( spl0_320
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2146,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4562,plain,
spl0_319,
inference(avatar_split_clause,[],[f2145,f4560]) ).
fof(f4560,plain,
( spl0_319
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2145,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4558,plain,
spl0_318,
inference(avatar_split_clause,[],[f2143,f4556]) ).
fof(f4556,plain,
( spl0_318
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2143,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4554,plain,
spl0_317,
inference(avatar_split_clause,[],[f2137,f4552]) ).
fof(f4552,plain,
( spl0_317
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2137,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4550,plain,
spl0_316,
inference(avatar_split_clause,[],[f2136,f4548]) ).
fof(f4548,plain,
( spl0_316
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f2136,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4546,plain,
spl0_315,
inference(avatar_split_clause,[],[f2134,f4544]) ).
fof(f4544,plain,
( spl0_315
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2134,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4542,plain,
spl0_314,
inference(avatar_split_clause,[],[f2133,f4540]) ).
fof(f4540,plain,
( spl0_314
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2133,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4538,plain,
spl0_313,
inference(avatar_split_clause,[],[f2126,f4536]) ).
fof(f4536,plain,
( spl0_313
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2126,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4534,plain,
spl0_312,
inference(avatar_split_clause,[],[f2125,f4532]) ).
fof(f4532,plain,
( spl0_312
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2125,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4530,plain,
spl0_311,
inference(avatar_split_clause,[],[f2123,f4528]) ).
fof(f4528,plain,
( spl0_311
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2123,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4526,plain,
spl0_310,
inference(avatar_split_clause,[],[f2122,f4524]) ).
fof(f4524,plain,
( spl0_310
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2122,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4522,plain,
spl0_309,
inference(avatar_split_clause,[],[f2121,f4520]) ).
fof(f4520,plain,
( spl0_309
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2121,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4518,plain,
spl0_308,
inference(avatar_split_clause,[],[f2119,f4516]) ).
fof(f4516,plain,
( spl0_308
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2119,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4514,plain,
spl0_307,
inference(avatar_split_clause,[],[f2118,f4512]) ).
fof(f4512,plain,
( spl0_307
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2118,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4510,plain,
spl0_306,
inference(avatar_split_clause,[],[f2117,f4508]) ).
fof(f4508,plain,
( spl0_306
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2117,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4506,plain,
spl0_305,
inference(avatar_split_clause,[],[f2116,f4504]) ).
fof(f4504,plain,
( spl0_305
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2116,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4502,plain,
spl0_304,
inference(avatar_split_clause,[],[f2115,f4500]) ).
fof(f4500,plain,
( spl0_304
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2115,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4498,plain,
spl0_303,
inference(avatar_split_clause,[],[f2114,f4496]) ).
fof(f4496,plain,
( spl0_303
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2114,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4494,plain,
spl0_302,
inference(avatar_split_clause,[],[f2113,f4492]) ).
fof(f4492,plain,
( spl0_302
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2113,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4490,plain,
spl0_301,
inference(avatar_split_clause,[],[f2112,f4488]) ).
fof(f4488,plain,
( spl0_301
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2112,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4486,plain,
spl0_300,
inference(avatar_split_clause,[],[f2111,f4484]) ).
fof(f4484,plain,
( spl0_300
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2111,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4482,plain,
spl0_299,
inference(avatar_split_clause,[],[f2110,f4480]) ).
fof(f4480,plain,
( spl0_299
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2110,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4478,plain,
spl0_298,
inference(avatar_split_clause,[],[f2107,f4476]) ).
fof(f4476,plain,
( spl0_298
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2107,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4474,plain,
spl0_297,
inference(avatar_split_clause,[],[f2105,f4472]) ).
fof(f4472,plain,
( spl0_297
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2105,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4470,plain,
spl0_296,
inference(avatar_split_clause,[],[f2103,f4468]) ).
fof(f4468,plain,
( spl0_296
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2103,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4466,plain,
spl0_295,
inference(avatar_split_clause,[],[f2100,f4464]) ).
fof(f4464,plain,
( spl0_295
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2100,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4462,plain,
spl0_294,
inference(avatar_split_clause,[],[f2099,f4460]) ).
fof(f4460,plain,
( spl0_294
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2099,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4458,plain,
spl0_293,
inference(avatar_split_clause,[],[f2098,f4456]) ).
fof(f4456,plain,
( spl0_293
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2098,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4454,plain,
spl0_292,
inference(avatar_split_clause,[],[f2095,f4452]) ).
fof(f4452,plain,
( spl0_292
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2095,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4450,plain,
spl0_291,
inference(avatar_split_clause,[],[f2092,f4448]) ).
fof(f4448,plain,
( spl0_291
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2092,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4446,plain,
spl0_290,
inference(avatar_split_clause,[],[f2091,f4444]) ).
fof(f4444,plain,
( spl0_290
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2091,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4442,plain,
spl0_289,
inference(avatar_split_clause,[],[f2089,f4440]) ).
fof(f4440,plain,
( spl0_289
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2089,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4438,plain,
spl0_288,
inference(avatar_split_clause,[],[f2088,f4436]) ).
fof(f4436,plain,
( spl0_288
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2088,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4434,plain,
spl0_287,
inference(avatar_split_clause,[],[f2087,f4432]) ).
fof(f4432,plain,
( spl0_287
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2087,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4430,plain,
spl0_286,
inference(avatar_split_clause,[],[f2086,f4428]) ).
fof(f4428,plain,
( spl0_286
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2086,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4426,plain,
spl0_285,
inference(avatar_split_clause,[],[f2085,f4424]) ).
fof(f4424,plain,
( spl0_285
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2085,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4422,plain,
spl0_284,
inference(avatar_split_clause,[],[f2083,f4420]) ).
fof(f4420,plain,
( spl0_284
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2083,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4418,plain,
spl0_283,
inference(avatar_split_clause,[],[f2080,f4416]) ).
fof(f4416,plain,
( spl0_283
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2080,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4414,plain,
spl0_282,
inference(avatar_split_clause,[],[f2079,f4412]) ).
fof(f4412,plain,
( spl0_282
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2079,axiom,
! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4410,plain,
spl0_281,
inference(avatar_split_clause,[],[f2075,f4408]) ).
fof(f4408,plain,
( spl0_281
<=> ! [X94] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2075,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4406,plain,
spl0_280,
inference(avatar_split_clause,[],[f2073,f4404]) ).
fof(f4404,plain,
( spl0_280
<=> ! [X94] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2073,axiom,
! [X94] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4402,plain,
spl0_279,
inference(avatar_split_clause,[],[f2065,f4400]) ).
fof(f4400,plain,
( spl0_279
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2065,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4398,plain,
spl0_278,
inference(avatar_split_clause,[],[f2064,f4396]) ).
fof(f4396,plain,
( spl0_278
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2064,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4394,plain,
spl0_277,
inference(avatar_split_clause,[],[f2063,f4392]) ).
fof(f4392,plain,
( spl0_277
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2063,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4390,plain,
spl0_276,
inference(avatar_split_clause,[],[f2062,f4388]) ).
fof(f4388,plain,
( spl0_276
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2062,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4386,plain,
spl0_275,
inference(avatar_split_clause,[],[f2061,f4384]) ).
fof(f4384,plain,
( spl0_275
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2061,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4382,plain,
spl0_274,
inference(avatar_split_clause,[],[f2060,f4380]) ).
fof(f4380,plain,
( spl0_274
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2060,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4378,plain,
spl0_273,
inference(avatar_split_clause,[],[f2059,f4376]) ).
fof(f4376,plain,
( spl0_273
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2059,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4374,plain,
spl0_272,
inference(avatar_split_clause,[],[f2058,f4372]) ).
fof(f4372,plain,
( spl0_272
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2058,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4370,plain,
spl0_271,
inference(avatar_split_clause,[],[f2057,f4368]) ).
fof(f4368,plain,
( spl0_271
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2057,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4366,plain,
spl0_270,
inference(avatar_split_clause,[],[f2056,f4364]) ).
fof(f4364,plain,
( spl0_270
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2056,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4362,plain,
spl0_269,
inference(avatar_split_clause,[],[f2055,f4360]) ).
fof(f4360,plain,
( spl0_269
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2055,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4358,plain,
spl0_268,
inference(avatar_split_clause,[],[f2054,f4356]) ).
fof(f4356,plain,
( spl0_268
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2054,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4354,plain,
spl0_267,
inference(avatar_split_clause,[],[f2053,f4352]) ).
fof(f4352,plain,
( spl0_267
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2053,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4350,plain,
spl0_266,
inference(avatar_split_clause,[],[f2052,f4348]) ).
fof(f4348,plain,
( spl0_266
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2052,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4346,plain,
spl0_265,
inference(avatar_split_clause,[],[f2051,f4344]) ).
fof(f4344,plain,
( spl0_265
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2051,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4342,plain,
spl0_264,
inference(avatar_split_clause,[],[f2050,f4340]) ).
fof(f4340,plain,
( spl0_264
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2050,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4338,plain,
spl0_263,
inference(avatar_split_clause,[],[f2049,f4336]) ).
fof(f4336,plain,
( spl0_263
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2049,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4334,plain,
spl0_262,
inference(avatar_split_clause,[],[f2046,f4332]) ).
fof(f4332,plain,
( spl0_262
<=> ! [X94] :
( ~ class_Orderings_Oorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2046,axiom,
! [X94] :
( ~ class_Orderings_Oorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4330,plain,
spl0_261,
inference(avatar_split_clause,[],[f2045,f4328]) ).
fof(f4328,plain,
( spl0_261
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2045,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4326,plain,
spl0_260,
inference(avatar_split_clause,[],[f2044,f4324]) ).
fof(f4324,plain,
( spl0_260
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2044,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4322,plain,
spl0_259,
inference(avatar_split_clause,[],[f2043,f4320]) ).
fof(f4320,plain,
( spl0_259
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2043,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4318,plain,
spl0_258,
inference(avatar_split_clause,[],[f2042,f4316]) ).
fof(f4316,plain,
( spl0_258
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2042,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4314,plain,
spl0_257,
inference(avatar_split_clause,[],[f2041,f4312]) ).
fof(f4312,plain,
( spl0_257
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2041,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4310,plain,
spl0_256,
inference(avatar_split_clause,[],[f2038,f4308]) ).
fof(f4308,plain,
( spl0_256
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2038,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4306,plain,
spl0_255,
inference(avatar_split_clause,[],[f2037,f4304]) ).
fof(f4304,plain,
( spl0_255
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2037,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4302,plain,
spl0_254,
inference(avatar_split_clause,[],[f2033,f4300]) ).
fof(f4300,plain,
( spl0_254
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2033,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4298,plain,
spl0_253,
inference(avatar_split_clause,[],[f2032,f4296]) ).
fof(f4296,plain,
( spl0_253
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2032,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4294,plain,
spl0_252,
inference(avatar_split_clause,[],[f2031,f4292]) ).
fof(f4292,plain,
( spl0_252
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2031,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4290,plain,
spl0_251,
inference(avatar_split_clause,[],[f2028,f4288]) ).
fof(f4288,plain,
( spl0_251
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2028,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4286,plain,
spl0_250,
inference(avatar_split_clause,[],[f2026,f4284]) ).
fof(f4284,plain,
( spl0_250
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2026,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4282,plain,
spl0_249,
inference(avatar_split_clause,[],[f2025,f4280]) ).
fof(f4280,plain,
( spl0_249
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2025,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4278,plain,
spl0_248,
inference(avatar_split_clause,[],[f2024,f4276]) ).
fof(f4276,plain,
( spl0_248
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2024,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4274,plain,
spl0_247,
inference(avatar_split_clause,[],[f2023,f4272]) ).
fof(f4272,plain,
( spl0_247
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2023,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4270,plain,
spl0_246,
inference(avatar_split_clause,[],[f2022,f4268]) ).
fof(f4268,plain,
( spl0_246
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2022,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4266,plain,
spl0_245,
inference(avatar_split_clause,[],[f2018,f4264]) ).
fof(f4264,plain,
( spl0_245
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2018,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4262,plain,
spl0_244,
inference(avatar_split_clause,[],[f2017,f4260]) ).
fof(f4260,plain,
( spl0_244
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2017,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4258,plain,
spl0_243,
inference(avatar_split_clause,[],[f2016,f4256]) ).
fof(f4256,plain,
( spl0_243
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2016,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4254,plain,
spl0_242,
inference(avatar_split_clause,[],[f2013,f4252]) ).
fof(f4252,plain,
( spl0_242
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2013,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4250,plain,
spl0_241,
inference(avatar_split_clause,[],[f2011,f4248]) ).
fof(f4248,plain,
( spl0_241
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2011,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4246,plain,
spl0_240,
inference(avatar_split_clause,[],[f2009,f4244]) ).
fof(f4244,plain,
( spl0_240
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2009,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4242,plain,
spl0_239,
inference(avatar_split_clause,[],[f2008,f4240]) ).
fof(f4240,plain,
( spl0_239
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2008,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4238,plain,
spl0_238,
inference(avatar_split_clause,[],[f2007,f4236]) ).
fof(f4236,plain,
( spl0_238
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2007,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4234,plain,
spl0_237,
inference(avatar_split_clause,[],[f2006,f4232]) ).
fof(f4232,plain,
( spl0_237
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2006,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4230,plain,
spl0_236,
inference(avatar_split_clause,[],[f2005,f4228]) ).
fof(f4228,plain,
( spl0_236
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2005,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4226,plain,
spl0_235,
inference(avatar_split_clause,[],[f2003,f4224]) ).
fof(f4224,plain,
( spl0_235
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2003,axiom,
! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4222,plain,
spl0_234,
inference(avatar_split_clause,[],[f2002,f4220]) ).
fof(f4220,plain,
( spl0_234
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2002,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Olinorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4218,plain,
spl0_233,
inference(avatar_split_clause,[],[f1999,f4216]) ).
fof(f4216,plain,
( spl0_233
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1999,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4214,plain,
spl0_232,
inference(avatar_split_clause,[],[f1997,f4212]) ).
fof(f4212,plain,
( spl0_232
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1997,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4210,plain,
spl0_231,
inference(avatar_split_clause,[],[f1996,f4208]) ).
fof(f4208,plain,
( spl0_231
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1996,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4206,plain,
spl0_230,
inference(avatar_split_clause,[],[f1995,f4204]) ).
fof(f4204,plain,
( spl0_230
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1995,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4202,plain,
spl0_229,
inference(avatar_split_clause,[],[f1994,f4200]) ).
fof(f4200,plain,
( spl0_229
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1994,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4198,plain,
spl0_228,
inference(avatar_split_clause,[],[f1993,f4196]) ).
fof(f4196,plain,
( spl0_228
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1993,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4194,plain,
spl0_227,
inference(avatar_split_clause,[],[f1992,f4192]) ).
fof(f4192,plain,
( spl0_227
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1992,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4190,plain,
spl0_226,
inference(avatar_split_clause,[],[f1991,f4188]) ).
fof(f4188,plain,
( spl0_226
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1991,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4186,plain,
spl0_225,
inference(avatar_split_clause,[],[f1990,f4184]) ).
fof(f4184,plain,
( spl0_225
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1990,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4182,plain,
spl0_224,
inference(avatar_split_clause,[],[f1989,f4180]) ).
fof(f4180,plain,
( spl0_224
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1989,axiom,
! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4178,plain,
spl0_223,
inference(avatar_split_clause,[],[f1986,f4176]) ).
fof(f4176,plain,
( spl0_223
<=> ! [X94] :
( ~ class_OrderedGroup_Omonoid__mult(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1986,axiom,
! [X94] :
( ~ class_OrderedGroup_Omonoid__mult(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4174,plain,
spl0_222,
inference(avatar_split_clause,[],[f1985,f4172]) ).
fof(f4172,plain,
( spl0_222
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1985,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4170,plain,
spl0_221,
inference(avatar_split_clause,[],[f1984,f4168]) ).
fof(f4168,plain,
( spl0_221
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1984,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4166,plain,
spl0_220,
inference(avatar_split_clause,[],[f1983,f4164]) ).
fof(f4164,plain,
( spl0_220
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1983,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4162,plain,
spl0_219,
inference(avatar_split_clause,[],[f1982,f4160]) ).
fof(f4160,plain,
( spl0_219
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1982,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4158,plain,
spl0_218,
inference(avatar_split_clause,[],[f1981,f4156]) ).
fof(f4156,plain,
( spl0_218
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1981,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4154,plain,
spl0_217,
inference(avatar_split_clause,[],[f1979,f4152]) ).
fof(f4152,plain,
( spl0_217
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1979,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4150,plain,
spl0_216,
inference(avatar_split_clause,[],[f1977,f4148]) ).
fof(f4148,plain,
( spl0_216
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1977,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4146,plain,
spl0_215,
inference(avatar_split_clause,[],[f1976,f4144]) ).
fof(f4144,plain,
( spl0_215
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1976,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4142,plain,
spl0_214,
inference(avatar_split_clause,[],[f1975,f4140]) ).
fof(f4140,plain,
( spl0_214
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1975,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4138,plain,
spl0_213,
inference(avatar_split_clause,[],[f1974,f4136]) ).
fof(f4136,plain,
( spl0_213
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1974,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4134,plain,
spl0_212,
inference(avatar_split_clause,[],[f1971,f4132]) ).
fof(f4132,plain,
( spl0_212
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1971,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4130,plain,
spl0_211,
inference(avatar_split_clause,[],[f1969,f4128]) ).
fof(f4128,plain,
( spl0_211
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1969,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4126,plain,
spl0_210,
inference(avatar_split_clause,[],[f1968,f4124]) ).
fof(f4124,plain,
( spl0_210
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1968,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4122,plain,
spl0_209,
inference(avatar_split_clause,[],[f1967,f4120]) ).
fof(f4120,plain,
( spl0_209
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1967,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4118,plain,
spl0_208,
inference(avatar_split_clause,[],[f1966,f4116]) ).
fof(f4116,plain,
( spl0_208
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1966,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4114,plain,
spl0_207,
inference(avatar_split_clause,[],[f1965,f4112]) ).
fof(f4112,plain,
( spl0_207
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1965,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4110,plain,
spl0_206,
inference(avatar_split_clause,[],[f1964,f4108]) ).
fof(f4108,plain,
( spl0_206
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1964,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4106,plain,
spl0_205,
inference(avatar_split_clause,[],[f1963,f4104]) ).
fof(f4104,plain,
( spl0_205
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1963,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4102,plain,
spl0_204,
inference(avatar_split_clause,[],[f1962,f4100]) ).
fof(f4100,plain,
( spl0_204
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1962,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4098,plain,
spl0_203,
inference(avatar_split_clause,[],[f1960,f4096]) ).
fof(f4096,plain,
( spl0_203
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1960,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4094,plain,
spl0_202,
inference(avatar_split_clause,[],[f1958,f4092]) ).
fof(f4092,plain,
( spl0_202
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1958,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4090,plain,
spl0_201,
inference(avatar_split_clause,[],[f1957,f4088]) ).
fof(f4088,plain,
( spl0_201
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1957,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4086,plain,
spl0_200,
inference(avatar_split_clause,[],[f1956,f4084]) ).
fof(f4084,plain,
( spl0_200
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1956,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4082,plain,
spl0_199,
inference(avatar_split_clause,[],[f1955,f4080]) ).
fof(f4080,plain,
( spl0_199
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1955,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4078,plain,
spl0_198,
inference(avatar_split_clause,[],[f1952,f4076]) ).
fof(f4076,plain,
( spl0_198
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1952,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4074,plain,
spl0_197,
inference(avatar_split_clause,[],[f1950,f4072]) ).
fof(f4072,plain,
( spl0_197
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1950,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4070,plain,
spl0_196,
inference(avatar_split_clause,[],[f1949,f4068]) ).
fof(f4068,plain,
( spl0_196
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1949,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4066,plain,
spl0_195,
inference(avatar_split_clause,[],[f1948,f4064]) ).
fof(f4064,plain,
( spl0_195
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1948,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4062,plain,
spl0_194,
inference(avatar_split_clause,[],[f1947,f4060]) ).
fof(f4060,plain,
( spl0_194
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1947,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4058,plain,
spl0_193,
inference(avatar_split_clause,[],[f1946,f4056]) ).
fof(f4056,plain,
( spl0_193
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1946,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4054,plain,
spl0_192,
inference(avatar_split_clause,[],[f1945,f4052]) ).
fof(f4052,plain,
( spl0_192
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1945,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4050,plain,
spl0_191,
inference(avatar_split_clause,[],[f1944,f4048]) ).
fof(f4048,plain,
( spl0_191
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1944,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4046,plain,
spl0_190,
inference(avatar_split_clause,[],[f1942,f4044]) ).
fof(f4044,plain,
( spl0_190
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1942,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4042,plain,
spl0_189,
inference(avatar_split_clause,[],[f1940,f4040]) ).
fof(f4040,plain,
( spl0_189
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1940,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4038,plain,
spl0_188,
inference(avatar_split_clause,[],[f1939,f4036]) ).
fof(f4036,plain,
( spl0_188
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1939,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4034,plain,
spl0_187,
inference(avatar_split_clause,[],[f1938,f4032]) ).
fof(f4032,plain,
( spl0_187
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1938,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4030,plain,
spl0_186,
inference(avatar_split_clause,[],[f1937,f4028]) ).
fof(f4028,plain,
( spl0_186
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1937,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4026,plain,
spl0_185,
inference(avatar_split_clause,[],[f1936,f4024]) ).
fof(f4024,plain,
( spl0_185
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1936,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4022,plain,
spl0_184,
inference(avatar_split_clause,[],[f1935,f4020]) ).
fof(f4020,plain,
( spl0_184
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1935,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4018,plain,
spl0_183,
inference(avatar_split_clause,[],[f1932,f4016]) ).
fof(f4016,plain,
( spl0_183
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1932,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4014,plain,
spl0_182,
inference(avatar_split_clause,[],[f1930,f4012]) ).
fof(f4012,plain,
( spl0_182
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1930,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4010,plain,
spl0_181,
inference(avatar_split_clause,[],[f1929,f4008]) ).
fof(f4008,plain,
( spl0_181
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1929,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4006,plain,
spl0_180,
inference(avatar_split_clause,[],[f1928,f4004]) ).
fof(f4004,plain,
( spl0_180
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1928,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4002,plain,
spl0_179,
inference(avatar_split_clause,[],[f1927,f4000]) ).
fof(f4000,plain,
( spl0_179
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1927,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f3998,plain,
spl0_178,
inference(avatar_split_clause,[],[f1926,f3996]) ).
fof(f3996,plain,
( spl0_178
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1926,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f3994,plain,
spl0_177,
inference(avatar_split_clause,[],[f1925,f3992]) ).
fof(f3992,plain,
( spl0_177
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1925,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f3990,plain,
spl0_176,
inference(avatar_split_clause,[],[f1924,f3988]) ).
fof(f3988,plain,
( spl0_176
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1924,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f3986,plain,
spl0_175,
inference(avatar_split_clause,[],[f1922,f3984]) ).
fof(f3984,plain,
( spl0_175
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1922,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f3982,plain,
spl0_174,
inference(avatar_split_clause,[],[f1920,f3980]) ).
fof(f3980,plain,
( spl0_174
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1920,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f3978,plain,
spl0_173,
inference(avatar_split_clause,[],[f1919,f3976]) ).
fof(f3976,plain,
( spl0_173
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1919,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f3974,plain,
spl0_172,
inference(avatar_split_clause,[],[f1918,f3972]) ).
fof(f3972,plain,
( spl0_172
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1918,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3970,plain,
spl0_171,
inference(avatar_split_clause,[],[f1915,f3968]) ).
fof(f3968,plain,
( spl0_171
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1915,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3966,plain,
spl0_170,
inference(avatar_split_clause,[],[f1913,f3964]) ).
fof(f3964,plain,
( spl0_170
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1913,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3962,plain,
spl0_169,
inference(avatar_split_clause,[],[f1912,f3960]) ).
fof(f3960,plain,
( spl0_169
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1912,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3958,plain,
spl0_168,
inference(avatar_split_clause,[],[f1911,f3956]) ).
fof(f3956,plain,
( spl0_168
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1911,axiom,
! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3954,plain,
spl0_167,
inference(avatar_split_clause,[],[f1910,f3952]) ).
fof(f3952,plain,
( spl0_167
<=> ! [X94] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1910,axiom,
! [X94] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3950,plain,
spl0_166,
inference(avatar_split_clause,[],[f1906,f3948]) ).
fof(f3948,plain,
( spl0_166
<=> ! [X94] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1906,axiom,
! [X94] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3946,plain,
spl0_165,
inference(avatar_split_clause,[],[f1899,f3944]) ).
fof(f3944,plain,
( spl0_165
<=> ! [X94] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1899,axiom,
! [X94] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3942,plain,
spl0_164,
inference(avatar_split_clause,[],[f1891,f3940]) ).
fof(f3940,plain,
( spl0_164
<=> ! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1891,axiom,
! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3938,plain,
spl0_163,
inference(avatar_split_clause,[],[f1890,f3936]) ).
fof(f3936,plain,
( spl0_163
<=> ! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1890,axiom,
! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3934,plain,
spl0_162,
inference(avatar_split_clause,[],[f1885,f3932]) ).
fof(f3932,plain,
( spl0_162
<=> ! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1885,axiom,
! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3930,plain,
spl0_161,
inference(avatar_split_clause,[],[f1883,f3928]) ).
fof(f3928,plain,
( spl0_161
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1883,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f3926,plain,
spl0_160,
inference(avatar_split_clause,[],[f1881,f3924]) ).
fof(f3924,plain,
( spl0_160
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1881,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f3922,plain,
spl0_159,
inference(avatar_split_clause,[],[f1880,f3920]) ).
fof(f3920,plain,
( spl0_159
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1880,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f3918,plain,
spl0_158,
inference(avatar_split_clause,[],[f1877,f3916]) ).
fof(f3916,plain,
( spl0_158
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Numeral_Onumber(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1877,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Numeral_Onumber(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f3914,plain,
spl0_157,
inference(avatar_split_clause,[],[f1875,f3912]) ).
fof(f3912,plain,
( spl0_157
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1875,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f3910,plain,
spl0_156,
inference(avatar_split_clause,[],[f1874,f3908]) ).
fof(f3908,plain,
( spl0_156
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1874,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f3906,plain,
spl0_155,
inference(avatar_split_clause,[],[f1873,f3904]) ).
fof(f3904,plain,
( spl0_155
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1873,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f3902,plain,
spl0_154,
inference(avatar_split_clause,[],[f1872,f3900]) ).
fof(f3900,plain,
( spl0_154
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1872,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f3898,plain,
spl0_153,
inference(avatar_split_clause,[],[f1871,f3896]) ).
fof(f3896,plain,
( spl0_153
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1871,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f3894,plain,
spl0_152,
inference(avatar_split_clause,[],[f1870,f3892]) ).
fof(f3892,plain,
( spl0_152
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1870,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f3890,plain,
spl0_151,
inference(avatar_split_clause,[],[f1869,f3888]) ).
fof(f3888,plain,
( spl0_151
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1869,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3886,plain,
spl0_150,
inference(avatar_split_clause,[],[f1868,f3884]) ).
fof(f3884,plain,
( spl0_150
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1868,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Omonoid__mult(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3882,plain,
spl0_149,
inference(avatar_split_clause,[],[f1867,f3880]) ).
fof(f3880,plain,
( spl0_149
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1867,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3878,plain,
spl0_148,
inference(avatar_split_clause,[],[f1866,f3876]) ).
fof(f3876,plain,
( spl0_148
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1866,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3874,plain,
spl0_147,
inference(avatar_split_clause,[],[f1864,f3872]) ).
fof(f3872,plain,
( spl0_147
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1864,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3870,plain,
spl0_146,
inference(avatar_split_clause,[],[f1863,f3868]) ).
fof(f3868,plain,
( spl0_146
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1863,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3866,plain,
spl0_145,
inference(avatar_split_clause,[],[f1862,f3864]) ).
fof(f3864,plain,
( spl0_145
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1862,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oring(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3862,plain,
spl0_144,
inference(avatar_split_clause,[],[f1861,f3860]) ).
fof(f3860,plain,
( spl0_144
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1861,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3858,plain,
spl0_143,
inference(avatar_split_clause,[],[f1860,f3856]) ).
fof(f3856,plain,
( spl0_143
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1860,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3854,plain,
spl0_142,
inference(avatar_split_clause,[],[f1859,f3852]) ).
fof(f3852,plain,
( spl0_142
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1859,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3850,plain,
spl0_141,
inference(avatar_split_clause,[],[f1858,f3848]) ).
fof(f3848,plain,
( spl0_141
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1858,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3846,plain,
spl0_140,
inference(avatar_split_clause,[],[f1856,f3844]) ).
fof(f3844,plain,
( spl0_140
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1856,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3842,plain,
spl0_139,
inference(avatar_split_clause,[],[f1855,f3840]) ).
fof(f3840,plain,
( spl0_139
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1855,axiom,
! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3838,plain,
spl0_138,
inference(avatar_split_clause,[],[f1852,f3836]) ).
fof(f3836,plain,
( spl0_138
<=> ! [X94] :
( ~ class_LOrder_Omeet__semilorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1852,axiom,
! [X94] :
( ~ class_LOrder_Omeet__semilorder(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3834,plain,
spl0_137,
inference(avatar_split_clause,[],[f1851,f3832]) ).
fof(f3832,plain,
( spl0_137
<=> ! [X94] :
( ~ class_LOrder_Omeet__semilorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1851,axiom,
! [X94] :
( ~ class_LOrder_Omeet__semilorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3830,plain,
spl0_136,
inference(avatar_split_clause,[],[f1850,f3828]) ).
fof(f3828,plain,
( spl0_136
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1850,axiom,
! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3826,plain,
spl0_135,
inference(avatar_split_clause,[],[f1849,f3824]) ).
fof(f3824,plain,
( spl0_135
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1849,axiom,
! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3822,plain,
spl0_134,
inference(avatar_split_clause,[],[f1848,f3820]) ).
fof(f3820,plain,
( spl0_134
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1848,axiom,
! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3818,plain,
spl0_133,
inference(avatar_split_clause,[],[f1847,f3816]) ).
fof(f3816,plain,
( spl0_133
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1847,axiom,
! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_LOrder_Omeet__semilorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3814,plain,
spl0_132,
inference(avatar_split_clause,[],[f1846,f3812]) ).
fof(f3812,plain,
( spl0_132
<=> ! [X94] :
( ~ class_LOrder_Ojoin__semilorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1846,axiom,
! [X94] :
( ~ class_LOrder_Ojoin__semilorder(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3810,plain,
spl0_131,
inference(avatar_split_clause,[],[f1845,f3808]) ).
fof(f3808,plain,
( spl0_131
<=> ! [X94] :
( ~ class_LOrder_Ojoin__semilorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1845,axiom,
! [X94] :
( ~ class_LOrder_Ojoin__semilorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3806,plain,
spl0_130,
inference(avatar_split_clause,[],[f1690,f3804]) ).
fof(f1690,axiom,
! [X4,X5] : c_in(X4,c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3802,plain,
spl0_129,
inference(avatar_split_clause,[],[f1658,f3800]) ).
fof(f3800,plain,
( spl0_129
<=> ! [X19] : ~ c_less(X19,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1658,axiom,
! [X19] : ~ c_less(X19,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3798,plain,
spl0_128,
inference(avatar_split_clause,[],[f1656,f3796]) ).
fof(f3796,plain,
( spl0_128
<=> ! [X19] : c_lessequals(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1656,axiom,
! [X19] : c_lessequals(c_0,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3794,plain,
spl0_127,
inference(avatar_split_clause,[],[f1632,f3792]) ).
fof(f3792,plain,
( spl0_127
<=> ! [X30] : c_Divides_Oop_Advd(c_1,X30,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1632,axiom,
! [X30] : c_Divides_Oop_Advd(c_1,X30,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3790,plain,
spl0_126,
inference(avatar_split_clause,[],[f1631,f3788]) ).
fof(f3788,plain,
( spl0_126
<=> ! [X30] : c_Divides_Oop_Advd(X30,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1631,axiom,
! [X30] : c_Divides_Oop_Advd(X30,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3786,plain,
spl0_125,
inference(avatar_split_clause,[],[f1615,f3784]) ).
fof(f3784,plain,
( spl0_125
<=> ! [X30] : c_Divides_Oop_Advd(X30,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1615,axiom,
! [X30] : c_Divides_Oop_Advd(X30,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3782,plain,
spl0_124,
inference(avatar_split_clause,[],[f1537,f3780]) ).
fof(f3780,plain,
( spl0_124
<=> ! [X5,X31] : ~ c_in(X31,c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1537,axiom,
! [X31,X5] : ~ c_in(X31,c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3778,plain,
spl0_123,
inference(avatar_split_clause,[],[f1020,f3775]) ).
fof(f3775,plain,
( spl0_123
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1020,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(f3773,plain,
spl0_122,
inference(avatar_split_clause,[],[f956,f3771]) ).
fof(f3771,plain,
( spl0_122
<=> ! [X19] : ~ c_less(X19,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f956,axiom,
! [X19] : ~ c_less(X19,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3769,plain,
spl0_121,
inference(avatar_split_clause,[],[f914,f3766]) ).
fof(f3766,plain,
( spl0_121
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f914,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3764,plain,
spl0_120,
inference(avatar_split_clause,[],[f574,f3762]) ).
fof(f3762,plain,
( spl0_120
<=> ! [X4,X21] : ~ c_List_Oop_Amem(X4,c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f574,axiom,
! [X21,X4] : ~ c_List_Oop_Amem(X4,c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f3760,plain,
spl0_119,
inference(avatar_split_clause,[],[f347,f3758]) ).
fof(f347,axiom,
! [X30] : c_Divides_Oop_Advd(X30,X30,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f3756,plain,
spl0_118,
inference(avatar_split_clause,[],[f258,f3754]) ).
fof(f258,axiom,
! [X19] : ~ c_IntDef_Oneg(c_IntDef_Oint(X19),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f3752,plain,
spl0_117,
inference(avatar_split_clause,[],[f251,f3749]) ).
fof(f3749,plain,
( spl0_117
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f251,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3747,plain,
spl0_116,
inference(avatar_split_clause,[],[f239,f3744]) ).
fof(f3742,plain,
spl0_115,
inference(avatar_split_clause,[],[f236,f3739]) ).
fof(f236,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3737,plain,
spl0_114,
inference(avatar_split_clause,[],[f94,f3735]) ).
fof(f3735,plain,
( spl0_114
<=> ! [X30] : c_Divides_Oop_Advd(X30,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f94,axiom,
! [X30] : c_Divides_Oop_Advd(X30,X30,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f3733,plain,
spl0_113,
inference(avatar_split_clause,[],[f1841,f3731]) ).
fof(f1841,axiom,
! [X92] : class_Orderings_Oorder(tc_set(X92)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3729,plain,
spl0_112,
inference(avatar_split_clause,[],[f1840,f3727]) ).
fof(f3727,plain,
( spl0_112
<=> ! [X92] : class_Orderings_Oord(tc_set(X92)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1840,axiom,
! [X92] : class_Orderings_Oord(tc_set(X92)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3725,plain,
spl0_111,
inference(avatar_split_clause,[],[f1718,f3722]) ).
fof(f3722,plain,
( spl0_111
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1718,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(f3720,plain,
spl0_110,
inference(avatar_split_clause,[],[f1716,f3717]) ).
fof(f3717,plain,
( spl0_110
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1716,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(f3715,plain,
spl0_109,
inference(avatar_split_clause,[],[f1715,f3713]) ).
fof(f3713,plain,
( spl0_109
<=> ! [X5] : c_Wellfounded__Recursion_Owf(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1715,axiom,
! [X5] : c_Wellfounded__Recursion_Owf(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3711,plain,
~ spl0_108,
inference(avatar_split_clause,[],[f1494,f3708]) ).
fof(f3708,plain,
( spl0_108
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1494,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3706,plain,
~ spl0_107,
inference(avatar_split_clause,[],[f1175,f3703]) ).
fof(f3703,plain,
( spl0_107
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1175,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3701,plain,
spl0_106,
inference(avatar_split_clause,[],[f1168,f3698]) ).
fof(f3698,plain,
( spl0_106
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1168,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3696,plain,
spl0_105,
inference(avatar_split_clause,[],[f1155,f3693]) ).
fof(f3693,plain,
( spl0_105
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1155,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3691,plain,
~ spl0_104,
inference(avatar_split_clause,[],[f1025,f3688]) ).
fof(f3688,plain,
( spl0_104
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1025,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2_0) ).
fof(f3686,plain,
spl0_103,
inference(avatar_split_clause,[],[f571,f3684]) ).
fof(f3684,plain,
( spl0_103
<=> ! [X21] : c_List_Onull(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f571,axiom,
! [X21] : c_List_Onull(c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3682,plain,
spl0_102,
inference(avatar_split_clause,[],[f416,f3680]) ).
fof(f3680,plain,
( spl0_102
<=> ! [X21] : c_List_Odistinct(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f416,axiom,
! [X21] : c_List_Odistinct(c_List_Olist_ONil,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3678,plain,
~ spl0_101,
inference(avatar_split_clause,[],[f235,f3675]) ).
fof(f3675,plain,
( spl0_101
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f235,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3673,plain,
~ spl0_100,
inference(avatar_split_clause,[],[f116,f3670]) ).
fof(f3670,plain,
( spl0_100
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f116,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2_0) ).
fof(f3668,plain,
spl0_99,
inference(avatar_split_clause,[],[f2754,f3665]) ).
fof(f2754,axiom,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3663,plain,
spl0_98,
inference(avatar_split_clause,[],[f1836,f3660]) ).
fof(f3660,plain,
( spl0_98
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1836,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3658,plain,
spl0_97,
inference(avatar_split_clause,[],[f1835,f3655]) ).
fof(f1835,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3653,plain,
spl0_96,
inference(avatar_split_clause,[],[f1834,f3650]) ).
fof(f3650,plain,
( spl0_96
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1834,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3648,plain,
spl0_95,
inference(avatar_split_clause,[],[f1833,f3645]) ).
fof(f1833,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3643,plain,
spl0_94,
inference(avatar_split_clause,[],[f1831,f3640]) ).
fof(f3640,plain,
( spl0_94
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1831,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3638,plain,
spl0_93,
inference(avatar_split_clause,[],[f1830,f3635]) ).
fof(f1830,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3633,plain,
spl0_92,
inference(avatar_split_clause,[],[f1828,f3630]) ).
fof(f3630,plain,
( spl0_92
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1828,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3628,plain,
spl0_91,
inference(avatar_split_clause,[],[f1827,f3625]) ).
fof(f3625,plain,
( spl0_91
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1827,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3623,plain,
spl0_90,
inference(avatar_split_clause,[],[f1826,f3620]) ).
fof(f3620,plain,
( spl0_90
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1826,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3618,plain,
spl0_89,
inference(avatar_split_clause,[],[f1825,f3615]) ).
fof(f3615,plain,
( spl0_89
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1825,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3613,plain,
spl0_88,
inference(avatar_split_clause,[],[f1824,f3610]) ).
fof(f1824,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3608,plain,
spl0_87,
inference(avatar_split_clause,[],[f1823,f3605]) ).
fof(f3605,plain,
( spl0_87
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1823,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3603,plain,
spl0_86,
inference(avatar_split_clause,[],[f1822,f3600]) ).
fof(f3600,plain,
( spl0_86
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1822,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3598,plain,
spl0_85,
inference(avatar_split_clause,[],[f1821,f3595]) ).
fof(f3595,plain,
( spl0_85
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1821,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3593,plain,
spl0_84,
inference(avatar_split_clause,[],[f1820,f3590]) ).
fof(f3590,plain,
( spl0_84
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1820,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3588,plain,
spl0_83,
inference(avatar_split_clause,[],[f1819,f3585]) ).
fof(f3585,plain,
( spl0_83
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1819,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3583,plain,
spl0_82,
inference(avatar_split_clause,[],[f1818,f3580]) ).
fof(f3580,plain,
( spl0_82
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1818,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3578,plain,
spl0_81,
inference(avatar_split_clause,[],[f1817,f3575]) ).
fof(f3575,plain,
( spl0_81
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1817,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3573,plain,
spl0_80,
inference(avatar_split_clause,[],[f1816,f3570]) ).
fof(f1816,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3568,plain,
spl0_79,
inference(avatar_split_clause,[],[f1815,f3565]) ).
fof(f3565,plain,
( spl0_79
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1815,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3563,plain,
spl0_78,
inference(avatar_split_clause,[],[f1814,f3560]) ).
fof(f3560,plain,
( spl0_78
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1814,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3558,plain,
spl0_77,
inference(avatar_split_clause,[],[f1813,f3555]) ).
fof(f3555,plain,
( spl0_77
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1813,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3553,plain,
spl0_76,
inference(avatar_split_clause,[],[f1812,f3550]) ).
fof(f3550,plain,
( spl0_76
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1812,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3548,plain,
spl0_75,
inference(avatar_split_clause,[],[f1811,f3545]) ).
fof(f3545,plain,
( spl0_75
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1811,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3543,plain,
spl0_74,
inference(avatar_split_clause,[],[f1810,f3540]) ).
fof(f3540,plain,
( spl0_74
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1810,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3538,plain,
spl0_73,
inference(avatar_split_clause,[],[f1809,f3535]) ).
fof(f3535,plain,
( spl0_73
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1809,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3533,plain,
spl0_72,
inference(avatar_split_clause,[],[f1808,f3530]) ).
fof(f3530,plain,
( spl0_72
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1808,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3528,plain,
spl0_71,
inference(avatar_split_clause,[],[f1807,f3525]) ).
fof(f3525,plain,
( spl0_71
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1807,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3523,plain,
spl0_70,
inference(avatar_split_clause,[],[f1806,f3520]) ).
fof(f1806,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3518,plain,
spl0_69,
inference(avatar_split_clause,[],[f1805,f3515]) ).
fof(f3515,plain,
( spl0_69
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1805,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3513,plain,
spl0_68,
inference(avatar_split_clause,[],[f1804,f3510]) ).
fof(f3510,plain,
( spl0_68
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1804,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3508,plain,
spl0_67,
inference(avatar_split_clause,[],[f1803,f3505]) ).
fof(f3505,plain,
( spl0_67
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1803,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3503,plain,
spl0_66,
inference(avatar_split_clause,[],[f1802,f3500]) ).
fof(f3500,plain,
( spl0_66
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1802,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3498,plain,
spl0_65,
inference(avatar_split_clause,[],[f1801,f3495]) ).
fof(f3495,plain,
( spl0_65
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1801,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3493,plain,
spl0_64,
inference(avatar_split_clause,[],[f1800,f3490]) ).
fof(f3490,plain,
( spl0_64
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1800,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3488,plain,
spl0_63,
inference(avatar_split_clause,[],[f1795,f3485]) ).
fof(f3485,plain,
( spl0_63
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1795,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3483,plain,
spl0_62,
inference(avatar_split_clause,[],[f1790,f3480]) ).
fof(f3480,plain,
( spl0_62
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1790,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3478,plain,
spl0_61,
inference(avatar_split_clause,[],[f1787,f3475]) ).
fof(f3475,plain,
( spl0_61
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1787,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3473,plain,
spl0_60,
inference(avatar_split_clause,[],[f1786,f3470]) ).
fof(f3470,plain,
( spl0_60
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1786,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3468,plain,
spl0_59,
inference(avatar_split_clause,[],[f1781,f3465]) ).
fof(f1781,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3463,plain,
spl0_58,
inference(avatar_split_clause,[],[f1778,f3460]) ).
fof(f1778,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3458,plain,
spl0_57,
inference(avatar_split_clause,[],[f1776,f3455]) ).
fof(f3455,plain,
( spl0_57
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1776,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3453,plain,
spl0_56,
inference(avatar_split_clause,[],[f1775,f3450]) ).
fof(f1775,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3448,plain,
spl0_55,
inference(avatar_split_clause,[],[f1774,f3445]) ).
fof(f3445,plain,
( spl0_55
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1774,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3443,plain,
spl0_54,
inference(avatar_split_clause,[],[f1773,f3440]) ).
fof(f1773,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3438,plain,
spl0_53,
inference(avatar_split_clause,[],[f1772,f3435]) ).
fof(f3435,plain,
( spl0_53
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1772,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3433,plain,
spl0_52,
inference(avatar_split_clause,[],[f1770,f3430]) ).
fof(f3430,plain,
( spl0_52
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1770,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3428,plain,
spl0_51,
inference(avatar_split_clause,[],[f1769,f3425]) ).
fof(f3425,plain,
( spl0_51
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1769,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3423,plain,
spl0_50,
inference(avatar_split_clause,[],[f1768,f3420]) ).
fof(f3420,plain,
( spl0_50
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1768,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3418,plain,
spl0_49,
inference(avatar_split_clause,[],[f1767,f3415]) ).
fof(f3415,plain,
( spl0_49
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1767,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3413,plain,
spl0_48,
inference(avatar_split_clause,[],[f1766,f3410]) ).
fof(f3410,plain,
( spl0_48
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1766,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3408,plain,
spl0_47,
inference(avatar_split_clause,[],[f1765,f3405]) ).
fof(f3405,plain,
( spl0_47
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1765,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3403,plain,
spl0_46,
inference(avatar_split_clause,[],[f1764,f3400]) ).
fof(f1764,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3398,plain,
spl0_45,
inference(avatar_split_clause,[],[f1763,f3395]) ).
fof(f3395,plain,
( spl0_45
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1763,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3393,plain,
spl0_44,
inference(avatar_split_clause,[],[f1762,f3390]) ).
fof(f3390,plain,
( spl0_44
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1762,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3388,plain,
spl0_43,
inference(avatar_split_clause,[],[f1761,f3385]) ).
fof(f3385,plain,
( spl0_43
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1761,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3383,plain,
spl0_42,
inference(avatar_split_clause,[],[f1760,f3380]) ).
fof(f3380,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1760,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3378,plain,
spl0_41,
inference(avatar_split_clause,[],[f1759,f3375]) ).
fof(f3375,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1759,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3373,plain,
spl0_40,
inference(avatar_split_clause,[],[f1758,f3370]) ).
fof(f3370,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1758,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3368,plain,
spl0_39,
inference(avatar_split_clause,[],[f1757,f3365]) ).
fof(f3365,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1757,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3363,plain,
spl0_38,
inference(avatar_split_clause,[],[f1756,f3360]) ).
fof(f3360,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1756,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3358,plain,
spl0_37,
inference(avatar_split_clause,[],[f1754,f3355]) ).
fof(f3355,plain,
( spl0_37
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1754,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3353,plain,
spl0_36,
inference(avatar_split_clause,[],[f1753,f3350]) ).
fof(f3350,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1753,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3348,plain,
spl0_35,
inference(avatar_split_clause,[],[f1752,f3345]) ).
fof(f3345,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1752,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3343,plain,
spl0_34,
inference(avatar_split_clause,[],[f1751,f3340]) ).
fof(f3340,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1751,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3338,plain,
spl0_33,
inference(avatar_split_clause,[],[f1750,f3335]) ).
fof(f1750,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3333,plain,
spl0_32,
inference(avatar_split_clause,[],[f1749,f3330]) ).
fof(f3330,plain,
( spl0_32
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1749,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3328,plain,
spl0_31,
inference(avatar_split_clause,[],[f1748,f3325]) ).
fof(f1748,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3323,plain,
spl0_30,
inference(avatar_split_clause,[],[f1747,f3320]) ).
fof(f1747,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3318,plain,
spl0_29,
inference(avatar_split_clause,[],[f1746,f3315]) ).
fof(f3315,plain,
( spl0_29
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1746,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3313,plain,
spl0_28,
inference(avatar_split_clause,[],[f1745,f3310]) ).
fof(f1745,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3308,plain,
spl0_27,
inference(avatar_split_clause,[],[f1743,f3305]) ).
fof(f1743,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3303,plain,
spl0_26,
inference(avatar_split_clause,[],[f1742,f3300]) ).
fof(f3300,plain,
( spl0_26
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1742,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3298,plain,
spl0_25,
inference(avatar_split_clause,[],[f1741,f3295]) ).
fof(f3295,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1741,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3293,plain,
spl0_24,
inference(avatar_split_clause,[],[f1740,f3290]) ).
fof(f3290,plain,
( spl0_24
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1740,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3288,plain,
spl0_23,
inference(avatar_split_clause,[],[f1739,f3285]) ).
fof(f3285,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1739,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3283,plain,
spl0_22,
inference(avatar_split_clause,[],[f1738,f3280]) ).
fof(f3280,plain,
( spl0_22
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1738,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3278,plain,
spl0_21,
inference(avatar_split_clause,[],[f1737,f3275]) ).
fof(f1737,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3273,plain,
spl0_20,
inference(avatar_split_clause,[],[f1736,f3270]) ).
fof(f3270,plain,
( spl0_20
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1736,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3268,plain,
spl0_19,
inference(avatar_split_clause,[],[f1735,f3265]) ).
fof(f3265,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1735,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3263,plain,
spl0_18,
inference(avatar_split_clause,[],[f1734,f3260]) ).
fof(f3260,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1734,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3258,plain,
spl0_17,
inference(avatar_split_clause,[],[f1732,f3255]) ).
fof(f3255,plain,
( spl0_17
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1732,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3253,plain,
spl0_16,
inference(avatar_split_clause,[],[f1731,f3250]) ).
fof(f3250,plain,
( spl0_16
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1731,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3248,plain,
spl0_15,
inference(avatar_split_clause,[],[f1730,f3245]) ).
fof(f1730,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3243,plain,
spl0_14,
inference(avatar_split_clause,[],[f1729,f3240]) ).
fof(f3240,plain,
( spl0_14
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1729,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3238,plain,
spl0_13,
inference(avatar_split_clause,[],[f1728,f3235]) ).
fof(f3235,plain,
( spl0_13
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1728,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3233,plain,
spl0_12,
inference(avatar_split_clause,[],[f1727,f3230]) ).
fof(f3230,plain,
( spl0_12
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1727,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3228,plain,
spl0_11,
inference(avatar_split_clause,[],[f1726,f3225]) ).
fof(f3225,plain,
( spl0_11
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1726,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3223,plain,
spl0_10,
inference(avatar_split_clause,[],[f1725,f3220]) ).
fof(f1725,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3218,plain,
spl0_9,
inference(avatar_split_clause,[],[f1724,f3215]) ).
fof(f3215,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1724,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3213,plain,
spl0_8,
inference(avatar_split_clause,[],[f1723,f3210]) ).
fof(f3210,plain,
( spl0_8
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1723,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3208,plain,
spl0_7,
inference(avatar_split_clause,[],[f1722,f3205]) ).
fof(f3205,plain,
( spl0_7
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1722,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3203,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f2757,f3200]) ).
fof(f3200,plain,
( spl0_6
<=> c_emptyset = c_Tarski_Ointerval(v_r,v_a,v_b,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f2757,axiom,
c_emptyset != c_Tarski_Ointerval(v_r,v_a,v_b,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f3198,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f2758,f3195]) ).
fof(f2758,axiom,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f3193,plain,
spl0_4,
inference(avatar_split_clause,[],[f2756,f3190]) ).
fof(f2756,axiom,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3188,plain,
spl0_3,
inference(avatar_split_clause,[],[f2753,f3185]) ).
fof(f2753,axiom,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3183,plain,
spl0_2,
inference(avatar_split_clause,[],[f2752,f3180]) ).
fof(f2752,axiom,
c_in(v_a,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3178,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2755,f3175]) ).
fof(f2755,axiom,
c_emptyset != v_S,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : LAT270-1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri May 3 12:26:01 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (28298)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.44 % (28302)WARNING: value z3 for option sas not known
% 0.17/0.44 % (28301)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.44 % (28306)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.44 % (28303)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.44 % (28300)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.44 % (28305)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.44 % (28304)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.44 % (28302)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)
% 1.87/0.72 TRYING [1]
% 5.25/1.15 % (28304)First to succeed.
% 5.51/1.20 TRYING [2]
% 5.51/1.23 % (28304)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28298"
% 5.51/1.23 % (28304)Refutation found. Thanks to Tanya!
% 5.51/1.23 % SZS status Unsatisfiable for theBenchmark
% 5.51/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 5.87/1.29 % (28304)------------------------------
% 5.87/1.29 % (28304)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.87/1.29 % (28304)Termination reason: Refutation
% 5.87/1.29
% 5.87/1.29 % (28304)Memory used [KB]: 13097
% 5.87/1.29 % (28304)Time elapsed: 0.791 s
% 5.87/1.29 % (28304)Instructions burned: 1472 (million)
% 5.87/1.29 % (28298)Success in time 0.927 s
%------------------------------------------------------------------------------