TSTP Solution File: LAT272-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LAT272-1 : 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 : n021.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 07:26:35 EDT 2024
% Result : Unsatisfiable 8.90s 1.72s
% Output : Refutation 9.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4330
% Syntax : Number of formulae : 7498 (2787 unt; 0 def)
% Number of atoms : 16541 (2975 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 15489 (6446 ~;6773 |; 0 &)
% (2270 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 2341 (2339 usr;2271 prp; 0-4 aty)
% Number of functors : 252 ( 252 usr; 54 con; 0-18 aty)
% Number of variables : 10944 (10944 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28694,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,f3683,f3687,f3691,f3696,f3701,f3706,f3711,f3716,f3720,f3725,f3730,f3734,f3738,f3742,f3747,f3752,f3757,f3761,f3765,f3769,f3774,f3778,f3783,f3787,f3791,f3795,f3799,f3803,f3807,f3811,f3815,f3819,f3823,f3827,f3831,f3835,f3839,f3843,f3847,f3851,f3855,f3859,f3863,f3867,f3871,f3875,f3879,f3883,f3887,f3891,f3895,f3899,f3903,f3907,f3911,f3915,f3919,f3923,f3927,f3931,f3935,f3939,f3943,f3947,f3951,f3955,f3959,f3963,f3967,f3971,f3975,f3979,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4011,f4015,f4019,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4123,f4127,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4167,f4171,f4175,f4179,f4183,f4187,f4191,f4195,f4199,f4203,f4207,f4211,f4215,f4219,f4223,f4227,f4231,f4235,f4239,f4243,f4247,f4251,f4255,f4259,f4263,f4267,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4327,f4331,f4335,f4339,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4383,f4387,f4391,f4395,f4399,f4403,f4407,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4555,f4559,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4595,f4599,f4603,f4607,f4611,f4615,f4619,f4623,f4627,f4631,f4635,f4639,f4643,f4647,f4651,f4655,f4659,f4663,f4667,f4671,f4675,f4679,f4683,f4687,f4691,f4695,f4699,f4703,f4707,f4711,f4715,f4719,f4723,f4727,f4731,f4735,f4739,f4743,f4747,f4751,f4755,f4759,f4763,f4767,f4771,f4775,f4779,f4783,f4787,f4791,f4795,f4799,f4803,f4807,f4811,f4815,f4819,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4863,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4899,f4903,f4907,f4911,f4915,f4919,f4923,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4967,f4971,f4975,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5135,f5139,f5143,f5147,f5151,f5155,f5159,f5163,f5167,f5171,f5175,f5179,f5183,f5187,f5191,f5195,f5199,f5203,f5207,f5211,f5215,f5219,f5223,f5227,f5231,f5235,f5239,f5243,f5247,f5251,f5255,f5259,f5263,f5267,f5271,f5275,f5279,f5283,f5287,f5291,f5295,f5299,f5303,f5307,f5311,f5315,f5319,f5323,f5327,f5331,f5335,f5339,f5343,f5347,f5351,f5355,f5359,f5363,f5367,f5371,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5419,f5423,f5427,f5431,f5435,f5439,f5443,f5447,f5451,f5455,f5459,f5463,f5467,f5471,f5475,f5479,f5483,f5487,f5491,f5495,f5499,f5503,f5507,f5511,f5515,f5519,f5523,f5527,f5531,f5535,f5539,f5543,f5547,f5551,f5555,f5559,f5563,f5567,f5571,f5575,f5579,f5583,f5587,f5591,f5595,f5599,f5603,f5607,f5611,f5615,f5619,f5623,f5627,f5631,f5635,f5639,f5643,f5647,f5651,f5655,f5659,f5663,f5667,f5671,f5675,f5679,f5683,f5687,f5691,f5695,f5699,f5703,f5707,f5711,f5715,f5719,f5723,f5727,f5731,f5735,f5739,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5783,f5787,f5791,f5795,f5799,f5803,f5807,f5811,f5815,f5819,f5823,f5827,f5831,f5835,f5839,f5843,f5847,f5851,f5855,f5859,f5863,f5867,f5871,f5875,f5879,f5883,f5887,f5891,f5895,f5899,f5903,f5907,f5912,f5917,f5921,f5926,f5933,f5942,f6702,f6706,f6710,f6714,f6719,f6724,f6729,f6733,f6737,f6741,f6746,f6750,f6754,f6758,f6762,f6766,f6770,f6774,f6779,f6784,f6789,f6794,f6799,f6804,f6809,f6814,f6819,f6824,f6829,f6834,f6839,f6844,f6849,f6854,f6858,f6862,f6866,f6870,f6874,f6878,f6883,f6888,f6893,f6897,f6901,f6905,f6909,f6913,f6917,f6922,f6927,f6931,f6936,f6941,f6945,f6949,f6953,f6957,f6961,f6965,f6969,f6973,f6977,f6981,f6985,f6989,f6993,f6997,f7002,f7006,f7011,f7022,f7027,f7032,f7039,f7043,f7047,f7051,f7055,f7059,f7063,f7067,f7071,f7075,f7080,f7084,f7088,f7092,f7096,f7100,f7104,f7108,f7112,f7116,f7120,f7124,f7128,f7132,f7136,f7140,f7144,f7148,f7152,f7156,f7160,f7164,f7168,f7172,f7176,f7180,f7184,f7188,f7192,f7196,f7200,f7204,f7208,f7212,f7216,f7220,f7224,f7229,f7233,f7237,f7241,f7245,f7249,f7253,f7257,f7261,f7265,f7269,f7273,f7277,f7281,f7285,f7289,f7293,f7297,f7301,f7305,f7309,f7314,f7318,f7323,f7327,f7332,f7336,f7340,f7344,f7348,f7352,f7356,f7360,f7364,f7368,f7372,f7376,f7380,f7384,f7388,f7392,f7396,f7400,f7404,f7408,f7412,f7416,f7420,f7424,f7428,f7432,f7436,f7440,f7444,f7448,f7452,f7456,f7460,f7464,f7468,f7472,f7476,f7480,f7484,f7488,f7492,f7496,f7500,f7504,f7508,f7512,f7516,f7520,f7524,f7528,f7532,f7536,f7540,f7544,f7548,f7552,f7556,f7560,f7564,f7568,f7572,f7577,f7582,f7586,f7590,f7594,f7612,f7643,f7655,f7670,f7682,f7688,f7693,f7697,f7701,f7705,f7709,f7713,f7717,f7721,f7726,f7730,f7734,f7738,f7742,f7746,f7750,f7754,f7758,f7762,f7766,f7771,f7775,f7779,f7783,f7787,f7791,f7795,f7799,f7803,f7807,f7811,f7820,f7824,f7828,f7832,f7836,f7840,f7844,f7848,f7852,f7856,f7860,f7864,f7868,f7872,f7876,f7880,f7884,f7888,f7892,f7896,f7900,f7904,f7908,f7912,f7916,f7920,f7924,f7928,f7932,f7936,f7940,f7944,f7949,f7953,f7957,f7961,f7965,f7969,f7973,f7977,f7981,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8014,f8018,f8022,f8026,f8031,f8035,f8055,f8159,f8163,f8167,f8171,f8175,f8179,f8183,f8187,f8191,f8195,f8200,f8204,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8241,f8245,f8249,f8253,f8257,f8261,f8265,f8269,f8273,f8277,f8281,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8326,f8330,f8334,f8338,f8342,f8346,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8382,f8386,f8390,f8394,f8398,f8402,f8406,f8411,f8415,f8419,f8423,f8427,f8431,f8435,f8439,f8443,f8447,f8451,f8455,f8459,f8463,f8467,f8471,f8475,f8479,f8483,f8491,f8544,f8595,f8640,f8663,f8705,f8709,f8713,f8717,f8721,f8725,f8730,f8734,f8738,f8742,f8746,f8750,f8754,f8758,f8762,f8766,f8770,f8774,f8778,f8782,f8786,f8790,f8794,f8798,f8802,f8806,f8810,f8814,f8818,f8822,f8827,f8831,f8835,f8839,f8843,f8847,f8851,f8855,f8859,f8863,f8867,f8871,f8875,f8879,f8883,f8887,f8891,f8895,f8899,f8903,f8907,f8911,f8915,f8919,f8923,f8927,f8931,f8935,f8939,f8943,f8948,f8952,f8956,f8960,f8964,f8968,f8972,f8976,f8980,f8984,f8989,f8993,f8998,f9005,f9009,f9013,f9017,f9021,f9032,f9092,f9128,f9182,f9206,f9220,f9244,f9248,f9252,f9256,f9260,f9264,f9268,f9272,f9276,f9280,f9284,f9289,f9293,f9297,f9301,f9305,f9309,f9313,f9317,f9321,f9325,f9329,f9333,f9337,f9341,f9345,f9349,f9353,f9357,f9361,f9365,f9369,f9373,f9377,f9381,f9385,f9389,f9393,f9397,f9401,f9405,f9409,f9413,f9417,f9421,f9425,f9429,f9433,f9437,f9441,f9445,f9449,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9501,f9505,f9509,f9513,f9517,f9521,f9525,f9529,f9533,f9538,f9546,f9550,f9554,f9558,f9562,f9566,f9570,f9602,f9608,f9636,f9688,f9735,f9802,f9941,f9954,f9958,f9962,f9966,f9970,f9974,f9979,f9983,f9987,f9991,f9995,f9999,f10003,f10007,f10011,f10015,f10019,f10024,f10028,f10032,f10036,f10040,f10044,f10048,f10052,f10056,f10060,f10065,f10075,f10079,f10083,f10087,f10091,f10095,f10099,f10103,f10107,f10117,f10121,f10125,f10129,f10133,f10137,f10141,f10145,f10149,f10153,f10163,f10167,f10171,f10175,f10179,f10183,f10187,f10191,f10195,f10199,f10203,f10207,f10211,f10215,f10219,f10223,f10227,f10231,f10235,f10239,f10243,f10251,f10255,f10259,f10263,f10267,f10271,f10275,f10279,f10283,f10287,f10291,f10295,f10299,f10303,f10307,f10311,f10315,f10319,f10323,f10327,f10331,f10336,f10340,f10344,f10348,f10352,f10356,f10360,f10364,f10368,f10372,f10376,f10380,f10384,f10388,f10392,f10396,f10400,f10404,f10408,f10412,f10416,f10420,f10424,f10428,f10432,f10436,f10440,f10444,f10448,f10452,f10456,f10460,f10464,f10468,f10472,f10476,f10623,f10680,f10868,f10971,f11017,f11149,f11327,f11331,f11335,f11339,f11343,f11347,f11351,f11364,f11368,f11372,f11376,f11380,f11384,f11388,f11392,f11396,f11400,f11404,f11408,f11412,f11416,f11420,f11424,f11428,f11432,f11436,f11440,f11444,f11448,f11452,f11456,f11460,f11464,f11468,f11472,f11476,f11480,f11484,f11488,f11492,f11496,f11500,f11504,f11508,f11512,f11516,f11520,f11524,f11529,f11533,f11537,f11541,f11545,f11549,f11553,f11557,f11561,f11565,f11569,f11573,f11577,f11581,f11585,f11589,f11593,f11597,f11601,f11605,f11609,f11613,f11617,f11621,f11625,f11629,f11633,f11637,f11641,f11645,f11649,f11653,f11664,f11668,f11672,f11676,f11680,f11684,f11688,f11692,f11697,f11711,f11715,f11719,f11723,f11728,f11736,f11740,f11745,f11786,f11790,f11794,f11798,f11802,f11806,f11810,f12415,f12773,f12887,f12891,f12895,f12899,f12903,f12907,f12911,f12915,f12919,f12923,f12927,f12931,f12935,f12939,f12943,f12947,f12951,f12955,f12959,f12963,f12967,f12971,f12975,f12979,f12983,f12987,f12991,f12995,f12999,f13003,f13007,f13011,f13015,f13019,f13023,f13027,f13031,f13035,f13039,f13043,f13047,f13051,f13055,f13059,f13063,f13067,f13071,f13075,f13079,f13083,f13088,f13092,f13096,f13100,f13104,f13108,f13112,f13116,f13120,f13124,f13128,f13133,f13137,f13141,f13145,f13149,f13153,f13157,f13161,f13165,f13169,f13173,f13185,f13189,f13193,f13198,f13206,f13210,f13214,f13218,f13349,f13636,f14144,f14169,f14173,f14177,f14181,f14185,f14189,f14193,f14197,f14201,f14205,f14209,f14213,f14217,f14221,f14225,f14229,f14233,f14237,f14241,f14245,f14249,f14253,f14257,f14261,f14265,f14269,f14273,f14277,f14281,f14285,f14289,f14293,f14297,f14301,f14305,f14309,f14313,f14317,f14324,f14328,f14332,f14336,f14340,f14344,f14348,f14352,f14356,f14360,f14361,f14365,f14369,f14373,f14377,f14381,f14385,f14389,f14393,f14397,f14401,f14418,f14442,f14447,f14465,f14470,f14490,f14494,f14499,f14503,f14507,f14511,f14515,f14519,f14523,f14527,f14531,f14535,f14758,f15287,f15479,f15483,f15487,f15491,f15495,f15499,f15503,f15507,f15511,f15515,f15519,f15523,f15527,f15531,f15535,f15540,f15544,f15548,f15552,f15556,f15560,f15564,f15568,f15573,f15577,f15583,f15587,f15591,f15595,f15599,f15603,f15607,f15611,f15615,f15619,f15624,f15628,f15632,f15636,f15640,f15644,f15648,f15652,f15656,f15660,f15666,f15670,f15674,f15678,f15682,f15686,f15690,f15694,f15698,f15702,f15707,f15711,f15715,f15719,f15723,f15727,f15732,f15757,f15762,f15829,f15834,f15929,f15934,f16033,f16038,f16068,f16074,f16078,f16095,f16100,f16108,f16113,f16121,f16127,f16132,f16137,f16141,f16145,f16151,f16157,f16161,f16165,f16169,f16173,f16179,f16184,f16219,f16223,f16237,f17334,f17338,f17342,f17346,f17350,f17354,f17358,f17362,f17366,f17370,f17374,f17389,f17393,f17397,f17401,f17405,f17409,f17413,f17417,f17421,f17425,f17429,f17433,f17437,f17441,f17445,f17449,f17453,f17457,f17461,f17465,f17469,f17484,f17488,f17492,f17496,f17500,f17504,f17508,f17512,f17516,f17520,f17524,f17528,f17532,f17536,f17540,f17544,f17548,f17552,f17556,f17560,f17564,f17570,f17574,f17578,f17584,f17610,f17616,f17701,f17706,f17710,f17733,f17737,f17741,f17746,f17751,f17756,f17761,f17778,f17783,f17787,f17791,f17795,f17800,f17820,f17824,f17828,f17832,f17837,f17842,f17847,f17852,f17857,f17862,f17869,f17877,f17881,f17886,f17894,f17898,f17902,f17906,f17910,f17914,f17992,f18196,f18472,f18767,f18771,f18775,f18779,f18780,f18784,f18788,f18792,f18798,f18804,f18808,f18812,f18816,f18820,f18824,f18828,f18832,f18836,f18840,f18844,f18848,f18852,f18856,f18860,f18864,f18870,f18874,f18878,f18882,f18886,f18890,f18894,f18898,f18902,f18908,f18912,f19233,f19237,f19905,f19909,f19913,f19917,f19922,f19926,f19930,f19934,f19939,f19943,f19947,f19951,f19955,f19959,f19963,f19967,f19973,f19977,f19981,f19985,f20046,f20078,f20492,f20496,f20500,f20504,f20508,f20512,f20516,f20520,f20524,f20528,f20532,f20536,f20540,f20544,f20548,f20552,f20556,f20560,f20564,f20568,f20573,f20578,f20584,f20605,f20610,f20622,f20626,f20630,f20634,f20639,f20659,f20664,f20684,f20688,f20692,f20696,f20701,f21001,f21005,f21009,f21102,f21106,f21110,f21114,f21118,f21122,f21126,f21130,f21134,f21138,f21142,f21146,f21150,f21173,f21177,f21181,f21185,f21189,f21193,f21197,f21201,f21205,f21209,f21230,f21234,f21238,f21242,f21246,f21250,f21254,f21258,f21262,f21266,f21270,f21274,f21278,f21282,f21286,f21290,f21294,f21298,f21302,f21306,f21310,f21314,f21318,f21322,f21326,f21330,f21334,f21338,f21342,f21346,f21350,f21354,f21358,f21362,f21366,f21370,f21374,f21378,f21382,f21389,f21407,f21414,f21475,f21479,f21483,f21487,f21493,f21569,f21573,f21577,f21582,f21586,f21590,f21594,f21598,f21602,f21607,f21634,f21640,f21885,f21889,f21893,f22489,f22493,f22497,f22507,f22511,f22515,f22519,f22523,f22527,f22531,f22535,f22539,f22543,f22553,f22557,f22561,f22565,f22569,f22573,f22577,f22581,f22585,f22589,f22593,f22597,f22601,f22605,f22609,f22613,f22617,f22621,f22704,f23054,f23289,f23293,f23297,f23321,f23325,f23329,f23333,f23337,f23341,f23345,f23349,f23353,f23357,f23362,f23366,f23370,f23374,f23378,f23382,f23386,f23390,f23394,f23398,f23403,f23408,f23433,f23438,f23489,f23493,f23497,f23502,f24129,f24320,f24324,f24328,f24332,f24336,f24340,f24345,f24350,f24354,f24358,f24362,f24366,f24370,f24374,f24378,f24384,f24390,f24472,f24476,f24480,f24484,f24489,f24499,f24503,f24526,f24559,f24563,f24770,f24894,f24948,f24952,f24956,f24960,f24964,f25094,f25098,f25102,f25106,f25110,f25114,f25118,f25122,f25126,f25130,f25134,f25138,f25142,f25146,f25150,f25154,f25158,f25482,f25486,f25490,f25494,f25498,f25503,f25664,f25668,f25672,f25676,f25680,f25684,f25688,f25693,f25697,f25701,f25705,f25709,f25713,f25717,f25721,f25725,f25729,f25733,f25738,f25742,f25746,f25750,f25754,f25758,f25762,f25766,f25770,f25776,f25781,f25789,f25795,f25803,f25809,f25825,f25831,f25881,f25885,f25891,f25904,f25909,f26627,f26631,f26635,f26645,f26649,f26653,f26657,f26661,f26666,f26748,f26752,f26756,f26760,f26764,f26769,f26773,f26777,f27062,f27077,f27149,f27153,f27157,f27161,f27165,f27169,f27173,f27178,f27182,f27186,f27192,f27212,f27425,f27429,f27433,f27437,f27527,f27581,f27586,f27591,f27596,f27601,f27605,f27609,f27613,f27617,f27621,f27625,f27679,f27685,f27689,f27693,f27697,f27701,f27705,f27849,f27854,f27858,f27885,f27889,f27896,f27900,f27904,f27908,f27912,f27917,f27922,f27927,f28014,f28018,f28022,f28026,f28036,f28046,f28050,f28054,f28059,f28084,f28125,f28132,f28159,f28164,f28178,f28182,f28187,f28226,f28231,f28242,f28246,f28250,f28293,f28297,f28301,f28305,f28438,f28444,f28448,f28485,f28489,f28507,f28528,f28551,f28555,f28559,f28601,f28624,f28693]) ).
fof(f28693,plain,
( ~ spl0_4
| spl0_100
| ~ spl0_1912 ),
inference(avatar_split_clause,[],[f28685,f20690,f3670,f3190]) ).
fof(f3190,plain,
( spl0_4
<=> c_in(v_x,v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f3670,plain,
( spl0_100
<=> c_in(c_Pair(v_x,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f20690,plain,
( spl0_1912
<=> ! [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_1912])]) ).
fof(f28685,plain,
( ~ c_in(v_x,v_S,t_a)
| spl0_100
| ~ spl0_1912 ),
inference(resolution,[],[f20691,f3672]) ).
fof(f3672,plain,
( ~ c_in(c_Pair(v_x,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| spl0_100 ),
inference(avatar_component_clause,[],[f3670]) ).
fof(f20691,plain,
( ! [X0] :
( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a) )
| ~ spl0_1912 ),
inference(avatar_component_clause,[],[f20690]) ).
fof(f28624,plain,
spl0_2270,
inference(avatar_split_clause,[],[f1598,f28622]) ).
fof(f28622,plain,
( spl0_2270
<=> ! [X6,X23,X24,X5,X27,X25,X28,X26] :
( ~ c_in(c_Pair(X25,X28,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| ~ c_in(c_Pair(X24,X27,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X24,X25,X5,X23),c_Datatype__Universe_OScons(X27,X28,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2270])]) ).
fof(f1598,axiom,
! [X28,X6,X26,X27,X24,X5,X25,X23] :
( ~ c_in(c_Pair(X25,X28,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| ~ c_in(c_Pair(X24,X27,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X24,X25,X5,X23),c_Datatype__Universe_OScons(X27,X28,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
fof(f28601,plain,
spl0_2269,
inference(avatar_split_clause,[],[f1602,f28599]) ).
fof(f28599,plain,
( spl0_2269
<=> ! [X5,X23,X6,X26,X39] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdsumE__3(X26,X39,X5,X23),c_Main_OdsumE__4(X26,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdsumE__1(X6,X39,X5,X23),c_Main_OdsumE__2(X6,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).
fof(f1602,axiom,
! [X39,X6,X26,X5,X23] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdsumE__3(X26,X39,X5,X23),c_Main_OdsumE__4(X26,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdsumE__1(X6,X39,X5,X23),c_Main_OdsumE__2(X6,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).
fof(f28559,plain,
spl0_2268,
inference(avatar_split_clause,[],[f1601,f28557]) ).
fof(f28557,plain,
( spl0_2268
<=> ! [X5,X23,X6,X26,X39] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X26,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X26,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39
| c_in(c_Pair(c_Main_OdsumE__1(X6,X39,X5,X23),c_Main_OdsumE__2(X6,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2268])]) ).
fof(f1601,axiom,
! [X39,X6,X26,X5,X23] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X26,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X26,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39
| c_in(c_Pair(c_Main_OdsumE__1(X6,X39,X5,X23),c_Main_OdsumE__2(X6,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
fof(f28555,plain,
( spl0_2267
| ~ spl0_1601
| ~ spl0_2060 ),
inference(avatar_split_clause,[],[f23777,f23405,f14371,f28553]) ).
fof(f28553,plain,
( spl0_2267
<=> ! [X0] : c_insert(X0,v_A,t_a) = c_union(v_A,c_insert(X0,v_S,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).
fof(f14371,plain,
( spl0_1601
<=> ! [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_1601])]) ).
fof(f23405,plain,
( spl0_2060
<=> v_A = c_union(v_A,v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f23777,plain,
( ! [X0] : c_insert(X0,v_A,t_a) = c_union(v_A,c_insert(X0,v_S,t_a),t_a)
| ~ spl0_1601
| ~ spl0_2060 ),
inference(superposition,[],[f14372,f23407]) ).
fof(f23407,plain,
( v_A = c_union(v_A,v_S,t_a)
| ~ spl0_2060 ),
inference(avatar_component_clause,[],[f23405]) ).
fof(f14372,plain,
( ! [X2,X1,X35,X5] : c_union(X1,c_insert(X2,X35,X5),X5) = c_insert(X2,c_union(X1,X35,X5),X5)
| ~ spl0_1601 ),
inference(avatar_component_clause,[],[f14371]) ).
fof(f28551,plain,
spl0_2266,
inference(avatar_split_clause,[],[f1600,f28549]) ).
fof(f28549,plain,
( spl0_2266
<=> ! [X5,X23,X6,X26,X39] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39
| c_in(c_Pair(c_Main_OdsumE__3(X26,X39,X5,X23),c_Main_OdsumE__4(X26,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2266])]) ).
fof(f1600,axiom,
! [X39,X6,X26,X5,X23] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39
| c_in(c_Pair(c_Main_OdsumE__3(X26,X39,X5,X23),c_Main_OdsumE__4(X26,X39,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
fof(f28528,plain,
spl0_2265,
inference(avatar_split_clause,[],[f1599,f28526]) ).
fof(f28526,plain,
( spl0_2265
<=> ! [X5,X23,X6,X26,X39] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X26,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X26,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2265])]) ).
fof(f1599,axiom,
! [X39,X6,X26,X5,X23] :
( ~ c_in(X39,c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X26,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X26,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X6,X39,X5,X23),X5,X23),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X6,X39,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
fof(f28507,plain,
spl0_2264,
inference(avatar_split_clause,[],[f1595,f28505]) ).
fof(f28505,plain,
( spl0_2264
<=> ! [X5,X31,X23,X6,X26] :
( ~ c_in(X31,c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X31,X6,X26,X5,X23),c_Main_OdprodE__2(X31,X6,X26,X5,X23),X5,X23),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X31,X6,X26,X5,X23),c_Main_OdprodE__4(X31,X6,X26,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2264])]) ).
fof(f1595,axiom,
! [X31,X6,X26,X5,X23] :
( ~ c_in(X31,c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X31,X6,X26,X5,X23),c_Main_OdprodE__2(X31,X6,X26,X5,X23),X5,X23),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X31,X6,X26,X5,X23),c_Main_OdprodE__4(X31,X6,X26,X5,X23),X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
fof(f28489,plain,
spl0_2263,
inference(avatar_split_clause,[],[f1604,f28487]) ).
fof(f28487,plain,
( spl0_2263
<=> ! [X6,X23,X5,X25,X28,X26] :
( ~ c_in(c_Pair(X25,X28,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X25,X5,X23),c_Datatype__Universe_OIn1(X28,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2263])]) ).
fof(f1604,axiom,
! [X28,X6,X26,X5,X25,X23] :
( ~ c_in(c_Pair(X25,X28,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X25,X5,X23),c_Datatype__Universe_OIn1(X28,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
fof(f28485,plain,
spl0_2262,
inference(avatar_split_clause,[],[f1603,f28483]) ).
fof(f28483,plain,
( spl0_2262
<=> ! [X5,X24,X23,X6,X27,X26] :
( ~ c_in(c_Pair(X24,X27,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X24,X5,X23),c_Datatype__Universe_OIn0(X27,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2262])]) ).
fof(f1603,axiom,
! [X6,X26,X27,X24,X5,X23] :
( ~ c_in(c_Pair(X24,X27,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X24,X5,X23),c_Datatype__Universe_OIn0(X27,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
fof(f28448,plain,
( spl0_2261
| ~ spl0_1601
| ~ spl0_2049 ),
inference(avatar_split_clause,[],[f23524,f23359,f14371,f28446]) ).
fof(f28446,plain,
( spl0_2261
<=> ! [X0] : c_insert(X0,v_A,t_a) = c_union(v_S,c_insert(X0,v_A,t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2261])]) ).
fof(f23359,plain,
( spl0_2049
<=> v_A = c_union(v_S,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f23524,plain,
( ! [X0] : c_insert(X0,v_A,t_a) = c_union(v_S,c_insert(X0,v_A,t_a),t_a)
| ~ spl0_1601
| ~ spl0_2049 ),
inference(superposition,[],[f14372,f23361]) ).
fof(f23361,plain,
( v_A = c_union(v_S,v_A,t_a)
| ~ spl0_2049 ),
inference(avatar_component_clause,[],[f23359]) ).
fof(f28444,plain,
( spl0_2260
| ~ spl0_58
| ~ spl0_1662
| ~ spl0_1663
| ~ spl0_2259 ),
inference(avatar_split_clause,[],[f28440,f28436,f15622,f15617,f3460,f28442]) ).
fof(f28442,plain,
( spl0_2260
<=> ! [X39,X40] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2260])]) ).
fof(f3460,plain,
( spl0_58
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f15617,plain,
( spl0_1662
<=> ! [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_1662])]) ).
fof(f15622,plain,
( spl0_1663
<=> ! [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_1663])]) ).
fof(f28436,plain,
( spl0_2259
<=> ! [X39,X40] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2259])]) ).
fof(f28440,plain,
( ! [X40,X39] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1662
| ~ spl0_1663
| ~ spl0_2259 ),
inference(forward_demodulation,[],[f28439,f16696]) ).
fof(f16696,plain,
( ! [X0,X1] : c_plus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,X1),tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1662 ),
inference(resolution,[],[f15618,f3462]) ).
fof(f3462,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f3460]) ).
fof(f15618,plain,
( ! [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) )
| ~ spl0_1662 ),
inference(avatar_component_clause,[],[f15617]) ).
fof(f28439,plain,
( ! [X40,X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1663
| ~ spl0_2259 ),
inference(forward_demodulation,[],[f28437,f16700]) ).
fof(f16700,plain,
( ! [X0,X1] : c_times(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X0,X1),tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1663 ),
inference(resolution,[],[f15623,f3462]) ).
fof(f15623,plain,
( ! [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) )
| ~ spl0_1663 ),
inference(avatar_component_clause,[],[f15622]) ).
fof(f28437,plain,
( ! [X40,X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2259 ),
inference(avatar_component_clause,[],[f28436]) ).
fof(f28438,plain,
spl0_2259,
inference(avatar_split_clause,[],[f3151,f28436]) ).
fof(f3151,plain,
! [X40,X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3150,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(f3150,plain,
! [X40,X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3149,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(f3149,plain,
! [X40,X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f317,f1021]) ).
fof(f317,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).
fof(f28305,plain,
spl0_2258,
inference(avatar_split_clause,[],[f1597,f28303]) ).
fof(f28303,plain,
( spl0_2258
<=> ! [X5,X31,X23,X6,X26] :
( ~ c_in(X31,c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdprodE__1(X31,X6,X26,X5,X23),c_Main_OdprodE__3(X31,X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2258])]) ).
fof(f1597,axiom,
! [X31,X6,X26,X5,X23] :
( ~ c_in(X31,c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdprodE__1(X31,X6,X26,X5,X23),c_Main_OdprodE__3(X31,X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
fof(f28301,plain,
spl0_2257,
inference(avatar_split_clause,[],[f1596,f28299]) ).
fof(f28299,plain,
( spl0_2257
<=> ! [X5,X31,X23,X6,X26] :
( ~ c_in(X31,c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdprodE__2(X31,X6,X26,X5,X23),c_Main_OdprodE__4(X31,X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2257])]) ).
fof(f1596,axiom,
! [X31,X6,X26,X5,X23] :
( ~ c_in(X31,c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))))
| c_in(c_Pair(c_Main_OdprodE__2(X31,X6,X26,X5,X23),c_Main_OdprodE__4(X31,X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X26,tc_prod(tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
fof(f28297,plain,
spl0_2256,
inference(avatar_split_clause,[],[f485,f28295]) ).
fof(f28295,plain,
( spl0_2256
<=> ! [X5,X4,X7,X8,X6,X2] :
( c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(X4,X8,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X7,X8,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_2256])]) ).
fof(f485,axiom,
! [X2,X8,X6,X7,X4,X5] :
( c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(X4,X8,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X7,X8,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__cons__cons_1) ).
fof(f28293,plain,
spl0_2255,
inference(avatar_split_clause,[],[f366,f28291]) ).
fof(f28291,plain,
( spl0_2255
<=> ! [X5,X44,X4,X45,X6,X8] :
( c_in(c_Pair(X4,X8,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(X44,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_2255])]) ).
fof(f366,axiom,
! [X8,X6,X44,X45,X4,X5] :
( c_in(c_Pair(X4,X8,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(X44,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_OCons__in__lex_1) ).
fof(f28250,plain,
spl0_2254,
inference(avatar_split_clause,[],[f368,f28248]) ).
fof(f28248,plain,
( spl0_2254
<=> ! [X44,X4,X8,X6,X5,X45] :
( c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(X45,tc_List_Olist(X5))
| c_in(c_Pair(X44,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_2254])]) ).
fof(f368,axiom,
! [X8,X44,X6,X45,X4,X5] :
( c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(X45,tc_List_Olist(X5))
| c_in(c_Pair(X44,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_OCons__in__lex_3) ).
fof(f28246,plain,
spl0_2253,
inference(avatar_split_clause,[],[f234,f28244]) ).
fof(f28244,plain,
( spl0_2253
<=> ! [X4,X8] :
( ~ c_in(c_Pair(X4,X8,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X4,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X8,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2253])]) ).
fof(f234,axiom,
! [X8,X4] :
( ~ c_in(c_Pair(X4,X8,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X4,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X8,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
fof(f28242,plain,
spl0_2252,
inference(avatar_split_clause,[],[f233,f28240]) ).
fof(f28240,plain,
( spl0_2252
<=> ! [X4,X8] :
( c_in(c_Pair(X4,X8,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X4,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X8,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2252])]) ).
fof(f233,axiom,
! [X8,X4] :
( c_in(c_Pair(X4,X8,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X4,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X8,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
fof(f28231,plain,
( spl0_2251
| ~ spl0_58
| ~ spl0_1663
| ~ spl0_2250 ),
inference(avatar_split_clause,[],[f28227,f28224,f15622,f3460,f28229]) ).
fof(f28229,plain,
( spl0_2251
<=> ! [X39,X40] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2251])]) ).
fof(f28224,plain,
( spl0_2250
<=> ! [X39,X40] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).
fof(f28227,plain,
( ! [X40,X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1663
| ~ spl0_2250 ),
inference(forward_demodulation,[],[f28225,f16700]) ).
fof(f28225,plain,
( ! [X40,X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2250 ),
inference(avatar_component_clause,[],[f28224]) ).
fof(f28226,plain,
spl0_2250,
inference(avatar_split_clause,[],[f3145,f28224]) ).
fof(f3145,plain,
! [X40,X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3144,f1021]) ).
fof(f3144,plain,
! [X40,X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3143,f1019]) ).
fof(f3143,plain,
! [X40,X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f326,f1021]) ).
fof(f326,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).
fof(f28187,plain,
( spl0_2249
| ~ spl0_1340
| ~ spl0_2093 ),
inference(avatar_split_clause,[],[f25543,f24524,f10434,f28185]) ).
fof(f28185,plain,
( spl0_2249
<=> ! [X0] :
( c_in(c_Main_OsubsetI__1(v_S,X0,t_a),v_A,t_a)
| c_lessequals(v_S,X0,tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).
fof(f10434,plain,
( spl0_1340
<=> ! [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_1340])]) ).
fof(f24524,plain,
( spl0_2093
<=> ! [X0] :
( c_in(X0,v_A,t_a)
| ~ c_in(X0,v_S,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f25543,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(v_S,X0,t_a),v_A,t_a)
| c_lessequals(v_S,X0,tc_set(t_a)) )
| ~ spl0_1340
| ~ spl0_2093 ),
inference(resolution,[],[f24525,f10435]) ).
fof(f10435,plain,
( ! [X1,X35,X5] :
( c_in(c_Main_OsubsetI__1(X1,X35,X5),X1,X5)
| c_lessequals(X1,X35,tc_set(X5)) )
| ~ spl0_1340 ),
inference(avatar_component_clause,[],[f10434]) ).
fof(f24525,plain,
( ! [X0] :
( ~ c_in(X0,v_S,t_a)
| c_in(X0,v_A,t_a) )
| ~ spl0_2093 ),
inference(avatar_component_clause,[],[f24524]) ).
fof(f28182,plain,
spl0_2248,
inference(avatar_split_clause,[],[f656,f28180]) ).
fof(f28180,plain,
( spl0_2248
<=> ! [X48,X49,X23,X44,X5,X45] :
( c_Nat_Osize(X45,tc_List_Olist(X5)) != c_Nat_Osize(X49,tc_List_Olist(X23))
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X48,tc_List_Olist(X23))
| c_List_Ozip(c_append(X44,X45,X5),c_append(X48,X49,X23),X5,X23) = c_append(c_List_Ozip(X44,X48,X5,X23),c_List_Ozip(X45,X49,X5,X23),tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).
fof(f656,axiom,
! [X48,X49,X44,X45,X5,X23] :
( c_Nat_Osize(X45,tc_List_Olist(X5)) != c_Nat_Osize(X49,tc_List_Olist(X23))
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X48,tc_List_Olist(X23))
| c_List_Ozip(c_append(X44,X45,X5),c_append(X48,X49,X23),X5,X23) = c_append(c_List_Ozip(X44,X48,X5,X23),c_List_Ozip(X45,X49,X5,X23),tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).
fof(f28178,plain,
spl0_2247,
inference(avatar_split_clause,[],[f4,f28176]) ).
fof(f28176,plain,
( spl0_2247
<=> ! [X0,X3,X2,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X2,v_sko__4mj(X0,X2,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X3,X0,v_r),X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2247])]) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X2,v_sko__4mj(X0,X2,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X3,X0,v_r),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_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3) ).
fof(f28164,plain,
( spl0_2246
| ~ spl0_58
| ~ spl0_1663
| ~ spl0_2245 ),
inference(avatar_split_clause,[],[f28160,f28157,f15622,f3460,f28162]) ).
fof(f28162,plain,
( spl0_2246
<=> ! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X39),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).
fof(f28157,plain,
( spl0_2245
<=> ! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2245])]) ).
fof(f28160,plain,
( ! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X39),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1663
| ~ spl0_2245 ),
inference(forward_demodulation,[],[f28158,f16700]) ).
fof(f28158,plain,
( ! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2245 ),
inference(avatar_component_clause,[],[f28157]) ).
fof(f28159,plain,
spl0_2245,
inference(avatar_split_clause,[],[f3148,f28157]) ).
fof(f3148,plain,
! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3147,f1021]) ).
fof(f3147,plain,
! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3146,f1019]) ).
fof(f3146,plain,
! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f315,f1021]) ).
fof(f315,axiom,
! [X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).
fof(f28132,plain,
( spl0_2244
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_1662
| ~ spl0_2243 ),
inference(avatar_split_clause,[],[f28128,f28123,f15617,f8336,f3460,f28130]) ).
fof(f28130,plain,
( spl0_2244
<=> ! [X39,X40] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2244])]) ).
fof(f8336,plain,
( spl0_1010
<=> ! [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_1010])]) ).
fof(f28123,plain,
( spl0_2243
<=> ! [X39,X40] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
fof(f28128,plain,
( ! [X40,X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_1662
| ~ spl0_2243 ),
inference(forward_demodulation,[],[f28127,f8622]) ).
fof(f8622,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1010 ),
inference(resolution,[],[f8337,f3462]) ).
fof(f8337,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_uminus(c_1,X5) )
| ~ spl0_1010 ),
inference(avatar_component_clause,[],[f8336]) ).
fof(f28127,plain,
( ! [X40,X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1662
| ~ spl0_2243 ),
inference(forward_demodulation,[],[f28126,f16696]) ).
fof(f28126,plain,
( ! [X40,X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X39,X40),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1662
| ~ spl0_2243 ),
inference(forward_demodulation,[],[f28124,f16696]) ).
fof(f28124,plain,
( ! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2243 ),
inference(avatar_component_clause,[],[f28123]) ).
fof(f28125,plain,
spl0_2243,
inference(avatar_split_clause,[],[f316,f28123]) ).
fof(f316,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).
fof(f28084,plain,
spl0_2242,
inference(avatar_split_clause,[],[f369,f28082]) ).
fof(f28082,plain,
( spl0_2242
<=> ! [X44,X4,X8,X6,X5,X45] :
( c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X5))
| ~ c_in(c_Pair(X4,X8,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_2242])]) ).
fof(f369,axiom,
! [X8,X44,X6,X45,X4,X5] :
( c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X5))
| ~ c_in(c_Pair(X4,X8,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_OCons__in__lex_4) ).
fof(f28059,plain,
( spl0_2241
| ~ spl0_58
| ~ spl0_1663
| ~ spl0_2240 ),
inference(avatar_split_clause,[],[f28055,f28052,f15622,f3460,f28057]) ).
fof(f28057,plain,
( spl0_2241
<=> ! [X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X39),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f28052,plain,
( spl0_2240
<=> ! [X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f28055,plain,
( ! [X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X39),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1663
| ~ spl0_2240 ),
inference(forward_demodulation,[],[f28053,f16700]) ).
fof(f28053,plain,
( ! [X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2240 ),
inference(avatar_component_clause,[],[f28052]) ).
fof(f28054,plain,
spl0_2240,
inference(avatar_split_clause,[],[f3142,f28052]) ).
fof(f3142,plain,
! [X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3141,f1021]) ).
fof(f3141,plain,
! [X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3140,f1019]) ).
fof(f3140,plain,
! [X39] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f324,f1021]) ).
fof(f324,axiom,
! [X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).
fof(f28050,plain,
spl0_2239,
inference(avatar_split_clause,[],[f1646,f28048]) ).
fof(f28048,plain,
( spl0_2239
<=> ! [X5,X44,X8,X6,X45] :
( ~ c_in(c_Pair(X44,c_List_Olist_OCons(X8,X45,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X6,X44,X8,X45,X5),X45,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_2239])]) ).
fof(f1646,axiom,
! [X8,X44,X6,X45,X5] :
( ~ c_in(c_Pair(X44,c_List_Olist_OCons(X8,X45,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X6,X44,X8,X45,X5),X45,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__Cons2_1) ).
fof(f28046,plain,
spl0_2238,
inference(avatar_split_clause,[],[f1643,f28044]) ).
fof(f28044,plain,
( spl0_2238
<=> ! [X5,X44,X8,X6,X45] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X8,X45,X5),X44,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(X45,c_Main_Olistrel__Cons1__2(X6,X44,X8,X45,X5),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_2238])]) ).
fof(f1643,axiom,
! [X8,X44,X6,X45,X5] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X8,X45,X5),X44,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(X45,c_Main_Olistrel__Cons1__2(X6,X44,X8,X45,X5),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__Cons1_1) ).
fof(f28036,plain,
( spl0_2237
| ~ spl0_1434
| ~ spl0_2049 ),
inference(avatar_split_clause,[],[f23521,f23359,f11635,f28034]) ).
fof(f28034,plain,
( spl0_2237
<=> ! [X0] :
( ~ c_lessequals(v_A,X0,tc_set(t_a))
| c_lessequals(v_S,X0,tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).
fof(f11635,plain,
( spl0_1434
<=> ! [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_1434])]) ).
fof(f23521,plain,
( ! [X0] :
( ~ c_lessequals(v_A,X0,tc_set(t_a))
| c_lessequals(v_S,X0,tc_set(t_a)) )
| ~ spl0_1434
| ~ spl0_2049 ),
inference(superposition,[],[f11636,f23361]) ).
fof(f11636,plain,
( ! [X83,X1,X35,X5] :
( ~ c_lessequals(c_union(X1,X35,X5),X83,tc_set(X5))
| c_lessequals(X1,X83,tc_set(X5)) )
| ~ spl0_1434 ),
inference(avatar_component_clause,[],[f11635]) ).
fof(f28026,plain,
( spl0_2236
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2232 ),
inference(avatar_split_clause,[],[f27928,f27925,f11575,f8937,f28024]) ).
fof(f28024,plain,
( spl0_2236
<=> ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2236])]) ).
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(f11575,plain,
( spl0_1419
<=> ! [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_1419])]) ).
fof(f27925,plain,
( spl0_2232
<=> ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2232])]) ).
fof(f27928,plain,
( ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2232 ),
inference(forward_demodulation,[],[f27926,f12564]) ).
fof(f12564,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1110
| ~ spl0_1419 ),
inference(superposition,[],[f8938,f11576]) ).
fof(f11576,plain,
( ! [X9,X5,X23] : c_Pair(c_Main_Osurj__pair__1(X9,X5,X23),c_Main_Osurj__pair__2(X9,X5,X23),X5,X23) = X9
| ~ spl0_1419 ),
inference(avatar_component_clause,[],[f11575]) ).
fof(f8938,plain,
( ! [X2,X8,X5,X23] : c_snd(c_Pair(X2,X8,X23,X5),X23,X5) = X8
| ~ spl0_1110 ),
inference(avatar_component_clause,[],[f8937]) ).
fof(f27926,plain,
( ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2232 ),
inference(avatar_component_clause,[],[f27925]) ).
fof(f28022,plain,
( spl0_2235
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2231 ),
inference(avatar_split_clause,[],[f27923,f27920,f11575,f8933,f28020]) ).
fof(f28020,plain,
( spl0_2235
<=> ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2235])]) ).
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(f27920,plain,
( spl0_2231
<=> ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2231])]) ).
fof(f27923,plain,
( ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2231 ),
inference(forward_demodulation,[],[f27921,f12565]) ).
fof(f12565,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1109
| ~ spl0_1419 ),
inference(superposition,[],[f8934,f11576]) ).
fof(f8934,plain,
( ! [X8,X7,X5,X23] : c_fst(c_Pair(X8,X7,X5,X23),X5,X23) = X8
| ~ spl0_1109 ),
inference(avatar_component_clause,[],[f8933]) ).
fof(f27921,plain,
( ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2231 ),
inference(avatar_component_clause,[],[f27920]) ).
fof(f28018,plain,
( spl0_2234
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2230 ),
inference(avatar_split_clause,[],[f27918,f27915,f11575,f8937,f28016]) ).
fof(f28016,plain,
( spl0_2234
<=> ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).
fof(f27915,plain,
( spl0_2230
<=> ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2230])]) ).
fof(f27918,plain,
( ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2230 ),
inference(forward_demodulation,[],[f27916,f12564]) ).
fof(f27916,plain,
( ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2230 ),
inference(avatar_component_clause,[],[f27915]) ).
fof(f28014,plain,
( spl0_2233
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2229 ),
inference(avatar_split_clause,[],[f27913,f27910,f11575,f8933,f28012]) ).
fof(f28012,plain,
( spl0_2233
<=> ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2233])]) ).
fof(f27910,plain,
( spl0_2229
<=> ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2229])]) ).
fof(f27913,plain,
( ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2229 ),
inference(forward_demodulation,[],[f27911,f12565]) ).
fof(f27911,plain,
( ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2229 ),
inference(avatar_component_clause,[],[f27910]) ).
fof(f27927,plain,
spl0_2232,
inference(avatar_split_clause,[],[f3139,f27925]) ).
fof(f3139,plain,
! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f311,f321]) ).
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(f311,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__number__of_0) ).
fof(f27922,plain,
spl0_2231,
inference(avatar_split_clause,[],[f3138,f27920]) ).
fof(f3138,plain,
! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f301,f321]) ).
fof(f301,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__number__of_0) ).
fof(f27917,plain,
spl0_2230,
inference(avatar_split_clause,[],[f3137,f27915]) ).
fof(f3137,plain,
! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f308,f321]) ).
fof(f308,axiom,
! [X40,X39] :
( ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__neg__number__of_0) ).
fof(f27912,plain,
spl0_2229,
inference(avatar_split_clause,[],[f3136,f27910]) ).
fof(f3136,plain,
! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f298,f321]) ).
fof(f298,axiom,
! [X40,X39] :
( ~ c_lessequals(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__neg__number__of_0) ).
fof(f27908,plain,
spl0_2228,
inference(avatar_split_clause,[],[f487,f27906]) ).
fof(f27906,plain,
( spl0_2228
<=> ! [X5,X4,X58,X6,X8] :
( ~ c_in(c_Pair(X58,X8,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X4,X58,X5),c_List_Olist_OCons(X4,X8,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_2228])]) ).
fof(f487,axiom,
! [X58,X8,X6,X4,X5] :
( ~ c_in(c_Pair(X58,X8,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X4,X58,X5),c_List_Olist_OCons(X4,X8,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__cons__cons_3) ).
fof(f27904,plain,
spl0_2227,
inference(avatar_split_clause,[],[f370,f27902]) ).
fof(f27902,plain,
( spl0_2227
<=> ! [X5,X44,X4,X6,X45] :
( ~ c_in(c_Pair(X44,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X4,X45,X5),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_2227])]) ).
fof(f370,axiom,
! [X44,X6,X45,X4,X5] :
( ~ c_in(c_Pair(X44,X45,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X6,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X4,X45,X5),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_OCons__in__lex_5) ).
fof(f27900,plain,
spl0_2226,
inference(avatar_split_clause,[],[f53,f27898]) ).
fof(f27898,plain,
( spl0_2226
<=> ! [X5,X23,X6,X26] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Relation_ODomain(X26,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2226])]) ).
fof(f53,axiom,
! [X6,X26,X5,X23] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Relation_ODomain(X26,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).
fof(f27896,plain,
spl0_2225,
inference(avatar_split_clause,[],[f52,f27894]) ).
fof(f27894,plain,
( spl0_2225
<=> ! [X5,X23,X6,X26] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Relation_ODomain(X26,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).
fof(f52,axiom,
! [X6,X26,X5,X23] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X6,X26,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),c_Relation_ODomain(X26,tc_set(tc_Datatype__Universe_Onode(X5,X23)),tc_set(tc_Datatype__Universe_Onode(X5,X23))),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
fof(f27889,plain,
spl0_2224,
inference(avatar_split_clause,[],[f3,f27887]) ).
fof(f27887,plain,
( spl0_2224
<=> ! [X0,X3,X2,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X2,v_sko__4mj(X0,X2,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X2,v_sko__4mj(X0,X2,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2) ).
fof(f27885,plain,
spl0_2223,
inference(avatar_split_clause,[],[f2,f27883]) ).
fof(f27883,plain,
( spl0_2223
<=> ! [X0,X3,X2,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X3,X0,v_r),X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2223])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X3,X0,v_r),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_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).
fof(f27858,plain,
( spl0_2222
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_2220 ),
inference(avatar_split_clause,[],[f27850,f27847,f8336,f3460,f27856]) ).
fof(f27856,plain,
( spl0_2222
<=> ! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2222])]) ).
fof(f27847,plain,
( spl0_2220
<=> ! [X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2220])]) ).
fof(f27850,plain,
( ! [X39] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_2220 ),
inference(forward_demodulation,[],[f27848,f8622]) ).
fof(f27848,plain,
( ! [X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2220 ),
inference(avatar_component_clause,[],[f27847]) ).
fof(f27854,plain,
spl0_2221,
inference(avatar_split_clause,[],[f570,f27852]) ).
fof(f27852,plain,
( spl0_2221
<=> ! [X5,X44,X23,X29,X45] :
( ~ c_less(X29,c_Nat_Osize(X45,tc_List_Olist(X23)),tc_nat)
| ~ c_less(X29,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Ozip(X44,X45,X5,X23),X29,tc_prod(X5,X23)) = c_Pair(c_List_Onth(X44,X29,X5),c_List_Onth(X45,X29,X23),X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2221])]) ).
fof(f570,axiom,
! [X29,X44,X45,X5,X23] :
( ~ c_less(X29,c_Nat_Osize(X45,tc_List_Olist(X23)),tc_nat)
| ~ c_less(X29,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Ozip(X44,X45,X5,X23),X29,tc_prod(X5,X23)) = c_Pair(c_List_Onth(X44,X29,X5),c_List_Onth(X45,X29,X23),X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
fof(f27849,plain,
spl0_2220,
inference(avatar_split_clause,[],[f314,f27847]) ).
fof(f314,axiom,
! [X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).
fof(f27705,plain,
spl0_2219,
inference(avatar_split_clause,[],[f1677,f27703]) ).
fof(f27703,plain,
( spl0_2219
<=> ! [X5,X31,X2,X23,X6,X87,X26,X7] :
( ~ c_in(c_Pair(X7,X31,X23,X87),X6,tc_prod(X23,X87))
| ~ c_in(c_Pair(X2,X7,X5,X23),X26,tc_prod(X5,X23))
| c_in(c_Pair(X2,X31,X5,X87),c_Relation_Orel__comp(X6,X26,X23,X87,X5),tc_prod(X5,X87)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).
fof(f1677,axiom,
! [X31,X2,X6,X26,X7,X87,X5,X23] :
( ~ c_in(c_Pair(X7,X31,X23,X87),X6,tc_prod(X23,X87))
| ~ c_in(c_Pair(X2,X7,X5,X23),X26,tc_prod(X5,X23))
| c_in(c_Pair(X2,X31,X5,X87),c_Relation_Orel__comp(X6,X26,X23,X87,X5),tc_prod(X5,X87)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
fof(f27701,plain,
spl0_2218,
inference(avatar_split_clause,[],[f1645,f27699]) ).
fof(f27699,plain,
( spl0_2218
<=> ! [X44,X8,X6,X5,X45] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X6,X44,X8,X45,X5),c_Main_Olistrel__Cons2__2(X6,X44,X8,X45,X5),X5) = X44
| ~ c_in(c_Pair(X44,c_List_Olist_OCons(X8,X45,X5),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_2218])]) ).
fof(f1645,axiom,
! [X8,X6,X44,X45,X5] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X6,X44,X8,X45,X5),c_Main_Olistrel__Cons2__2(X6,X44,X8,X45,X5),X5) = X44
| ~ c_in(c_Pair(X44,c_List_Olist_OCons(X8,X45,X5),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__Cons2_0) ).
fof(f27697,plain,
spl0_2217,
inference(avatar_split_clause,[],[f1642,f27695]) ).
fof(f27695,plain,
( spl0_2217
<=> ! [X44,X8,X6,X5,X45] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X6,X44,X8,X45,X5),c_Main_Olistrel__Cons1__2(X6,X44,X8,X45,X5),X5) = X44
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X45,X5),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_2217])]) ).
fof(f1642,axiom,
! [X8,X6,X44,X45,X5] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X6,X44,X8,X45,X5),c_Main_Olistrel__Cons1__2(X6,X44,X8,X45,X5),X5) = X44
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X45,X5),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__Cons1_0) ).
fof(f27693,plain,
spl0_2216,
inference(avatar_split_clause,[],[f484,f27691]) ).
fof(f27691,plain,
( spl0_2216
<=> ! [X5,X4,X7,X8,X6,X2] :
( X2 = X7
| c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X7,X8,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_2216])]) ).
fof(f484,axiom,
! [X2,X8,X6,X7,X4,X5] :
( X2 = X7
| c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X7,X8,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__cons__cons_0) ).
fof(f27689,plain,
spl0_2215,
inference(avatar_split_clause,[],[f365,f27687]) ).
fof(f27687,plain,
( spl0_2215
<=> ! [X5,X44,X4,X45,X6,X8] :
( X4 = X8
| c_in(c_Pair(X4,X8,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_2215])]) ).
fof(f365,axiom,
! [X8,X6,X44,X45,X4,X5] :
( X4 = X8
| c_in(c_Pair(X4,X8,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_OCons__in__lex_0) ).
fof(f27685,plain,
spl0_2214,
inference(avatar_split_clause,[],[f248,f27683]) ).
fof(f27683,plain,
( spl0_2214
<=> ! [X41,X4,X40,X8] :
( c_plus(X4,X40,tc_nat) != c_plus(X41,X8,tc_nat)
| c_in(c_Pair(c_Pair(X4,X8,tc_nat,tc_nat),c_Pair(X41,X40,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f248,axiom,
! [X40,X41,X8,X4] :
( c_plus(X4,X40,tc_nat) != c_plus(X41,X8,tc_nat)
| c_in(c_Pair(c_Pair(X4,X8,tc_nat,tc_nat),c_Pair(X41,X40,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
fof(f27679,plain,
spl0_2213,
inference(avatar_split_clause,[],[f247,f27677]) ).
fof(f27677,plain,
( spl0_2213
<=> ! [X41,X4,X40,X8] :
( c_plus(X4,X40,tc_nat) = c_plus(X41,X8,tc_nat)
| ~ c_in(c_Pair(c_Pair(X4,X8,tc_nat,tc_nat),c_Pair(X41,X40,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f247,axiom,
! [X40,X41,X8,X4] :
( c_plus(X4,X40,tc_nat) = c_plus(X41,X8,tc_nat)
| ~ c_in(c_Pair(c_Pair(X4,X8,tc_nat,tc_nat),c_Pair(X41,X40,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
fof(f27625,plain,
( spl0_2212
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2205 ),
inference(avatar_split_clause,[],[f27597,f27594,f11575,f8937,f27623]) ).
fof(f27623,plain,
( spl0_2212
<=> ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).
fof(f27594,plain,
( spl0_2205
<=> ! [X40,X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f27597,plain,
( ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2205 ),
inference(forward_demodulation,[],[f27595,f12564]) ).
fof(f27595,plain,
( ! [X40,X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2205 ),
inference(avatar_component_clause,[],[f27594]) ).
fof(f27621,plain,
( spl0_2211
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2204 ),
inference(avatar_split_clause,[],[f27592,f27589,f11575,f8937,f27619]) ).
fof(f27619,plain,
( spl0_2211
<=> ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).
fof(f27589,plain,
( spl0_2204
<=> ! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f27592,plain,
( ! [X40,X39] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2204 ),
inference(forward_demodulation,[],[f27590,f12564]) ).
fof(f27590,plain,
( ! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2204 ),
inference(avatar_component_clause,[],[f27589]) ).
fof(f27617,plain,
( spl0_2210
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2203 ),
inference(avatar_split_clause,[],[f27587,f27584,f11575,f8933,f27615]) ).
fof(f27615,plain,
( spl0_2210
<=> ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).
fof(f27584,plain,
( spl0_2203
<=> ! [X40,X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).
fof(f27587,plain,
( ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2203 ),
inference(forward_demodulation,[],[f27585,f12565]) ).
fof(f27585,plain,
( ! [X40,X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2203 ),
inference(avatar_component_clause,[],[f27584]) ).
fof(f27613,plain,
( spl0_2209
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2202 ),
inference(avatar_split_clause,[],[f27582,f27579,f11575,f8933,f27611]) ).
fof(f27611,plain,
( spl0_2209
<=> ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).
fof(f27579,plain,
( spl0_2202
<=> ! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).
fof(f27582,plain,
( ! [X40,X39] :
( c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2202 ),
inference(forward_demodulation,[],[f27580,f12565]) ).
fof(f27580,plain,
( ! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2202 ),
inference(avatar_component_clause,[],[f27579]) ).
fof(f27609,plain,
spl0_2208,
inference(avatar_split_clause,[],[f1647,f27607]) ).
fof(f27607,plain,
( spl0_2208
<=> ! [X5,X44,X8,X6,X45] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X6,X44,X8,X45,X5),X8,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(X44,c_List_Olist_OCons(X8,X45,X5),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_2208])]) ).
fof(f1647,axiom,
! [X8,X6,X44,X45,X5] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X6,X44,X8,X45,X5),X8,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(X44,c_List_Olist_OCons(X8,X45,X5),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__Cons2_2) ).
fof(f27605,plain,
spl0_2207,
inference(avatar_split_clause,[],[f1644,f27603]) ).
fof(f27603,plain,
( spl0_2207
<=> ! [X5,X44,X8,X6,X45] :
( c_in(c_Pair(X8,c_Main_Olistrel__Cons1__1(X6,X44,X8,X45,X5),X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X45,X5),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_2207])]) ).
fof(f1644,axiom,
! [X8,X6,X44,X45,X5] :
( c_in(c_Pair(X8,c_Main_Olistrel__Cons1__1(X6,X44,X8,X45,X5),X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X45,X5),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__Cons1_2) ).
fof(f27601,plain,
spl0_2206,
inference(avatar_split_clause,[],[f367,f27599]) ).
fof(f27599,plain,
( spl0_2206
<=> ! [X44,X4,X8,X6,X5,X45] :
( X4 = X8
| c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(X45,tc_List_Olist(X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_2206])]) ).
fof(f367,axiom,
! [X8,X44,X6,X45,X4,X5] :
( X4 = X8
| c_Nat_Osize(X44,tc_List_Olist(X5)) = c_Nat_Osize(X45,tc_List_Olist(X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X5),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_OCons__in__lex_2) ).
fof(f27596,plain,
spl0_2205,
inference(avatar_split_clause,[],[f313,f27594]) ).
fof(f313,axiom,
! [X40,X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__number__of_0) ).
fof(f27591,plain,
spl0_2204,
inference(avatar_split_clause,[],[f309,f27589]) ).
fof(f309,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__pos__number__of_0) ).
fof(f27586,plain,
spl0_2203,
inference(avatar_split_clause,[],[f303,f27584]) ).
fof(f303,axiom,
! [X40,X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__number__of_0) ).
fof(f27581,plain,
spl0_2202,
inference(avatar_split_clause,[],[f299,f27579]) ).
fof(f299,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__pos__number__of_0) ).
fof(f27527,plain,
( spl0_2201
| ~ spl0_3
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f24931,f24122,f3185,f27524]) ).
fof(f27524,plain,
( spl0_2201
<=> c_in(v_b,v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f3185,plain,
( spl0_3
<=> c_in(v_b,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f24122,plain,
( spl0_2067
<=> v_A = v_S ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
fof(f24931,plain,
( c_in(v_b,v_S,t_a)
| ~ spl0_3
| ~ spl0_2067 ),
inference(superposition,[],[f3187,f24124]) ).
fof(f24124,plain,
( v_A = v_S
| ~ spl0_2067 ),
inference(avatar_component_clause,[],[f24122]) ).
fof(f3187,plain,
( c_in(v_b,v_A,t_a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f3185]) ).
fof(f27437,plain,
spl0_2200,
inference(avatar_split_clause,[],[f1675,f27435]) ).
fof(f27435,plain,
( spl0_2200
<=> ! [X6,X23,X5,X87,X26,X86] :
( ~ c_in(X86,c_Relation_Orel__comp(X6,X26,X87,X23,X5),tc_prod(X5,X23))
| c_in(c_Pair(c_Main_Orel__compE__1(X6,X26,X86,X87,X23,X5),c_Main_Orel__compE__2(X6,X26,X86,X87,X23,X5),X5,X87),X26,tc_prod(X5,X87)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).
fof(f1675,axiom,
! [X6,X86,X26,X87,X5,X23] :
( ~ c_in(X86,c_Relation_Orel__comp(X6,X26,X87,X23,X5),tc_prod(X5,X23))
| c_in(c_Pair(c_Main_Orel__compE__1(X6,X26,X86,X87,X23,X5),c_Main_Orel__compE__2(X6,X26,X86,X87,X23,X5),X5,X87),X26,tc_prod(X5,X87)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
fof(f27433,plain,
spl0_2199,
inference(avatar_split_clause,[],[f1674,f27431]) ).
fof(f27431,plain,
( spl0_2199
<=> ! [X6,X23,X5,X87,X26,X86] :
( ~ c_in(X86,c_Relation_Orel__comp(X6,X26,X87,X23,X5),tc_prod(X5,X23))
| c_in(c_Pair(c_Main_Orel__compE__2(X6,X26,X86,X87,X23,X5),c_Main_Orel__compE__3(X6,X26,X86,X87,X23,X5),X87,X23),X6,tc_prod(X87,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).
fof(f1674,axiom,
! [X6,X86,X26,X87,X5,X23] :
( ~ c_in(X86,c_Relation_Orel__comp(X6,X26,X87,X23,X5),tc_prod(X5,X23))
| c_in(c_Pair(c_Main_Orel__compE__2(X6,X26,X86,X87,X23,X5),c_Main_Orel__compE__3(X6,X26,X86,X87,X23,X5),X87,X23),X6,tc_prod(X87,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
fof(f27429,plain,
spl0_2198,
inference(avatar_split_clause,[],[f1612,f27427]) ).
fof(f27427,plain,
( spl0_2198
<=> ! [X35,X41,X23,X5,X1] :
( ~ c_in(X41,c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__2(X35,X41,X5,X23),X35,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__1(X1,X41,X5,X23),X1,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
fof(f1612,axiom,
! [X41,X1,X35,X5,X23] :
( ~ c_in(X41,c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__2(X35,X41,X5,X23),X35,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__1(X1,X41,X5,X23),X1,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
fof(f27425,plain,
spl0_2197,
inference(avatar_split_clause,[],[f335,f27423]) ).
fof(f27423,plain,
( spl0_2197
<=> ! [X39,X40,X7] :
( c_Numeral_Obit_OB0 = X7
| c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X40,X7),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
fof(f335,axiom,
! [X40,X39,X7] :
( c_Numeral_Obit_OB0 = X7
| c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X40,X7),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X39,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
fof(f27212,plain,
spl0_2196,
inference(avatar_split_clause,[],[f3045,f27210]) ).
fof(f27210,plain,
( spl0_2196
<=> ! [X40,X30] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).
fof(f3045,plain,
! [X40,X30] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3044,f1021]) ).
fof(f3044,plain,
! [X40,X30] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3043,f2811]) ).
fof(f2811,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(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(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(f3043,plain,
! [X40,X30] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2861,f3010]) ).
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,[],[f2830,f1021]) ).
fof(f2830,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(f2861,plain,
! [X40,X30] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(definition_unfolding,[],[f745,f1409,f1409,f1409]) ).
fof(f745,axiom,
! [X40,X30] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X30))),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f27192,plain,
( spl0_2195
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2194 ),
inference(avatar_split_clause,[],[f27188,f27184,f18906,f10450,f10135,f6752,f3744,f27190]) ).
fof(f27190,plain,
( spl0_2195
<=> ! [X40,X30] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X30,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).
fof(f3744,plain,
( spl0_116
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f6752,plain,
( spl0_674
<=> ! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f10135,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(f10450,plain,
( spl0_1344
<=> ! [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_1344])]) ).
fof(f18906,plain,
( spl0_1852
<=> ! [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_1852])]) ).
fof(f27184,plain,
( spl0_2194
<=> ! [X40,X30] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).
fof(f27188,plain,
( ! [X40,X30] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X30,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2194 ),
inference(forward_demodulation,[],[f27187,f18907]) ).
fof(f18907,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_1852 ),
inference(avatar_component_clause,[],[f18906]) ).
fof(f27187,plain,
( ! [X40,X30] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2194 ),
inference(forward_demodulation,[],[f27185,f11244]) ).
fof(f11244,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344 ),
inference(forward_demodulation,[],[f11243,f6753]) ).
fof(f6753,plain,
( ! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f6752]) ).
fof(f11243,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344 ),
inference(forward_demodulation,[],[f11205,f10708]) ).
fof(f10708,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_116
| ~ spl0_1267 ),
inference(superposition,[],[f10136,f3746]) ).
fof(f3746,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f3744]) ).
fof(f10136,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,[],[f10135]) ).
fof(f11205,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_674
| ~ spl0_1344 ),
inference(superposition,[],[f6753,f10451]) ).
fof(f10451,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_1344 ),
inference(avatar_component_clause,[],[f10450]) ).
fof(f27185,plain,
( ! [X40,X30] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat)
| ~ spl0_2194 ),
inference(avatar_component_clause,[],[f27184]) ).
fof(f27186,plain,
spl0_2194,
inference(avatar_split_clause,[],[f3042,f27184]) ).
fof(f3042,plain,
! [X40,X30] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3041,f1021]) ).
fof(f3041,plain,
! [X40,X30] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3040,f2811]) ).
fof(f3040,plain,
! [X40,X30] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2860,f3010]) ).
fof(f2860,plain,
! [X40,X30] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
inference(definition_unfolding,[],[f744,f1409,f1409,f1409]) ).
fof(f744,axiom,
! [X40,X30] : c_div(c_Suc(c_Suc(c_Suc(X30))),c_Numeral_Onumber__of(X40,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X30,tc_nat),c_Numeral_Onumber__of(X40,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f27182,plain,
spl0_2193,
inference(avatar_split_clause,[],[f2938,f27180]) ).
fof(f27180,plain,
( spl0_2193
<=> ! [X5,X4,X6,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)
| c_in(c_Pair(X4,X8,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_2193])]) ).
fof(f2938,plain,
! [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)
| c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1589,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(f1589,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)
| c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Ortrancl(X6,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f27178,plain,
( spl0_2192
| ~ spl0_1355
| ~ spl0_1303
| ~ spl0_2096 ),
inference(avatar_split_clause,[],[f25449,f24767,f10285,f10968,f27175]) ).
fof(f27175,plain,
( spl0_2192
<=> c_emptyset = c_SetInterval_OatLeastAtMost(v_A,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).
fof(f10968,plain,
( spl0_1355
<=> class_Orderings_Oorder(tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f10285,plain,
( spl0_1303
<=> ! [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_1303])]) ).
fof(f24767,plain,
( spl0_2096
<=> c_less(v_S,v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).
fof(f25449,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| c_emptyset = c_SetInterval_OatLeastAtMost(v_A,v_S,tc_set(t_a))
| ~ spl0_1303
| ~ spl0_2096 ),
inference(resolution,[],[f24769,f10286]) ).
fof(f10286,plain,
( ! [X19,X5,X30] :
( ~ c_less(X19,X30,X5)
| ~ class_Orderings_Oorder(X5)
| c_emptyset = c_SetInterval_OatLeastAtMost(X30,X19,X5) )
| ~ spl0_1303 ),
inference(avatar_component_clause,[],[f10285]) ).
fof(f24769,plain,
( c_less(v_S,v_A,tc_set(t_a))
| ~ spl0_2096 ),
inference(avatar_component_clause,[],[f24767]) ).
fof(f27173,plain,
spl0_2191,
inference(avatar_split_clause,[],[f2937,f27171]) ).
fof(f27171,plain,
( spl0_2191
<=> ! [X5,X4,X6,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)
| c_in(c_Pair(X4,X8,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_2191])]) ).
fof(f2937,plain,
! [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)
| c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1586,f1581]) ).
fof(f1586,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)
| c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Ortrancl(X6,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f27169,plain,
spl0_2190,
inference(avatar_split_clause,[],[f1611,f27167]) ).
fof(f27167,plain,
( spl0_2190
<=> ! [X41,X23,X5,X35,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X35,X41,X5,X23),X5,X23) = X41
| ~ c_in(X41,c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__1(X1,X41,X5,X23),X1,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f1611,axiom,
! [X41,X1,X35,X5,X23] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X35,X41,X5,X23),X5,X23) = X41
| ~ c_in(X41,c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__1(X1,X41,X5,X23),X1,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f27165,plain,
spl0_2189,
inference(avatar_split_clause,[],[f1610,f27163]) ).
fof(f27163,plain,
( spl0_2189
<=> ! [X41,X23,X5,X35,X1] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X1,X41,X5,X23),X5,X23) = X41
| ~ c_in(X41,c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__2(X35,X41,X5,X23),X35,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f1610,axiom,
! [X41,X1,X5,X35,X23] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X1,X41,X5,X23),X5,X23) = X41
| ~ c_in(X41,c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OusumE__2(X35,X41,X5,X23),X35,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f27161,plain,
spl0_2188,
inference(avatar_split_clause,[],[f486,f27159]) ).
fof(f27159,plain,
( spl0_2188
<=> ! [X5,X4,X7,X8,X6,X2] :
( ~ c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X7,X8,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_2188])]) ).
fof(f486,axiom,
! [X2,X8,X6,X7,X4,X5] :
( ~ c_in(c_Pair(X2,X7,X5,X5),X6,tc_prod(X5,X5))
| c_in(c_Pair(c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X7,X8,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__cons__cons_2) ).
fof(f27157,plain,
spl0_2187,
inference(avatar_split_clause,[],[f325,f27155]) ).
fof(f27155,plain,
( spl0_2187
<=> ! [X39,X40] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).
fof(f325,axiom,
! [X40,X39] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f27153,plain,
spl0_2186,
inference(avatar_split_clause,[],[f11,f27151]) ).
fof(f27151,plain,
( spl0_2186
<=> ! [X9,X0,X3] :
( ~ c_in(X9,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X3,t_a)
| c_in(c_Pair(X3,X9,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,X9),X9,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).
fof(f11,axiom,
! [X3,X0,X9] :
( ~ c_in(X9,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X3,t_a)
| c_in(c_Pair(X3,X9,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,X9),X9,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_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1) ).
fof(f27149,plain,
spl0_2185,
inference(avatar_split_clause,[],[f1,f27147]) ).
fof(f27147,plain,
( spl0_2185
<=> ! [X0,X3,X2,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_emptyset = X0
| ~ c_lessequals(X0,X1,tc_set(t_a))
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(c_Pair(X2,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_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).
fof(f27077,plain,
spl0_2184,
inference(avatar_split_clause,[],[f2909,f27075]) ).
fof(f27075,plain,
( spl0_2184
<=> ! [X44,X4,X40,X5] :
( c_0 = c_Numeral_Onumber__of(X40,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X4,X44,X5),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),X5) = c_List_Olist_OCons(X4,c_List_Osublist(X44,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X40,tc_nat),c_1,tc_nat),tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f2909,plain,
! [X40,X44,X4,X5] :
( c_0 = c_Numeral_Onumber__of(X40,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X4,X44,X5),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X40,tc_nat),tc_nat),X5) = c_List_Olist_OCons(X4,c_List_Osublist(X44,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X40,tc_nat),c_1,tc_nat),tc_nat),X5),X5) ),
inference(definition_unfolding,[],[f633,f631,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(f633,axiom,
! [X40,X44,X4,X5] :
( c_0 = c_Numeral_Onumber__of(X40,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X40,tc_nat),c_List_Olist_OCons(X4,X44,X5),X5) = c_List_Olist_OCons(X4,c_List_Otake(c_minus(c_Numeral_Onumber__of(X40,tc_nat),c_1,tc_nat),X44,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).
fof(f27062,plain,
spl0_2183,
inference(avatar_split_clause,[],[f1609,f27060]) ).
fof(f27060,plain,
( spl0_2183
<=> ! [X41,X23,X5,X35,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X35,X41,X5,X23),X5,X23) = X41
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X1,X41,X5,X23),X5,X23) = X41
| ~ c_in(X41,c_Datatype__Universe_Ousum(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f1609,axiom,
! [X41,X1,X35,X5,X23] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X35,X41,X5,X23),X5,X23) = X41
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X1,X41,X5,X23),X5,X23) = X41
| ~ c_in(X41,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_OusumE_0) ).
fof(f26777,plain,
spl0_2182,
inference(avatar_split_clause,[],[f2857,f26775]) ).
fof(f26775,plain,
( spl0_2182
<=> ! [X44,X19,X5,X45] : c_List_Osublist(c_append(X44,X45,X5),c_SetInterval_OlessThan(X19,tc_nat),X5) = c_append(c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),c_List_Osublist(X45,c_SetInterval_OlessThan(c_minus(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat),tc_nat),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f2857,plain,
! [X44,X19,X45,X5] : c_List_Osublist(c_append(X44,X45,X5),c_SetInterval_OlessThan(X19,tc_nat),X5) = c_append(c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),c_List_Osublist(X45,c_SetInterval_OlessThan(c_minus(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat),tc_nat),X5),X5),
inference(definition_unfolding,[],[f636,f631,f631,f631]) ).
fof(f636,axiom,
! [X19,X44,X45,X5] : c_List_Otake(X19,c_append(X44,X45,X5),X5) = c_append(c_List_Otake(X19,X44,X5),c_List_Otake(c_minus(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat),X45,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).
fof(f26773,plain,
spl0_2181,
inference(avatar_split_clause,[],[f1707,f26771]) ).
fof(f26771,plain,
( spl0_2181
<=> ! [X35,X41,X23,X5,X1] :
( ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X35,X41,X23,X5),X23,X5) = X41
| c_Sum__Type_OInl(c_Main_OPlusE__1(X1,X41,X5,X23),X5,X23) = X41 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f1707,axiom,
! [X41,X1,X35,X5,X23] :
( ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X35,X41,X23,X5),X23,X5) = X41
| c_Sum__Type_OInl(c_Main_OPlusE__1(X1,X41,X5,X23),X5,X23) = X41 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f26769,plain,
( spl0_2180
| ~ spl0_1355
| ~ spl0_1304
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f22887,f22701,f10289,f10968,f26766]) ).
fof(f26766,plain,
( spl0_2180
<=> c_emptyset = c_SetInterval_OatLeastLessThan(v_A,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f10289,plain,
( spl0_1304
<=> ! [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_1304])]) ).
fof(f22701,plain,
( spl0_2034
<=> c_lessequals(v_S,v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f22887,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| c_emptyset = c_SetInterval_OatLeastLessThan(v_A,v_S,tc_set(t_a))
| ~ spl0_1304
| ~ spl0_2034 ),
inference(resolution,[],[f22703,f10290]) ).
fof(f10290,plain,
( ! [X19,X5,X30] :
( ~ c_lessequals(X19,X30,X5)
| ~ class_Orderings_Oorder(X5)
| c_emptyset = c_SetInterval_OatLeastLessThan(X30,X19,X5) )
| ~ spl0_1304 ),
inference(avatar_component_clause,[],[f10289]) ).
fof(f22703,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
| ~ spl0_2034 ),
inference(avatar_component_clause,[],[f22701]) ).
fof(f26764,plain,
spl0_2179,
inference(avatar_split_clause,[],[f1676,f26762]) ).
fof(f26762,plain,
( spl0_2179
<=> ! [X6,X23,X5,X87,X26,X86] :
( ~ c_in(X86,c_Relation_Orel__comp(X6,X26,X87,X23,X5),tc_prod(X5,X23))
| c_Pair(c_Main_Orel__compE__1(X6,X26,X86,X87,X23,X5),c_Main_Orel__compE__3(X6,X26,X86,X87,X23,X5),X5,X23) = X86 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f1676,axiom,
! [X6,X86,X26,X87,X5,X23] :
( ~ c_in(X86,c_Relation_Orel__comp(X6,X26,X87,X23,X5),tc_prod(X5,X23))
| c_Pair(c_Main_Orel__compE__1(X6,X26,X86,X87,X23,X5),c_Main_Orel__compE__3(X6,X26,X86,X87,X23,X5),X5,X23) = X86 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f26760,plain,
spl0_2178,
inference(avatar_split_clause,[],[f863,f26758]) ).
fof(f26758,plain,
( spl0_2178
<=> ! [X2,X40,X23,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).
fof(f863,axiom,
! [X40,X2,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f26756,plain,
spl0_2177,
inference(avatar_split_clause,[],[f857,f26754]) ).
fof(f26754,plain,
( spl0_2177
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f857,axiom,
! [X40,X2,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f26752,plain,
spl0_2176,
inference(avatar_split_clause,[],[f851,f26750]) ).
fof(f26750,plain,
( spl0_2176
<=> ! [X2,X40,X23,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f851,axiom,
! [X40,X2,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f26748,plain,
spl0_2175,
inference(avatar_split_clause,[],[f845,f26746]) ).
fof(f26746,plain,
( spl0_2175
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f845,axiom,
! [X40,X2,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f26666,plain,
( spl0_2174
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_2173 ),
inference(avatar_split_clause,[],[f26662,f26659,f18906,f7218,f7182,f26664]) ).
fof(f26664,plain,
( spl0_2174
<=> ! [X2,X5,X19] :
( c_Nat_Opower(c_uminus(X2,X5),c_times(c_plus(c_1,c_1,tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_plus(c_1,c_1,tc_nat),X19,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f7182,plain,
( spl0_772
<=> ! [X8] : c_plus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f7218,plain,
( spl0_781
<=> ! [X8] : c_plus(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f26659,plain,
( spl0_2173
<=> ! [X2,X5,X19] :
( c_Nat_Opower(c_uminus(X2,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X19,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).
fof(f26662,plain,
( ! [X2,X19,X5] :
( c_Nat_Opower(c_uminus(X2,X5),c_times(c_plus(c_1,c_1,tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_plus(c_1,c_1,tc_nat),X19,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) )
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_2173 ),
inference(forward_demodulation,[],[f26660,f18994]) ).
fof(f18994,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_772
| ~ spl0_781
| ~ spl0_1852 ),
inference(forward_demodulation,[],[f18915,f7183]) ).
fof(f7183,plain,
( ! [X8] : c_plus(X8,c_0,tc_nat) = X8
| ~ spl0_772 ),
inference(avatar_component_clause,[],[f7182]) ).
fof(f18915,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_781
| ~ spl0_1852 ),
inference(superposition,[],[f18907,f7219]) ).
fof(f7219,plain,
( ! [X8] : c_plus(c_0,X8,tc_nat) = X8
| ~ spl0_781 ),
inference(avatar_component_clause,[],[f7218]) ).
fof(f26660,plain,
( ! [X2,X19,X5] :
( c_Nat_Opower(c_uminus(X2,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X19,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) )
| ~ spl0_2173 ),
inference(avatar_component_clause,[],[f26659]) ).
fof(f26661,plain,
spl0_2173,
inference(avatar_split_clause,[],[f3133,f26659]) ).
fof(f3133,plain,
! [X2,X19,X5] :
( c_Nat_Opower(c_uminus(X2,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X19,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(forward_demodulation,[],[f3132,f1021]) ).
fof(f3132,plain,
! [X2,X19,X5] :
( c_Nat_Opower(c_uminus(X2,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X19,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(forward_demodulation,[],[f3131,f1019]) ).
fof(f3131,plain,
! [X2,X19,X5] :
( c_Nat_Opower(c_uminus(X2,X5),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X19,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(forward_demodulation,[],[f740,f1021]) ).
fof(f740,axiom,
! [X2,X19,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Nat_Opower(c_uminus(X2,X5),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X19,tc_nat),X5) = c_Nat_Opower(X2,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X19,tc_nat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).
fof(f26657,plain,
spl0_2172,
inference(avatar_split_clause,[],[f2925,f26655]) ).
fof(f26655,plain,
( spl0_2172
<=> ! [X5,X4,X6,X8] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X4,X8,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_2172])]) ).
fof(f2925,plain,
! [X8,X6,X4,X5] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1588,f1581]) ).
fof(f1588,axiom,
! [X8,X6,X4,X5] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Ortrancl(X6,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f26653,plain,
spl0_2171,
inference(avatar_split_clause,[],[f2924,f26651]) ).
fof(f26651,plain,
( spl0_2171
<=> ! [X5,X4,X6,X8] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X4,X8,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_2171])]) ).
fof(f2924,plain,
! [X8,X6,X4,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1585,f1581]) ).
fof(f1585,axiom,
! [X8,X6,X4,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X8,X4,X5,X5),X6,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X4,X8,X5,X5),c_Transitive__Closure_Ortrancl(X6,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f26649,plain,
spl0_2170,
inference(avatar_split_clause,[],[f2831,f26647]) ).
fof(f26647,plain,
( spl0_2170
<=> ! [X82,X5] : c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).
fof(f2831,plain,
! [X82,X5] : c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),c_Transitive__Closure_Otrancl(c_union(X82,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5,X5),
inference(definition_unfolding,[],[f1576,f1581,f1581,f1581]) ).
fof(f1576,axiom,
! [X82,X5] : c_Transitive__Closure_Ortrancl(X82,X5) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X82,X5),c_Transitive__Closure_Ortrancl(X82,X5),X5,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f26645,plain,
spl0_2169,
inference(avatar_split_clause,[],[f1608,f26643]) ).
fof(f26643,plain,
( spl0_2169
<=> ! [X35,X23,X5,X24,X25,X1] :
( ~ c_in(X25,X35,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| ~ c_in(X24,X1,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Datatype__Universe_OScons(X24,X25,X5,X23),c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f1608,axiom,
! [X1,X24,X35,X25,X5,X23] :
( ~ c_in(X25,X35,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| ~ c_in(X24,X1,tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Datatype__Universe_OScons(X24,X25,X5,X23),c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f26635,plain,
( spl0_2168
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2165 ),
inference(avatar_split_clause,[],[f25910,f25907,f11575,f8937,f26633]) ).
fof(f26633,plain,
( spl0_2168
<=> ! [X39] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f25907,plain,
( spl0_2165
<=> ! [X39] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f25910,plain,
( ! [X39] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2165 ),
inference(forward_demodulation,[],[f25908,f12564]) ).
fof(f25908,plain,
( ! [X39] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2165 ),
inference(avatar_component_clause,[],[f25907]) ).
fof(f26631,plain,
( spl0_2167
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2164 ),
inference(avatar_split_clause,[],[f25905,f25902,f11575,f8933,f26629]) ).
fof(f26629,plain,
( spl0_2167
<=> ! [X39] :
( c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f25902,plain,
( spl0_2164
<=> ! [X39] :
( c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f25905,plain,
( ! [X39] :
( c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2164 ),
inference(forward_demodulation,[],[f25903,f12565]) ).
fof(f25903,plain,
( ! [X39] :
( c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2164 ),
inference(avatar_component_clause,[],[f25902]) ).
fof(f26627,plain,
( spl0_2166
| ~ spl0_1355
| ~ spl0_1313
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f22886,f22701,f10325,f10968,f26624]) ).
fof(f26624,plain,
( spl0_2166
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(v_A,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).
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(f22886,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(v_A,v_S,tc_set(t_a))
| ~ spl0_1313
| ~ spl0_2034 ),
inference(resolution,[],[f22703,f10326]) ).
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(f25909,plain,
spl0_2165,
inference(avatar_split_clause,[],[f3090,f25907]) ).
fof(f3090,plain,
! [X39] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f310,f321]) ).
fof(f310,axiom,
! [X39] :
( ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).
fof(f25904,plain,
spl0_2164,
inference(avatar_split_clause,[],[f3089,f25902]) ).
fof(f3089,plain,
! [X39] :
( c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f300,f321]) ).
fof(f300,axiom,
! [X39] :
( ~ c_less(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).
fof(f25891,plain,
( spl0_2163
| ~ spl0_116
| ~ spl0_674
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2162 ),
inference(avatar_split_clause,[],[f25887,f25883,f18906,f10450,f10135,f7218,f7182,f6752,f3744,f25889]) ).
fof(f25889,plain,
( spl0_2163
<=> ! [X30] : c_div(c_plus(X30,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X30,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f25883,plain,
( spl0_2162
<=> ! [X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f25887,plain,
( ! [X30] : c_div(c_plus(X30,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X30,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2162 ),
inference(forward_demodulation,[],[f25886,f11244]) ).
fof(f25886,plain,
( ! [X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X30,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X30,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_2162 ),
inference(forward_demodulation,[],[f25884,f18994]) ).
fof(f25884,plain,
( ! [X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2162 ),
inference(avatar_component_clause,[],[f25883]) ).
fof(f25885,plain,
spl0_2162,
inference(avatar_split_clause,[],[f3039,f25883]) ).
fof(f3039,plain,
! [X30] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3038,f3010]) ).
fof(f3038,plain,
! [X30] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X30,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3037,f1021]) ).
fof(f3037,plain,
! [X30] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(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),tc_nat),
inference(forward_demodulation,[],[f3036,f1019]) ).
fof(f3036,plain,
! [X30] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(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),tc_nat),
inference(forward_demodulation,[],[f2859,f1021]) ).
fof(f2859,plain,
! [X30] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(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),tc_nat),
inference(definition_unfolding,[],[f749,f1409,f1409,f1409]) ).
fof(f749,axiom,
! [X30] : c_div(c_Suc(c_Suc(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_Suc(c_div(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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
fof(f25881,plain,
( spl0_1
| spl0_2161
| ~ spl0_1027
| ~ spl0_2093 ),
inference(avatar_split_clause,[],[f25537,f24524,f8404,f25878,f3175]) ).
fof(f3175,plain,
( spl0_1
<=> c_emptyset = v_S ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f25878,plain,
( spl0_2161
<=> c_in(c_Main_Oall__not__in__conv__1(v_S,t_a),v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
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(f25537,plain,
( c_in(c_Main_Oall__not__in__conv__1(v_S,t_a),v_A,t_a)
| c_emptyset = v_S
| ~ spl0_1027
| ~ spl0_2093 ),
inference(resolution,[],[f24525,f8405]) ).
fof(f8405,plain,
( ! [X1,X5] :
( c_in(c_Main_Oall__not__in__conv__1(X1,X5),X1,X5)
| c_emptyset = X1 )
| ~ spl0_1027 ),
inference(avatar_component_clause,[],[f8404]) ).
fof(f25831,plain,
( spl0_2160
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2159 ),
inference(avatar_split_clause,[],[f25827,f25823,f18906,f10450,f10135,f6752,f3744,f25829]) ).
fof(f25829,plain,
( spl0_2160
<=> ! [X30,X19] : c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_1,c_plus(c_1,c_plus(c_1,X19,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f25823,plain,
( spl0_2159
<=> ! [X30,X19] : c_Divides_Oop_Amod(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f25827,plain,
( ! [X19,X30] : c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_1,c_plus(c_1,c_plus(c_1,X19,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2159 ),
inference(forward_demodulation,[],[f25826,f18907]) ).
fof(f25826,plain,
( ! [X19,X30] : c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_1,c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2159 ),
inference(forward_demodulation,[],[f25824,f11244]) ).
fof(f25824,plain,
( ! [X19,X30] : c_Divides_Oop_Amod(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat)
| ~ spl0_2159 ),
inference(avatar_component_clause,[],[f25823]) ).
fof(f25825,plain,
spl0_2159,
inference(avatar_split_clause,[],[f3031,f25823]) ).
fof(f3031,plain,
! [X19,X30] : c_Divides_Oop_Amod(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3030,f1021]) ).
fof(f3030,plain,
! [X19,X30] : c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3029,f2811]) ).
fof(f3029,plain,
! [X19,X30] : c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2854,f3010]) ).
fof(f2854,plain,
! [X19,X30] : c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_Divides_Oop_Amod(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f842,f1409,f1409,f1409]) ).
fof(f842,axiom,
! [X19,X30] : c_Divides_Oop_Amod(X30,c_Suc(c_Suc(c_Suc(X19))),tc_nat) = c_Divides_Oop_Amod(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f25809,plain,
( spl0_2158
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2157 ),
inference(avatar_split_clause,[],[f25805,f25801,f18906,f10450,f10135,f6752,f3744,f25807]) ).
fof(f25807,plain,
( spl0_2158
<=> ! [X30,X19] : c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_div(X30,c_plus(c_1,c_plus(c_1,c_plus(c_1,X19,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f25801,plain,
( spl0_2157
<=> ! [X30,X19] : c_div(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2157])]) ).
fof(f25805,plain,
( ! [X19,X30] : c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_div(X30,c_plus(c_1,c_plus(c_1,c_plus(c_1,X19,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2157 ),
inference(forward_demodulation,[],[f25804,f18907]) ).
fof(f25804,plain,
( ! [X19,X30] : c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_div(X30,c_plus(c_1,c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2157 ),
inference(forward_demodulation,[],[f25802,f11244]) ).
fof(f25802,plain,
( ! [X19,X30] : c_div(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat)
| ~ spl0_2157 ),
inference(avatar_component_clause,[],[f25801]) ).
fof(f25803,plain,
spl0_2157,
inference(avatar_split_clause,[],[f3028,f25801]) ).
fof(f3028,plain,
! [X19,X30] : c_div(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3027,f1021]) ).
fof(f3027,plain,
! [X19,X30] : c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_div(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X19,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3026,f2811]) ).
fof(f3026,plain,
! [X19,X30] : c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_div(X30,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2853,f3010]) ).
fof(f2853,plain,
! [X19,X30] : c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat) = c_div(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f750,f1409,f1409,f1409]) ).
fof(f750,axiom,
! [X19,X30] : c_div(X30,c_Suc(c_Suc(c_Suc(X19))),tc_nat) = c_div(X30,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X19,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f25795,plain,
( spl0_2156
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2155 ),
inference(avatar_split_clause,[],[f25791,f25787,f18906,f10450,f10135,f6752,f3744,f25793]) ).
fof(f25793,plain,
( spl0_2156
<=> ! [X24,X23,X18,X5] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),X24,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f25787,plain,
( spl0_2155
<=> ! [X24,X23,X18,X5] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).
fof(f25791,plain,
( ! [X18,X24,X5,X23] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),X24,X5,X23),X5,X23)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2155 ),
inference(forward_demodulation,[],[f25790,f11244]) ).
fof(f25790,plain,
( ! [X18,X24,X5,X23] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23)
| ~ spl0_1852
| ~ spl0_2155 ),
inference(forward_demodulation,[],[f25788,f18907]) ).
fof(f25788,plain,
( ! [X18,X24,X5,X23] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23)
| ~ spl0_2155 ),
inference(avatar_component_clause,[],[f25787]) ).
fof(f25789,plain,
spl0_2155,
inference(avatar_split_clause,[],[f3025,f25787]) ).
fof(f3025,plain,
! [X18,X24,X5,X23] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23),
inference(forward_demodulation,[],[f2852,f3010]) ).
fof(f2852,plain,
! [X18,X24,X5,X23] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23),
inference(definition_unfolding,[],[f69,f1409,f1409,f1409]) ).
fof(f69,axiom,
! [X18,X24,X5,X23] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X18)),c_Datatype__Universe_OIn0(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X18),X24,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f25781,plain,
( spl0_2154
| ~ spl0_796
| ~ spl0_1678
| ~ spl0_2035 ),
inference(avatar_split_clause,[],[f23317,f23051,f15684,f7279,f25778]) ).
fof(f25778,plain,
( spl0_2154
<=> c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).
fof(f7279,plain,
( spl0_796
<=> ! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f15684,plain,
( spl0_1678
<=> ! [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_1678])]) ).
fof(f23051,plain,
( spl0_2035
<=> c_emptyset = c_minus(v_S,v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f23317,plain,
( c_UNIV = c_union(c_uminus(v_S,tc_set(t_a)),v_A,t_a)
| ~ spl0_796
| ~ spl0_1678
| ~ spl0_2035 ),
inference(forward_demodulation,[],[f23306,f7280]) ).
fof(f7280,plain,
( ! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5))
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f7279]) ).
fof(f23306,plain,
( c_uminus(c_emptyset,tc_set(t_a)) = c_union(c_uminus(v_S,tc_set(t_a)),v_A,t_a)
| ~ spl0_1678
| ~ spl0_2035 ),
inference(superposition,[],[f15685,f23053]) ).
fof(f23053,plain,
( c_emptyset = c_minus(v_S,v_A,tc_set(t_a))
| ~ spl0_2035 ),
inference(avatar_component_clause,[],[f23051]) ).
fof(f15685,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_1678 ),
inference(avatar_component_clause,[],[f15684]) ).
fof(f25776,plain,
( spl0_2153
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2152 ),
inference(avatar_split_clause,[],[f25772,f25768,f18906,f10450,f10135,f6752,f3744,f25774]) ).
fof(f25774,plain,
( spl0_2153
<=> ! [X24,X23,X18,X5] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),X24,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).
fof(f25768,plain,
( spl0_2152
<=> ! [X24,X23,X18,X5] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).
fof(f25772,plain,
( ! [X18,X24,X5,X23] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),X24,X5,X23),X5,X23)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1852
| ~ spl0_2152 ),
inference(forward_demodulation,[],[f25771,f11244]) ).
fof(f25771,plain,
( ! [X18,X24,X5,X23] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23)
| ~ spl0_1852
| ~ spl0_2152 ),
inference(forward_demodulation,[],[f25769,f18907]) ).
fof(f25769,plain,
( ! [X18,X24,X5,X23] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23)
| ~ spl0_2152 ),
inference(avatar_component_clause,[],[f25768]) ).
fof(f25770,plain,
spl0_2152,
inference(avatar_split_clause,[],[f3024,f25768]) ).
fof(f3024,plain,
! [X18,X24,X5,X23] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23),
inference(forward_demodulation,[],[f2851,f3010]) ).
fof(f2851,plain,
! [X18,X24,X5,X23] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X24,X5,X23),X5,X23),
inference(definition_unfolding,[],[f70,f1409,f1409,f1409]) ).
fof(f70,axiom,
! [X18,X24,X5,X23] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X18)),c_Datatype__Universe_OIn1(X24,X5,X23),X5,X23) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X18),X24,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f25766,plain,
spl0_2151,
inference(avatar_split_clause,[],[f1709,f25764]) ).
fof(f25764,plain,
( spl0_2151
<=> ! [X41,X23,X5,X35,X1] :
( c_in(c_Main_OPlusE__1(X1,X41,X5,X23),X1,X5)
| ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X35,X41,X23,X5),X23,X5) = X41 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).
fof(f1709,axiom,
! [X41,X1,X5,X35,X23] :
( c_in(c_Main_OPlusE__1(X1,X41,X5,X23),X1,X5)
| ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X35,X41,X23,X5),X23,X5) = X41 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f25762,plain,
spl0_2150,
inference(avatar_split_clause,[],[f1708,f25760]) ).
fof(f25760,plain,
( spl0_2150
<=> ! [X41,X23,X5,X35,X1] :
( c_in(c_Main_OPlusE__2(X35,X41,X23,X5),X35,X23)
| ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X1,X41,X5,X23),X5,X23) = X41 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).
fof(f1708,axiom,
! [X41,X1,X35,X5,X23] :
( c_in(c_Main_OPlusE__2(X35,X41,X23,X5),X35,X23)
| ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X1,X41,X5,X23),X5,X23) = X41 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f25758,plain,
spl0_2149,
inference(avatar_split_clause,[],[f1605,f25756]) ).
fof(f25756,plain,
( spl0_2149
<=> ! [X35,X23,X31,X5,X1] :
( ~ c_in(X31,c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X1,X35,X31,X5,X23),c_Main_OuprodE__2(X1,X35,X31,X5,X23),X5,X23) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).
fof(f1605,axiom,
! [X31,X1,X35,X5,X23] :
( ~ c_in(X31,c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X1,X35,X31,X5,X23),c_Main_OuprodE__2(X1,X35,X31,X5,X23),X5,X23) = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f25754,plain,
spl0_2148,
inference(avatar_split_clause,[],[f868,f25752]) ).
fof(f25752,plain,
( spl0_2148
<=> ! [X31,X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Osemiring(X23)
| c_times(c_Numeral_Onumber__of(X40,X23),c_plus(X7,X31,X23),X23) = c_plus(c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),c_times(c_Numeral_Onumber__of(X40,X23),X31,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).
fof(f868,axiom,
! [X40,X31,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Osemiring(X23)
| c_times(c_Numeral_Onumber__of(X40,X23),c_plus(X7,X31,X23),X23) = c_plus(c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),c_times(c_Numeral_Onumber__of(X40,X23),X31,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f25750,plain,
spl0_2147,
inference(avatar_split_clause,[],[f867,f25748]) ).
fof(f25748,plain,
( spl0_2147
<=> ! [X31,X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Oring(X23)
| c_times(c_Numeral_Onumber__of(X40,X23),c_minus(X7,X31,X23),X23) = c_minus(c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),c_times(c_Numeral_Onumber__of(X40,X23),X31,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).
fof(f867,axiom,
! [X40,X31,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Oring(X23)
| c_times(c_Numeral_Onumber__of(X40,X23),c_minus(X7,X31,X23),X23) = c_minus(c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),c_times(c_Numeral_Onumber__of(X40,X23),X31,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f25746,plain,
spl0_2146,
inference(avatar_split_clause,[],[f865,f25744]) ).
fof(f25744,plain,
( spl0_2146
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f865,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f25742,plain,
spl0_2145,
inference(avatar_split_clause,[],[f864,f25740]) ).
fof(f25740,plain,
( spl0_2145
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X7,X2,X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f864,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X7,X2,X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f25738,plain,
spl0_2144,
inference(avatar_split_clause,[],[f862,f25736]) ).
fof(f25736,plain,
( spl0_2144
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X7,X2,X23)
| ~ c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).
fof(f862,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X7,X2,X23)
| ~ c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f25733,plain,
spl0_2143,
inference(avatar_split_clause,[],[f861,f25731]) ).
fof(f25731,plain,
( spl0_2143
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X2,X7,X23)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).
fof(f861,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X2,X7,X23)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f25729,plain,
spl0_2142,
inference(avatar_split_clause,[],[f859,f25727]) ).
fof(f25727,plain,
( spl0_2142
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).
fof(f859,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f25725,plain,
spl0_2141,
inference(avatar_split_clause,[],[f858,f25723]) ).
fof(f25723,plain,
( spl0_2141
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X7,X2,X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).
fof(f858,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X7,X2,X23)
| c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f25721,plain,
spl0_2140,
inference(avatar_split_clause,[],[f856,f25719]) ).
fof(f25719,plain,
( spl0_2140
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X7,X2,X23)
| ~ c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).
fof(f856,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X7,X2,X23)
| ~ c_lessequals(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f25717,plain,
spl0_2139,
inference(avatar_split_clause,[],[f855,f25715]) ).
fof(f25715,plain,
( spl0_2139
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X2,X7,X23)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).
fof(f855,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_less(X2,X7,X23)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f25713,plain,
spl0_2138,
inference(avatar_split_clause,[],[f853,f25711]) ).
fof(f25711,plain,
( spl0_2138
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).
fof(f853,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f25709,plain,
spl0_2137,
inference(avatar_split_clause,[],[f852,f25707]) ).
fof(f25707,plain,
( spl0_2137
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X7,X2,X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).
fof(f852,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X7,X2,X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f25705,plain,
spl0_2136,
inference(avatar_split_clause,[],[f850,f25703]) ).
fof(f25703,plain,
( spl0_2136
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X7,X2,X23)
| ~ c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).
fof(f850,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X7,X2,X23)
| ~ c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f25701,plain,
spl0_2135,
inference(avatar_split_clause,[],[f849,f25699]) ).
fof(f25699,plain,
( spl0_2135
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X2,X7,X23)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f849,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X2,X7,X23)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f25697,plain,
spl0_2134,
inference(avatar_split_clause,[],[f847,f25695]) ).
fof(f25695,plain,
( spl0_2134
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f847,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f25693,plain,
( spl0_2133
| ~ spl0_4
| ~ spl0_2093 ),
inference(avatar_split_clause,[],[f25534,f24524,f3190,f25690]) ).
fof(f25690,plain,
( spl0_2133
<=> c_in(v_x,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).
fof(f25534,plain,
( c_in(v_x,v_A,t_a)
| ~ spl0_4
| ~ spl0_2093 ),
inference(resolution,[],[f24525,f3192]) ).
fof(f3192,plain,
( c_in(v_x,v_S,t_a)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3190]) ).
fof(f25688,plain,
spl0_2132,
inference(avatar_split_clause,[],[f846,f25686]) ).
fof(f25686,plain,
( spl0_2132
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X7,X2,X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).
fof(f846,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X7,X2,X23)
| c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f25684,plain,
spl0_2131,
inference(avatar_split_clause,[],[f844,f25682]) ).
fof(f25682,plain,
( spl0_2131
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X7,X2,X23)
| ~ c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).
fof(f844,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X7,X2,X23)
| ~ c_less(c_Numeral_Onumber__of(X40,X23),c_0,X23)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f25680,plain,
spl0_2130,
inference(avatar_split_clause,[],[f843,f25678]) ).
fof(f25678,plain,
( spl0_2130
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X2,X7,X23)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).
fof(f843,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| c_lessequals(X2,X7,X23)
| ~ c_less(c_0,c_Numeral_Onumber__of(X40,X23),X23)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f25676,plain,
spl0_2129,
inference(avatar_split_clause,[],[f813,f25674]) ).
fof(f25674,plain,
( spl0_2129
<=> ! [X40,X7,X23,X2] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Osemiring(X23)
| c_times(c_plus(X2,X7,X23),c_Numeral_Onumber__of(X40,X23),X23) = c_plus(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).
fof(f813,axiom,
! [X2,X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Osemiring(X23)
| c_times(c_plus(X2,X7,X23),c_Numeral_Onumber__of(X40,X23),X23) = c_plus(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f25672,plain,
spl0_2128,
inference(avatar_split_clause,[],[f812,f25670]) ).
fof(f25670,plain,
( spl0_2128
<=> ! [X40,X7,X23,X2] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Oring(X23)
| c_times(c_minus(X2,X7,X23),c_Numeral_Onumber__of(X40,X23),X23) = c_minus(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f812,axiom,
! [X2,X40,X7,X23] :
( ~ class_Numeral_Onumber(X23)
| ~ class_Ring__and__Field_Oring(X23)
| c_times(c_minus(X2,X7,X23),c_Numeral_Onumber__of(X40,X23),X23) = c_minus(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f25668,plain,
spl0_2127,
inference(avatar_split_clause,[],[f727,f25666]) ).
fof(f25666,plain,
( spl0_2127
<=> ! [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_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f727,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_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
fof(f25664,plain,
spl0_2126,
inference(avatar_split_clause,[],[f7,f25662]) ).
fof(f25662,plain,
( spl0_2126
<=> ! [X5,X4,X7,X6,X2] :
( c_in(X4,c_Tarski_Ointerval(X6,X2,X7,X5),X5)
| ~ c_in(c_Pair(X2,X4,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(X4,X7,X5,X5),X6,tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).
fof(f7,axiom,
! [X2,X6,X7,X4,X5] :
( c_in(X4,c_Tarski_Ointerval(X6,X2,X7,X5),X5)
| ~ c_in(c_Pair(X2,X4,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(c_Pair(X4,X7,X5,X5),X6,tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0) ).
fof(f25503,plain,
( spl0_2125
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2124 ),
inference(avatar_split_clause,[],[f25499,f25496,f10450,f10135,f6752,f3744,f25501]) ).
fof(f25501,plain,
( spl0_2125
<=> ! [X24,X23,X18,X5,X25] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X18,X24,X5,X23),c_Datatype__Universe_Ontrunc(X18,X25,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_OScons(X24,X25,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).
fof(f25496,plain,
( spl0_2124
<=> ! [X24,X23,X18,X5,X25] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X18,X24,X5,X23),c_Datatype__Universe_Ontrunc(X18,X25,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OScons(X24,X25,X5,X23),X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).
fof(f25499,plain,
( ! [X18,X24,X5,X25,X23] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X18,X24,X5,X23),c_Datatype__Universe_Ontrunc(X18,X25,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X18,tc_nat),c_Datatype__Universe_OScons(X24,X25,X5,X23),X5,X23)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2124 ),
inference(forward_demodulation,[],[f25497,f11244]) ).
fof(f25497,plain,
( ! [X18,X24,X5,X25,X23] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X18,X24,X5,X23),c_Datatype__Universe_Ontrunc(X18,X25,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OScons(X24,X25,X5,X23),X5,X23)
| ~ spl0_2124 ),
inference(avatar_component_clause,[],[f25496]) ).
fof(f25498,plain,
spl0_2124,
inference(avatar_split_clause,[],[f2858,f25496]) ).
fof(f2858,plain,
! [X18,X24,X5,X25,X23] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X18,X24,X5,X23),c_Datatype__Universe_Ontrunc(X18,X25,X5,X23),X5,X23) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Datatype__Universe_OScons(X24,X25,X5,X23),X5,X23),
inference(definition_unfolding,[],[f73,f1409]) ).
fof(f73,axiom,
! [X18,X24,X5,X25,X23] : c_Datatype__Universe_Ontrunc(c_Suc(X18),c_Datatype__Universe_OScons(X24,X25,X5,X23),X5,X23) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X18,X24,X5,X23),c_Datatype__Universe_Ontrunc(X18,X25,X5,X23),X5,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f25494,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1669,f25492]) ).
fof(f25492,plain,
( spl0_2123
<=> ! [X5,X23,X6,X85] :
( ~ c_in(X85,c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23))
| c_in(c_Pair(c_Main_OconverseE__1(X6,X85,X23,X5),c_Main_OconverseE__2(X6,X85,X23,X5),X23,X5),X6,tc_prod(X23,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).
fof(f1669,axiom,
! [X6,X5,X85,X23] :
( ~ c_in(X85,c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23))
| c_in(c_Pair(c_Main_OconverseE__1(X6,X85,X23,X5),c_Main_OconverseE__2(X6,X85,X23,X5),X23,X5),X6,tc_prod(X23,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f25490,plain,
spl0_2122,
inference(avatar_split_clause,[],[f1196,f25488]) ).
fof(f25488,plain,
( spl0_2122
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X4,X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| 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_2122])]) ).
fof(f1196,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X4,X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| 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_0) ).
fof(f25486,plain,
spl0_2121,
inference(avatar_split_clause,[],[f1186,f25484]) ).
fof(f25484,plain,
( spl0_2121
<=> ! [X4,X5,X39] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X4,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| 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_2121])]) ).
fof(f1186,axiom,
! [X39,X4,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X4,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X39,tc_nat)
| 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_4) ).
fof(f25482,plain,
spl0_2120,
inference(avatar_split_clause,[],[f334,f25480]) ).
fof(f25480,plain,
( spl0_2120
<=> ! [X40,X39,X7] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| 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,X7),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_2120])]) ).
fof(f334,axiom,
! [X40,X39,X7] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| 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,X7),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_1) ).
fof(f25158,plain,
spl0_2119,
inference(avatar_split_clause,[],[f2979,f25156]) ).
fof(f25156,plain,
( spl0_2119
<=> ! [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_Numeral_Onumber__of(X80,tc_nat)
| ~ c_IntDef_Oiszero(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_2119])]) ).
fof(f2979,plain,
! [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_Numeral_Onumber__of(X80,tc_nat)
| ~ c_IntDef_Oiszero(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,[],[f705,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(f705,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_Numeral_Onumber__of(X80,tc_nat)
| ~ c_IntDef_Oiszero(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_Oeq__nat__number__of_3) ).
fof(f25154,plain,
spl0_2118,
inference(avatar_split_clause,[],[f2978,f25152]) ).
fof(f25152,plain,
( spl0_2118
<=> ! [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)
| c_IntDef_Oiszero(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_2118])]) ).
fof(f2978,plain,
! [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)
| c_IntDef_Oiszero(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,[],[f704,f994]) ).
fof(f704,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)
| c_IntDef_Oiszero(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_Oeq__nat__number__of_2) ).
fof(f25150,plain,
spl0_2117,
inference(avatar_split_clause,[],[f2977,f25148]) ).
fof(f25148,plain,
( spl0_2117
<=> ! [X80,X40] :
( ~ 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)
| ~ c_IntDef_Oiszero(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_2117])]) ).
fof(f2977,plain,
! [X40,X80] :
( ~ 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)
| ~ c_IntDef_Oiszero(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,[],[f707,f994]) ).
fof(f707,axiom,
! [X40,X80] :
( ~ 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)
| ~ c_IntDef_Oiszero(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_Oeq__nat__number__of_5) ).
fof(f25146,plain,
spl0_2116,
inference(avatar_split_clause,[],[f2976,f25144]) ).
fof(f25144,plain,
( spl0_2116
<=> ! [X80,X40] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X80,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)
| ~ c_IntDef_Oiszero(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_2116])]) ).
fof(f2976,plain,
! [X40,X80] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X80,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)
| ~ c_IntDef_Oiszero(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,[],[f709,f994]) ).
fof(f709,axiom,
! [X40,X80] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X80,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)
| ~ c_IntDef_Oiszero(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_Oeq__nat__number__of_7) ).
fof(f25142,plain,
spl0_2115,
inference(avatar_split_clause,[],[f2974,f25140]) ).
fof(f25140,plain,
( spl0_2115
<=> ! [X80,X40] :
( ~ c_IntDef_Oiszero(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_Numeral_Onumber__of(X40,tc_nat) = c_Numeral_Onumber__of(X80,tc_nat)
| ~ c_IntDef_Oiszero(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_2115])]) ).
fof(f2974,plain,
! [X40,X80] :
( ~ c_IntDef_Oiszero(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_Numeral_Onumber__of(X40,tc_nat) = c_Numeral_Onumber__of(X80,tc_nat)
| ~ c_IntDef_Oiszero(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,[],[f711,f994]) ).
fof(f711,axiom,
! [X40,X80] :
( ~ c_IntDef_Oiszero(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_Numeral_Onumber__of(X40,tc_nat) = c_Numeral_Onumber__of(X80,tc_nat)
| ~ c_IntDef_Oiszero(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_Oeq__nat__number__of_9) ).
fof(f25138,plain,
spl0_2114,
inference(avatar_split_clause,[],[f1710,f25136]) ).
fof(f25136,plain,
( spl0_2114
<=> ! [X41,X23,X5,X35,X1] :
( c_in(c_Main_OPlusE__2(X35,X41,X23,X5),X35,X23)
| c_in(c_Main_OPlusE__1(X1,X41,X5,X23),X1,X5)
| ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f1710,axiom,
! [X41,X1,X35,X5,X23] :
( c_in(c_Main_OPlusE__2(X35,X41,X23,X5),X35,X23)
| c_in(c_Main_OPlusE__1(X1,X41,X5,X23),X1,X5)
| ~ c_in(X41,c_Sum__Type_OPlus(X1,X35,X5,X23),tc_sum(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f25134,plain,
spl0_2113,
inference(avatar_split_clause,[],[f866,f25132]) ).
fof(f25132,plain,
( spl0_2113
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| ~ c_less(X7,X2,X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).
fof(f866,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| ~ c_less(X7,X2,X23)
| c_less(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f25130,plain,
spl0_2112,
inference(avatar_split_clause,[],[f860,f25128]) ).
fof(f25128,plain,
( spl0_2112
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| ~ c_less(X7,X2,X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).
fof(f860,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_less(X2,X7,X23)
| ~ c_less(X7,X2,X23)
| c_less(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f25126,plain,
spl0_2111,
inference(avatar_split_clause,[],[f854,f25124]) ).
fof(f25124,plain,
( spl0_2111
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| ~ c_lessequals(X7,X2,X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).
fof(f854,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| ~ c_lessequals(X7,X2,X23)
| c_lessequals(c_times(X2,c_Numeral_Onumber__of(X40,X23),X23),c_times(X7,c_Numeral_Onumber__of(X40,X23),X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f25122,plain,
spl0_2110,
inference(avatar_split_clause,[],[f848,f25120]) ).
fof(f25120,plain,
( spl0_2110
<=> ! [X40,X7,X23,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| ~ c_lessequals(X7,X2,X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).
fof(f848,axiom,
! [X2,X40,X7,X23] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X23)
| ~ class_Numeral_Onumber(X23)
| ~ c_lessequals(X2,X7,X23)
| ~ c_lessequals(X7,X2,X23)
| c_lessequals(c_times(c_Numeral_Onumber__of(X40,X23),X2,X23),c_times(c_Numeral_Onumber__of(X40,X23),X7,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f25118,plain,
spl0_2109,
inference(avatar_split_clause,[],[f659,f25116]) ).
fof(f25116,plain,
( spl0_2109
<=> ! [X44,X4,X23,X5,X45] :
( c_in(X4,c_List_Oset(X44,X5),X5)
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X23))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X44,X45,X5,X23),X4,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).
fof(f659,axiom,
! [X44,X45,X4,X5,X23] :
( c_in(X4,c_List_Oset(X44,X5),X5)
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X23))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X44,X45,X5,X23),X4,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
fof(f25114,plain,
spl0_2108,
inference(avatar_split_clause,[],[f658,f25112]) ).
fof(f25112,plain,
( spl0_2108
<=> ! [X44,X4,X23,X5,X45] :
( ~ c_in(X4,c_List_Oset(X44,X5),X5)
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X23))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X44,X45,X5,X23),X4,X5,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).
fof(f658,axiom,
! [X44,X45,X4,X5,X23] :
( ~ c_in(X4,c_List_Oset(X44,X5),X5)
| c_Nat_Osize(X44,tc_List_Olist(X5)) != c_Nat_Osize(X45,tc_List_Olist(X23))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X44,X45,X5,X23),X4,X5,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
fof(f25110,plain,
spl0_2107,
inference(avatar_split_clause,[],[f654,f25108]) ).
fof(f25108,plain,
( spl0_2107
<=> ! [X44,X4,X23,X8,X5,X45] : c_List_Ozip(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X23),X5,X23) = c_List_Olist_OCons(c_Pair(X4,X8,X5,X23),c_List_Ozip(X44,X45,X5,X23),tc_prod(X5,X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).
fof(f654,axiom,
! [X8,X44,X45,X4,X5,X23] : c_List_Ozip(c_List_Olist_OCons(X4,X44,X5),c_List_Olist_OCons(X8,X45,X23),X5,X23) = c_List_Olist_OCons(c_Pair(X4,X8,X5,X23),c_List_Ozip(X44,X45,X5,X23),tc_prod(X5,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
fof(f25106,plain,
spl0_2106,
inference(avatar_split_clause,[],[f481,f25104]) ).
fof(f25104,plain,
( spl0_2106
<=> ! [X6,X5,X8] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X8,X5),c_Main_Olexord__Nil__left__2(X8,X5),X5) = X8
| ~ c_in(c_Pair(c_List_Olist_ONil,X8,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_2106])]) ).
fof(f481,axiom,
! [X8,X6,X5] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X8,X5),c_Main_Olexord__Nil__left__2(X8,X5),X5) = X8
| ~ c_in(c_Pair(c_List_Olist_ONil,X8,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_0) ).
fof(f25102,plain,
spl0_2105,
inference(avatar_split_clause,[],[f323,f25100]) ).
fof(f25100,plain,
( spl0_2105
<=> ! [X39] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f323,axiom,
! [X39] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
fof(f25098,plain,
spl0_2104,
inference(avatar_split_clause,[],[f10,f25096]) ).
fof(f25096,plain,
( spl0_2104
<=> ! [X9,X0,X3] :
( ~ c_in(X9,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X3,t_a)
| c_in(v_sko__4mi(X0,v_r,X9),X0,t_a)
| c_in(c_Pair(X3,X9,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).
fof(f10,axiom,
! [X3,X0,X9] :
( ~ c_in(X9,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X3,t_a)
| c_in(v_sko__4mi(X0,v_r,X9),X0,t_a)
| c_in(c_Pair(X3,X9,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_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0) ).
fof(f25094,plain,
( spl0_2103
| ~ spl0_2
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f24930,f24122,f3180,f25091]) ).
fof(f25091,plain,
( spl0_2103
<=> c_in(v_a,v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).
fof(f3180,plain,
( spl0_2
<=> c_in(v_a,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f24930,plain,
( c_in(v_a,v_S,t_a)
| ~ spl0_2
| ~ spl0_2067 ),
inference(superposition,[],[f3182,f24124]) ).
fof(f3182,plain,
( c_in(v_a,v_A,t_a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f24964,plain,
spl0_2102,
inference(avatar_split_clause,[],[f2973,f24962]) ).
fof(f24962,plain,
( spl0_2102
<=> ! [X45,X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f2973,plain,
! [X44,X45,X5] :
( ~ c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(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,[],[f423,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(f423,axiom,
! [X44,X45,X5] :
( ~ c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(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_3) ).
fof(f24960,plain,
spl0_2101,
inference(avatar_split_clause,[],[f2945,f24958]) ).
fof(f24958,plain,
( spl0_2101
<=> ! [X35,X5,X2,X1] :
( c_in(X2,X35,X5)
| 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_2101])]) ).
fof(f2945,plain,
! [X2,X1,X35,X5] :
( c_in(X2,X35,X5)
| 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,[],[f1547,f1238,f1238]) ).
fof(f1547,axiom,
! [X2,X1,X35,X5] :
( c_in(X2,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_2) ).
fof(f24956,plain,
spl0_2100,
inference(avatar_split_clause,[],[f2943,f24954]) ).
fof(f24954,plain,
( spl0_2100
<=> ! [X35,X5,X2,X1] :
( c_in(X2,X35,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X35,X5),X1,X5,X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X35,X5),c_insert(X2,X1,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).
fof(f2943,plain,
! [X2,X1,X35,X5] :
( c_in(X2,X35,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X35,X5),X1,X5,X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X35,X5),c_insert(X2,X1,X5),X5,X5) ),
inference(definition_unfolding,[],[f1528,f1238,f1238]) ).
fof(f1528,axiom,
! [X2,X1,X35,X5] :
( c_in(X2,X35,X5)
| c_emptyset != c_inter(X35,X1,X5)
| c_emptyset = c_inter(X35,c_insert(X2,X1,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
fof(f24952,plain,
spl0_2099,
inference(avatar_split_clause,[],[f657,f24950]) ).
fof(f24950,plain,
( spl0_2099
<=> ! [X55,X4,X29,X23,X5,X8] : c_List_Ozip(c_List_Oreplicate(X29,X4,X5),c_List_Oreplicate(X55,X8,X23),X5,X23) = c_List_Oreplicate(c_Orderings_Omin(X29,X55,tc_nat),c_Pair(X4,X8,X5,X23),tc_prod(X5,X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).
fof(f657,axiom,
! [X29,X8,X55,X4,X5,X23] : c_List_Ozip(c_List_Oreplicate(X29,X4,X5),c_List_Oreplicate(X55,X8,X23),X5,X23) = c_List_Oreplicate(c_Orderings_Omin(X29,X55,tc_nat),c_Pair(X4,X8,X5,X23),tc_prod(X5,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
fof(f24948,plain,
spl0_2098,
inference(avatar_split_clause,[],[f563,f24946]) ).
fof(f24946,plain,
( spl0_2098
<=> ! [X5,X44,X29,X19] :
( ~ c_lessequals(c_plus(X19,X29,tc_nat),c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Odrop(X19,X44,X5),X29,X5) = c_List_Onth(X44,c_plus(X19,X29,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2098])]) ).
fof(f563,axiom,
! [X29,X19,X44,X5] :
( ~ c_lessequals(c_plus(X19,X29,tc_nat),c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Odrop(X19,X44,X5),X29,X5) = c_List_Onth(X44,c_plus(X19,X29,tc_nat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
fof(f24894,plain,
( spl0_2097
| ~ spl0_58
| ~ spl0_1453
| ~ spl0_2092 ),
inference(avatar_split_clause,[],[f24504,f24501,f11734,f3460,f24892]) ).
fof(f24892,plain,
( spl0_2097
<=> ! [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(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_2097])]) ).
fof(f11734,plain,
( spl0_1453
<=> ! [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_1453])]) ).
fof(f24501,plain,
( spl0_2092
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),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_2092])]) ).
fof(f24504,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(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) )
| ~ spl0_58
| ~ spl0_1453
| ~ spl0_2092 ),
inference(forward_demodulation,[],[f24502,f12822]) ).
fof(f12822,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_1453 ),
inference(resolution,[],[f11735,f3462]) ).
fof(f11735,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_1453 ),
inference(avatar_component_clause,[],[f11734]) ).
fof(f24502,plain,
( ! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),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) )
| ~ spl0_2092 ),
inference(avatar_component_clause,[],[f24501]) ).
fof(f24770,plain,
( spl0_2096
| spl0_2067
| ~ spl0_1443
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f22884,f22701,f11678,f24122,f24767]) ).
fof(f11678,plain,
( spl0_1443
<=> ! [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_1443])]) ).
fof(f22884,plain,
( v_A = v_S
| c_less(v_S,v_A,tc_set(t_a))
| ~ spl0_1443
| ~ spl0_2034 ),
inference(resolution,[],[f22703,f11679]) ).
fof(f11679,plain,
( ! [X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| X1 = X35
| c_less(X1,X35,tc_set(X5)) )
| ~ spl0_1443 ),
inference(avatar_component_clause,[],[f11678]) ).
fof(f24563,plain,
( spl0_2095
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2075 ),
inference(avatar_split_clause,[],[f24346,f24343,f11575,f8937,f24561]) ).
fof(f24561,plain,
( spl0_2095
<=> ! [X39] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f24343,plain,
( spl0_2075
<=> ! [X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).
fof(f24346,plain,
( ! [X39] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1110
| ~ spl0_1419
| ~ spl0_2075 ),
inference(forward_demodulation,[],[f24344,f12564]) ).
fof(f24344,plain,
( ! [X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2075 ),
inference(avatar_component_clause,[],[f24343]) ).
fof(f24559,plain,
( spl0_2094
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2074 ),
inference(avatar_split_clause,[],[f24341,f24338,f11575,f8933,f24557]) ).
fof(f24557,plain,
( spl0_2094
<=> ! [X39] :
( c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f24338,plain,
( spl0_2074
<=> ! [X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).
fof(f24341,plain,
( ! [X39] :
( c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1419
| ~ spl0_2074 ),
inference(forward_demodulation,[],[f24339,f12565]) ).
fof(f24339,plain,
( ! [X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2074 ),
inference(avatar_component_clause,[],[f24338]) ).
fof(f24526,plain,
( spl0_2093
| ~ spl0_1444
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f22883,f22701,f11682,f24524]) ).
fof(f11682,plain,
( spl0_1444
<=> ! [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_1444])]) ).
fof(f22883,plain,
( ! [X0] :
( c_in(X0,v_A,t_a)
| ~ c_in(X0,v_S,t_a) )
| ~ spl0_1444
| ~ spl0_2034 ),
inference(resolution,[],[f22703,f11683]) ).
fof(f11683,plain,
( ! [X31,X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_in(X31,X35,X5)
| ~ c_in(X31,X1,X5) )
| ~ spl0_1444 ),
inference(avatar_component_clause,[],[f11682]) ).
fof(f24503,plain,
spl0_2092,
inference(avatar_split_clause,[],[f2952,f24501]) ).
fof(f2952,plain,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X80),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,[],[f724,f994,f994]) ).
fof(f724,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X80),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_4) ).
fof(f24499,plain,
spl0_2091,
inference(avatar_split_clause,[],[f2867,f24497]) ).
fof(f24497,plain,
( spl0_2091
<=> ! [X31,X40,X5,X39] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X40,X5),c_minus(X31,c_Numeral_Onumber__of(X39,X5),X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X39)),X5),X31,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).
fof(f2867,plain,
! [X40,X31,X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X40,X5),c_minus(X31,c_Numeral_Onumber__of(X39,X5),X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__mult(c_Numeral_OMin,X39)),X5),X31,X5) ),
inference(definition_unfolding,[],[f972,f994]) ).
fof(f972,axiom,
! [X40,X31,X39,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X40,X5),c_minus(X31,c_Numeral_Onumber__of(X39,X5),X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,c_Numeral_Obin__minus(X39)),X5),X31,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f24489,plain,
( spl0_2090
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2089 ),
inference(avatar_split_clause,[],[f24485,f24482,f10450,f10135,f6752,f3744,f24487]) ).
fof(f24487,plain,
( spl0_2090
<=> ! [X82,X21,X19] : c_Relation_Orel__comp(X82,c_Nat_Opower(X82,X19,tc_set(tc_prod(X21,X21))),X21,X21,X21) = c_Nat_Opower(X82,c_plus(c_1,X19,tc_nat),tc_set(tc_prod(X21,X21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).
fof(f24482,plain,
( spl0_2089
<=> ! [X82,X21,X19] : c_Relation_Orel__comp(X82,c_Nat_Opower(X82,X19,tc_set(tc_prod(X21,X21))),X21,X21,X21) = c_Nat_Opower(X82,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_set(tc_prod(X21,X21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).
fof(f24485,plain,
( ! [X82,X21,X19] : c_Relation_Orel__comp(X82,c_Nat_Opower(X82,X19,tc_set(tc_prod(X21,X21))),X21,X21,X21) = c_Nat_Opower(X82,c_plus(c_1,X19,tc_nat),tc_set(tc_prod(X21,X21)))
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2089 ),
inference(forward_demodulation,[],[f24483,f11244]) ).
fof(f24483,plain,
( ! [X82,X21,X19] : c_Relation_Orel__comp(X82,c_Nat_Opower(X82,X19,tc_set(tc_prod(X21,X21))),X21,X21,X21) = c_Nat_Opower(X82,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_set(tc_prod(X21,X21)))
| ~ spl0_2089 ),
inference(avatar_component_clause,[],[f24482]) ).
fof(f24484,plain,
spl0_2089,
inference(avatar_split_clause,[],[f2855,f24482]) ).
fof(f2855,plain,
! [X82,X21,X19] : c_Relation_Orel__comp(X82,c_Nat_Opower(X82,X19,tc_set(tc_prod(X21,X21))),X21,X21,X21) = c_Nat_Opower(X82,c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_set(tc_prod(X21,X21))),
inference(definition_unfolding,[],[f1256,f1409]) ).
fof(f1256,axiom,
! [X82,X21,X19] : c_Nat_Opower(X82,c_Suc(X19),tc_set(tc_prod(X21,X21))) = c_Relation_Orel__comp(X82,c_Nat_Opower(X82,X19,tc_set(tc_prod(X21,X21))),X21,X21,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f24480,plain,
spl0_2088,
inference(avatar_split_clause,[],[f2850,f24478]) ).
fof(f24478,plain,
( spl0_2088
<=> ! [X35,X5,X2,X1] : c_Relation_OImage(c_Relation_Odiag(c_insert(X2,X1,X5),X5),c_insert(X2,X35,X5),X5,X5) = c_insert(X2,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f2850,plain,
! [X2,X1,X5,X35] : c_Relation_OImage(c_Relation_Odiag(c_insert(X2,X1,X5),X5),c_insert(X2,X35,X5),X5,X5) = c_insert(X2,c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5),
inference(definition_unfolding,[],[f1551,f1238,f1238]) ).
fof(f1551,axiom,
! [X2,X1,X5,X35] : c_inter(c_insert(X2,X1,X5),c_insert(X2,X35,X5),X5) = c_insert(X2,c_inter(X1,X35,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
fof(f24476,plain,
spl0_2087,
inference(avatar_split_clause,[],[f2844,f24474]) ).
fof(f24474,plain,
( spl0_2087
<=> ! [X5,X1,X35] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X1,X5),tc_List_Olist(X5)),c_List_Olists(X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).
fof(f2844,plain,
! [X1,X5,X35] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X1,X5),tc_List_Olist(X5)),c_List_Olists(X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),
inference(definition_unfolding,[],[f502,f1238,f1238]) ).
fof(f502,axiom,
! [X1,X35,X5] : c_List_Olists(c_inter(X1,X35,X5),X5) = c_inter(c_List_Olists(X1,X5),c_List_Olists(X35,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
fof(f24472,plain,
spl0_2086,
inference(avatar_split_clause,[],[f2843,f24470]) ).
fof(f24470,plain,
( spl0_2086
<=> ! [X5,X1,X35] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X1,X5),tc_set(X5)),c_Pow(X35,X5),tc_set(X5),tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f2843,plain,
! [X1,X5,X35] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X1,X5),X35,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X1,X5),tc_set(X5)),c_Pow(X35,X5),tc_set(X5),tc_set(X5)),
inference(definition_unfolding,[],[f1489,f1238,f1238]) ).
fof(f1489,axiom,
! [X1,X35,X5] : c_Pow(c_inter(X1,X35,X5),X5) = c_inter(c_Pow(X1,X5),c_Pow(X35,X5),tc_set(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
fof(f24390,plain,
( spl0_2085
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2084 ),
inference(avatar_split_clause,[],[f24386,f24382,f10450,f10135,f6752,f3744,f24388]) ).
fof(f24388,plain,
( spl0_2085
<=> ! [X18,X19] : c_plus(c_Binomial_Obinomial(X19,X18),c_Binomial_Obinomial(X19,c_plus(c_1,X18,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X19,tc_nat),c_plus(c_1,X18,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).
fof(f24382,plain,
( spl0_2084
<=> ! [X18,X19] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X19,X18),c_Binomial_Obinomial(X19,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).
fof(f24386,plain,
( ! [X18,X19] : c_plus(c_Binomial_Obinomial(X19,X18),c_Binomial_Obinomial(X19,c_plus(c_1,X18,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X19,tc_nat),c_plus(c_1,X18,tc_nat))
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2084 ),
inference(forward_demodulation,[],[f24385,f11244]) ).
fof(f24385,plain,
( ! [X18,X19] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_plus(c_1,X18,tc_nat)) = c_plus(c_Binomial_Obinomial(X19,X18),c_Binomial_Obinomial(X19,c_plus(c_1,X18,tc_nat)),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2084 ),
inference(forward_demodulation,[],[f24383,f11244]) ).
fof(f24383,plain,
( ! [X18,X19] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X19,X18),c_Binomial_Obinomial(X19,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2084 ),
inference(avatar_component_clause,[],[f24382]) ).
fof(f24384,plain,
spl0_2084,
inference(avatar_split_clause,[],[f2837,f24382]) ).
fof(f2837,plain,
! [X18,X19] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X19,X18),c_Binomial_Obinomial(X19,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)),tc_nat),
inference(definition_unfolding,[],[f27,f1409,f1409,f1409]) ).
fof(f27,axiom,
! [X18,X19] : c_Binomial_Obinomial(c_Suc(X19),c_Suc(X18)) = c_plus(c_Binomial_Obinomial(X19,X18),c_Binomial_Obinomial(X19,c_Suc(X18)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f24378,plain,
spl0_2083,
inference(avatar_split_clause,[],[f2801,f24376]) ).
fof(f24376,plain,
( spl0_2083
<=> ! [X6,X5] : c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).
fof(f2801,plain,
! [X6,X5] : c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X6,c_Relation_OId,tc_prod(X5,X5)),X5),c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1575,f1581,f1581,f1581]) ).
fof(f1575,axiom,
! [X6,X5] : c_Transitive__Closure_Ortrancl(X6,X5) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X6,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f24374,plain,
spl0_2082,
inference(avatar_split_clause,[],[f1670,f24372]) ).
fof(f24372,plain,
( spl0_2082
<=> ! [X5,X23,X6,X85] :
( ~ c_in(X85,c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23))
| c_Pair(c_Main_OconverseE__2(X6,X85,X23,X5),c_Main_OconverseE__1(X6,X85,X23,X5),X5,X23) = X85 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f1670,axiom,
! [X6,X5,X85,X23] :
( ~ c_in(X85,c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23))
| c_Pair(c_Main_OconverseE__2(X6,X85,X23,X5),c_Main_OconverseE__1(X6,X85,X23,X5),X5,X23) = X85 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f24370,plain,
spl0_2081,
inference(avatar_split_clause,[],[f1181,f24368]) ).
fof(f24368,plain,
( spl0_2081
<=> ! [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_Nat_Opower(c_HOL_Oabs(X4,X5),c_Numeral_Onumber__of(X39,tc_nat),X5) = c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f1181,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_Nat_Opower(c_HOL_Oabs(X4,X5),c_Numeral_Onumber__of(X39,tc_nat),X5) = c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f24366,plain,
spl0_2080,
inference(avatar_split_clause,[],[f691,f24364]) ).
fof(f24364,plain,
( spl0_2080
<=> ! [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_plus(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,X80),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f691,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_plus(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X40,X80),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f24362,plain,
spl0_2079,
inference(avatar_split_clause,[],[f560,f24360]) ).
fof(f24360,plain,
( spl0_2079
<=> ! [X4,X5,X44,X40] :
( c_0 = c_Numeral_Onumber__of(X40,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_Numeral_Onumber__of(X40,tc_nat),X5) = c_List_Onth(X44,c_minus(c_Numeral_Onumber__of(X40,tc_nat),c_1,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f560,axiom,
! [X40,X44,X4,X5] :
( c_0 = c_Numeral_Onumber__of(X40,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X4,X44,X5),c_Numeral_Onumber__of(X40,tc_nat),X5) = c_List_Onth(X44,c_minus(c_Numeral_Onumber__of(X40,tc_nat),c_1,tc_nat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).
fof(f24358,plain,
spl0_2078,
inference(avatar_split_clause,[],[f438,f24356]) ).
fof(f24356,plain,
( spl0_2078
<=> ! [X44,X19,X5,X45] : c_List_Odrop(X19,c_append(X44,X45,X5),X5) = c_append(c_List_Odrop(X19,X44,X5),c_List_Odrop(c_minus(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat),X45,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).
fof(f438,axiom,
! [X19,X44,X45,X5] : c_List_Odrop(X19,c_append(X44,X45,X5),X5) = c_append(c_List_Odrop(X19,X44,X5),c_List_Odrop(c_minus(X19,c_Nat_Osize(X44,tc_List_Olist(X5)),tc_nat),X45,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).
fof(f24354,plain,
spl0_2077,
inference(avatar_split_clause,[],[f436,f24352]) ).
fof(f24352,plain,
( spl0_2077
<=> ! [X44,X4,X40,X5] :
( c_0 = c_Numeral_Onumber__of(X40,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X40,tc_nat),c_List_Olist_OCons(X4,X44,X5),X5) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X40,tc_nat),c_1,tc_nat),X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).
fof(f436,axiom,
! [X40,X44,X4,X5] :
( c_0 = c_Numeral_Onumber__of(X40,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X40,tc_nat),c_List_Olist_OCons(X4,X44,X5),X5) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X40,tc_nat),c_1,tc_nat),X44,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
fof(f24350,plain,
spl0_2076,
inference(avatar_split_clause,[],[f391,f24348]) ).
fof(f24348,plain,
( spl0_2076
<=> ! [X44,X5,X45,X1] :
( ~ c_in(X45,c_List_Olists(X1,X5),tc_List_Olist(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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f391,axiom,
! [X1,X44,X45,X5] :
( ~ c_in(X45,c_List_Olists(X1,X5),tc_List_Olist(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_2) ).
fof(f24345,plain,
spl0_2075,
inference(avatar_split_clause,[],[f312,f24343]) ).
fof(f312,axiom,
! [X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).
fof(f24340,plain,
spl0_2074,
inference(avatar_split_clause,[],[f302,f24338]) ).
fof(f302,axiom,
! [X39] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X39,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).
fof(f24336,plain,
spl0_2073,
inference(avatar_split_clause,[],[f246,f24334]) ).
fof(f24334,plain,
( spl0_2073
<=> ! [X4,X8] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X4,X8,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).
fof(f246,axiom,
! [X8,X4] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X4,X8,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
fof(f24332,plain,
spl0_2072,
inference(avatar_split_clause,[],[f134,f24330]) ).
fof(f24330,plain,
( spl0_2072
<=> ! [X4,X34,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_less(X4,X34,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(X4,c_Finite__Set_OMin(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).
fof(f134,axiom,
! [X1,X4,X34,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_less(X4,X34,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(X4,c_Finite__Set_OMin(X1,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f24328,plain,
spl0_2071,
inference(avatar_split_clause,[],[f131,f24326]) ).
fof(f24326,plain,
( spl0_2071
<=> ! [X4,X34,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_lessequals(X4,X34,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(X4,c_Finite__Set_OMin(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f131,axiom,
! [X1,X4,X34,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_lessequals(X4,X34,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(X4,c_Finite__Set_OMin(X1,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f24324,plain,
spl0_2070,
inference(avatar_split_clause,[],[f127,f24322]) ).
fof(f24322,plain,
( spl0_2070
<=> ! [X4,X34,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_less(X34,X4,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(c_Finite__Set_OMax(X1,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f127,axiom,
! [X1,X4,X34,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_less(X34,X4,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(c_Finite__Set_OMax(X1,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
fof(f24320,plain,
spl0_2069,
inference(avatar_split_clause,[],[f124,f24318]) ).
fof(f24318,plain,
( spl0_2069
<=> ! [X4,X34,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_lessequals(X34,X4,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(c_Finite__Set_OMax(X1,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).
fof(f124,axiom,
! [X1,X4,X34,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X34,X1,X5)
| c_lessequals(X34,X4,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(c_Finite__Set_OMax(X1,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
fof(f24129,plain,
( spl0_2067
| ~ spl0_2068
| ~ spl0_1445
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f22882,f22701,f11686,f24126,f24122]) ).
fof(f24126,plain,
( spl0_2068
<=> c_lessequals(v_A,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2068])]) ).
fof(f11686,plain,
( spl0_1445
<=> ! [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_1445])]) ).
fof(f22882,plain,
( ~ c_lessequals(v_A,v_S,tc_set(t_a))
| v_A = v_S
| ~ spl0_1445
| ~ spl0_2034 ),
inference(resolution,[],[f22703,f11687]) ).
fof(f11687,plain,
( ! [X1,X35,X5] :
( ~ c_lessequals(X35,X1,tc_set(X5))
| ~ c_lessequals(X1,X35,tc_set(X5))
| X1 = X35 )
| ~ spl0_1445 ),
inference(avatar_component_clause,[],[f11686]) ).
fof(f23502,plain,
( spl0_2066
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_2065 ),
inference(avatar_split_clause,[],[f23498,f23495,f18906,f7218,f7182,f23500]) ).
fof(f23500,plain,
( spl0_2066
<=> ! [X39,X23] :
( c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) = c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_plus(c_1,c_1,tc_nat),X23)
| ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).
fof(f23495,plain,
( spl0_2065
<=> ! [X39,X23] :
( c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) = c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X23)
| ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).
fof(f23498,plain,
( ! [X39,X23] :
( c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) = c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_plus(c_1,c_1,tc_nat),X23)
| ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23) )
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_2065 ),
inference(forward_demodulation,[],[f23496,f18994]) ).
fof(f23496,plain,
( ! [X39,X23] :
( c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) = c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X23)
| ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23) )
| ~ spl0_2065 ),
inference(avatar_component_clause,[],[f23495]) ).
fof(f23497,plain,
spl0_2065,
inference(avatar_split_clause,[],[f3130,f23495]) ).
fof(f3130,plain,
! [X39,X23] :
( c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) = c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X23)
| ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23) ),
inference(forward_demodulation,[],[f3129,f1021]) ).
fof(f3129,plain,
! [X39,X23] :
( c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) = c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X23)
| ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23) ),
inference(forward_demodulation,[],[f3128,f1019]) ).
fof(f3128,plain,
! [X39,X23] :
( c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) = c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X23)
| ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23) ),
inference(forward_demodulation,[],[f739,f1021]) ).
fof(f739,axiom,
! [X39,X23] :
( ~ class_Power_Orecpower(X23)
| ~ class_Numeral_Onumber(X23)
| c_Nat_Opower(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X23) = c_times(c_Numeral_Onumber__of(X39,X23),c_Numeral_Onumber__of(X39,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f23493,plain,
spl0_2064,
inference(avatar_split_clause,[],[f3065,f23491]) ).
fof(f23491,plain,
( spl0_2064
<=> ! [X18,X55,X30] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X18,X30,tc_nat),X55,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X30,c_minus(X55,X18,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X18,X55,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).
fof(f3065,plain,
! [X18,X55,X30] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X18,X30,tc_nat),X55,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X30,c_minus(X55,X18,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X18,X55,tc_nat) ),
inference(forward_demodulation,[],[f3064,f2816]) ).
fof(f2816,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(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(f3064,plain,
! [X18,X55,X30] :
( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X55,X18,tc_nat),tc_nat),tc_nat),X30,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X18,X30,tc_nat),X55,tc_nat),tc_nat)
| ~ c_lessequals(X18,X55,tc_nat) ),
inference(forward_demodulation,[],[f2884,f2816]) ).
fof(f2884,plain,
! [X18,X55,X30] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X55,X18,tc_nat),tc_nat),tc_nat),X30,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat),c_plus(X18,X30,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f663,f1409,f1409]) ).
fof(f663,axiom,
! [X18,X55,X30] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_minus(c_Suc(c_minus(X55,X18,tc_nat)),X30,tc_nat) = c_minus(c_Suc(X55),c_plus(X18,X30,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f23489,plain,
spl0_2063,
inference(avatar_split_clause,[],[f3063,f23487]) ).
fof(f23487,plain,
( spl0_2063
<=> ! [X18,X55,X30] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X55,c_plus(X30,X18,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X55,X18,tc_nat),X30,tc_nat),tc_nat)
| ~ c_lessequals(X18,X55,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).
fof(f3063,plain,
! [X18,X55,X30] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X55,c_plus(X30,X18,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X55,X18,tc_nat),X30,tc_nat),tc_nat)
| ~ c_lessequals(X18,X55,tc_nat) ),
inference(forward_demodulation,[],[f3062,f2815]) ).
fof(f2815,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(f3062,plain,
! [X18,X55,X30] :
( c_minus(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X55,X18,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X55,c_plus(X30,X18,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X18,X55,tc_nat) ),
inference(forward_demodulation,[],[f2883,f2815]) ).
fof(f2883,plain,
! [X18,X55,X30] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_minus(X30,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X55,X18,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X30,X18,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X55,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f662,f1409,f1409]) ).
fof(f662,axiom,
! [X18,X55,X30] :
( ~ c_lessequals(X18,X55,tc_nat)
| c_minus(X30,c_Suc(c_minus(X55,X18,tc_nat)),tc_nat) = c_minus(c_plus(X30,X18,tc_nat),c_Suc(X55),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f23438,plain,
( spl0_2062
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2061 ),
inference(avatar_split_clause,[],[f23434,f23431,f10450,f10135,f6752,f3744,f23436]) ).
fof(f23436,plain,
( spl0_2062
<=> ! [X4,X5,X1] :
( c_Finite__Set_Ocard(c_insert(X4,X1,X5),X5) = c_plus(c_1,c_Finite__Set_Ocard(X1,X5),tc_nat)
| c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).
fof(f23431,plain,
( spl0_2061
<=> ! [X4,X5,X1] :
( c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X4,X1,X5),X5) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X1,X5),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).
fof(f23434,plain,
( ! [X1,X4,X5] :
( c_Finite__Set_Ocard(c_insert(X4,X1,X5),X5) = c_plus(c_1,c_Finite__Set_Ocard(X1,X5),tc_nat)
| c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5)) )
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2061 ),
inference(forward_demodulation,[],[f23432,f11244]) ).
fof(f23432,plain,
( ! [X1,X4,X5] :
( c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X4,X1,X5),X5) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X1,X5),tc_nat),tc_nat) )
| ~ spl0_2061 ),
inference(avatar_component_clause,[],[f23431]) ).
fof(f23433,plain,
spl0_2061,
inference(avatar_split_clause,[],[f2942,f23431]) ).
fof(f2942,plain,
! [X1,X4,X5] :
( c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X4,X1,X5),X5) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X1,X5),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f145,f1409]) ).
fof(f145,axiom,
! [X1,X4,X5] :
( c_in(X4,X1,X5)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X4,X1,X5),X5) = c_Suc(c_Finite__Set_Ocard(X1,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f23408,plain,
( spl0_2060
| ~ spl0_801
| ~ spl0_1433
| ~ spl0_2035 ),
inference(avatar_split_clause,[],[f23316,f23051,f11631,f7299,f23405]) ).
fof(f7299,plain,
( spl0_801
<=> ! [X5,X8] : c_union(X8,c_emptyset,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f11631,plain,
( spl0_1433
<=> ! [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_1433])]) ).
fof(f23316,plain,
( v_A = c_union(v_A,v_S,t_a)
| ~ spl0_801
| ~ spl0_1433
| ~ spl0_2035 ),
inference(forward_demodulation,[],[f23302,f7300]) ).
fof(f7300,plain,
( ! [X8,X5] : c_union(X8,c_emptyset,X5) = X8
| ~ spl0_801 ),
inference(avatar_component_clause,[],[f7299]) ).
fof(f23302,plain,
( c_union(v_A,c_emptyset,t_a) = c_union(v_A,v_S,t_a)
| ~ spl0_1433
| ~ spl0_2035 ),
inference(superposition,[],[f11632,f23053]) ).
fof(f11632,plain,
( ! [X1,X35,X5] : c_union(X1,X35,X5) = c_union(X1,c_minus(X35,X1,tc_set(X5)),X5)
| ~ spl0_1433 ),
inference(avatar_component_clause,[],[f11631]) ).
fof(f23403,plain,
( spl0_2059
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2058 ),
inference(avatar_split_clause,[],[f23399,f23396,f10450,f10135,f6752,f3744,f23401]) ).
fof(f23401,plain,
( spl0_2059
<=> ! [X44,X4,X5,X19] : c_List_Olist_OCons(X4,c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),X5) = c_List_Osublist(c_List_Olist_OCons(X4,X44,X5),c_SetInterval_OlessThan(c_plus(c_1,X19,tc_nat),tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).
fof(f23396,plain,
( spl0_2058
<=> ! [X44,X4,X5,X19] : c_List_Osublist(c_List_Olist_OCons(X4,X44,X5),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),X5) = c_List_Olist_OCons(X4,c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).
fof(f23399,plain,
( ! [X44,X19,X4,X5] : c_List_Olist_OCons(X4,c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),X5) = c_List_Osublist(c_List_Olist_OCons(X4,X44,X5),c_SetInterval_OlessThan(c_plus(c_1,X19,tc_nat),tc_nat),X5)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_2058 ),
inference(forward_demodulation,[],[f23397,f11244]) ).
fof(f23397,plain,
( ! [X44,X19,X4,X5] : c_List_Osublist(c_List_Olist_OCons(X4,X44,X5),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),X5) = c_List_Olist_OCons(X4,c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),X5)
| ~ spl0_2058 ),
inference(avatar_component_clause,[],[f23396]) ).
fof(f23398,plain,
spl0_2058,
inference(avatar_split_clause,[],[f2846,f23396]) ).
fof(f2846,plain,
! [X44,X19,X4,X5] : c_List_Osublist(c_List_Olist_OCons(X4,X44,X5),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat),X5) = c_List_Olist_OCons(X4,c_List_Osublist(X44,c_SetInterval_OlessThan(X19,tc_nat),X5),X5),
inference(definition_unfolding,[],[f634,f631,f1409,f631]) ).
fof(f634,axiom,
! [X19,X44,X4,X5] : c_List_Otake(c_Suc(X19),c_List_Olist_OCons(X4,X44,X5),X5) = c_List_Olist_OCons(X4,c_List_Otake(X19,X44,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).
fof(f23394,plain,
spl0_2057,
inference(avatar_split_clause,[],[f1665,f23392]) ).
fof(f23392,plain,
( spl0_2057
<=> ! [X5,X23,X6,X1,X7] :
( ~ c_in(X7,c_Relation_OImage(X6,X1,X23,X5),X5)
| c_in(c_Pair(c_Main_OImageE__1(X1,X7,X6,X23,X5),X7,X23,X5),X6,tc_prod(X23,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).
fof(f1665,axiom,
! [X1,X6,X7,X5,X23] :
( ~ c_in(X7,c_Relation_OImage(X6,X1,X23,X5),X5)
| c_in(c_Pair(c_Main_OImageE__1(X1,X7,X6,X23,X5),X7,X23,X5),X6,tc_prod(X23,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f23390,plain,
spl0_2056,
inference(avatar_split_clause,[],[f1607,f23388]) ).
fof(f23388,plain,
( spl0_2056
<=> ! [X35,X23,X31,X5,X1] :
( ~ c_in(X31,c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OuprodE__1(X1,X35,X31,X5,X23),X1,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f1607,axiom,
! [X31,X1,X35,X5,X23] :
( ~ c_in(X31,c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OuprodE__1(X1,X35,X31,X5,X23),X1,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f23386,plain,
spl0_2055,
inference(avatar_split_clause,[],[f1606,f23384]) ).
fof(f23384,plain,
( spl0_2055
<=> ! [X35,X23,X31,X5,X1] :
( ~ c_in(X31,c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OuprodE__2(X1,X35,X31,X5,X23),X35,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).
fof(f1606,axiom,
! [X31,X1,X35,X5,X23] :
( ~ c_in(X31,c_Datatype__Universe_Ouprod(X1,X35,X5,X23),tc_set(tc_Datatype__Universe_Onode(X5,X23)))
| c_in(c_Main_OuprodE__2(X1,X35,X31,X5,X23),X35,tc_set(tc_Datatype__Universe_Onode(X5,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f23382,plain,
spl0_2054,
inference(avatar_split_clause,[],[f1250,f23380]) ).
fof(f23380,plain,
( spl0_2054
<=> ! [X5,X23,X6,X2,X7] :
( ~ c_in(c_Pair(X7,X2,X23,X5),X6,tc_prod(X23,X5))
| c_in(c_Pair(X2,X7,X5,X23),c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f1250,axiom,
! [X2,X6,X7,X5,X23] :
( ~ c_in(c_Pair(X7,X2,X23,X5),X6,tc_prod(X23,X5))
| c_in(c_Pair(X2,X7,X5,X23),c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
fof(f23378,plain,
spl0_2053,
inference(avatar_split_clause,[],[f1249,f23376]) ).
fof(f23376,plain,
( spl0_2053
<=> ! [X5,X23,X6,X2,X7] :
( c_in(c_Pair(X7,X2,X23,X5),X6,tc_prod(X23,X5))
| ~ c_in(c_Pair(X2,X7,X5,X23),c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).
fof(f1249,axiom,
! [X2,X6,X7,X5,X23] :
( c_in(c_Pair(X7,X2,X23,X5),X6,tc_prod(X23,X5))
| ~ c_in(c_Pair(X2,X7,X5,X23),c_Relation_Oconverse(X6,X23,X5),tc_prod(X5,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
fof(f23374,plain,
spl0_2052,
inference(avatar_split_clause,[],[f1197,f23372]) ).
fof(f23372,plain,
( spl0_2052
<=> ! [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_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_2052])]) ).
fof(f1197,axiom,
! [X39,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_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_1) ).
fof(f23370,plain,
spl0_2051,
inference(avatar_split_clause,[],[f1187,f23368]) ).
fof(f23368,plain,
( spl0_2051
<=> ! [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_0 = c_Numeral_Onumber__of(X39,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f1187,axiom,
! [X39,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_0 = c_Numeral_Onumber__of(X39,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,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_5) ).
fof(f23366,plain,
spl0_2050,
inference(avatar_split_clause,[],[f742,f23364]) ).
fof(f23364,plain,
( spl0_2050
<=> ! [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_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_nat),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f742,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_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X39,tc_nat),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f23362,plain,
( spl0_2049
| ~ spl0_800
| ~ spl0_1432
| ~ spl0_2035 ),
inference(avatar_split_clause,[],[f23315,f23051,f11627,f7295,f23359]) ).
fof(f7295,plain,
( spl0_800
<=> ! [X5,X8] : c_union(c_emptyset,X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f11627,plain,
( spl0_1432
<=> ! [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_1432])]) ).
fof(f23315,plain,
( v_A = c_union(v_S,v_A,t_a)
| ~ spl0_800
| ~ spl0_1432
| ~ spl0_2035 ),
inference(forward_demodulation,[],[f23301,f7296]) ).
fof(f7296,plain,
( ! [X8,X5] : c_union(c_emptyset,X8,X5) = X8
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f7295]) ).
fof(f23301,plain,
( c_union(c_emptyset,v_A,t_a) = c_union(v_S,v_A,t_a)
| ~ spl0_1432
| ~ spl0_2035 ),
inference(superposition,[],[f11628,f23053]) ).
fof(f11628,plain,
( ! [X1,X35,X5] : c_union(c_minus(X35,X1,tc_set(X5)),X1,X5) = c_union(X35,X1,X5)
| ~ spl0_1432 ),
inference(avatar_component_clause,[],[f11627]) ).
fof(f23357,plain,
spl0_2048,
inference(avatar_split_clause,[],[f693,f23355]) ).
fof(f23355,plain,
( spl0_2048
<=> ! [X80,X40] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f693,axiom,
! [X40,X80] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X40,tc_nat),c_Numeral_Onumber__of(X80,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),c_Numeral_Onumber__of(X80,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f23353,plain,
spl0_2047,
inference(avatar_split_clause,[],[f138,f23351]) ).
fof(f23351,plain,
( spl0_2047
<=> ! [X4,X1,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Finite__Set_OMin(c_insert(X4,X1,X23),X23) = c_Orderings_Omin(X4,c_Finite__Set_OMin(X1,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).
fof(f138,axiom,
! [X1,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Finite__Set_OMin(c_insert(X4,X1,X23),X23) = c_Orderings_Omin(X4,c_Finite__Set_OMin(X1,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
fof(f23349,plain,
spl0_2046,
inference(avatar_split_clause,[],[f136,f23347]) ).
fof(f23347,plain,
( spl0_2046
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X4,c_Finite__Set_OMin(X1,X5),X5)
| ~ c_less(X4,c_Main_OMin__gr__iff__1(X1,X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).
fof(f136,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X4,c_Finite__Set_OMin(X1,X5),X5)
| ~ c_less(X4,c_Main_OMin__gr__iff__1(X1,X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f23345,plain,
spl0_2045,
inference(avatar_split_clause,[],[f135,f23343]) ).
fof(f23343,plain,
( spl0_2045
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X4,c_Finite__Set_OMin(X1,X5),X5)
| c_in(c_Main_OMin__gr__iff__1(X1,X4,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f135,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X4,c_Finite__Set_OMin(X1,X5),X5)
| c_in(c_Main_OMin__gr__iff__1(X1,X4,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f23341,plain,
spl0_2044,
inference(avatar_split_clause,[],[f133,f23339]) ).
fof(f23339,plain,
( spl0_2044
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X4,c_Finite__Set_OMin(X1,X5),X5)
| ~ c_lessequals(X4,c_Main_OMin__ge__iff__1(X1,X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).
fof(f133,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X4,c_Finite__Set_OMin(X1,X5),X5)
| ~ c_lessequals(X4,c_Main_OMin__ge__iff__1(X1,X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f23337,plain,
spl0_2043,
inference(avatar_split_clause,[],[f132,f23335]) ).
fof(f23335,plain,
( spl0_2043
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X4,c_Finite__Set_OMin(X1,X5),X5)
| c_in(c_Main_OMin__ge__iff__1(X1,X4,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).
fof(f132,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X4,c_Finite__Set_OMin(X1,X5),X5)
| c_in(c_Main_OMin__ge__iff__1(X1,X4,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f23333,plain,
spl0_2042,
inference(avatar_split_clause,[],[f129,f23331]) ).
fof(f23331,plain,
( spl0_2042
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X1,X5),X4,X5)
| ~ c_less(c_Main_OMax__less__iff__1(X1,X4,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).
fof(f129,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X1,X5),X4,X5)
| ~ c_less(c_Main_OMax__less__iff__1(X1,X4,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
fof(f23329,plain,
spl0_2041,
inference(avatar_split_clause,[],[f128,f23327]) ).
fof(f23327,plain,
( spl0_2041
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X1,X5),X4,X5)
| c_in(c_Main_OMax__less__iff__1(X1,X4,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).
fof(f128,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X1,X5),X4,X5)
| c_in(c_Main_OMax__less__iff__1(X1,X4,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
fof(f23325,plain,
spl0_2040,
inference(avatar_split_clause,[],[f126,f23323]) ).
fof(f23323,plain,
( spl0_2040
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X1,X5),X4,X5)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X4,X5),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).
fof(f126,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X1,X5),X4,X5)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X1,X4,X5),X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
fof(f23321,plain,
spl0_2039,
inference(avatar_split_clause,[],[f125,f23319]) ).
fof(f23319,plain,
( spl0_2039
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X1,X5),X4,X5)
| c_in(c_Main_OMax__le__iff__1(X1,X4,X5),X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).
fof(f125,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X1,X5),X4,X5)
| c_in(c_Main_OMax__le__iff__1(X1,X4,X5),X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
fof(f23297,plain,
spl0_2038,
inference(avatar_split_clause,[],[f123,f23295]) ).
fof(f23295,plain,
( spl0_2038
<=> ! [X4,X1,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Finite__Set_OMax(c_insert(X4,X1,X23),X23) = c_Orderings_Omax(X4,c_Finite__Set_OMax(X1,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f123,axiom,
! [X1,X4,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_emptyset = X1
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X23))
| c_Finite__Set_OMax(c_insert(X4,X1,X23),X23) = c_Orderings_Omax(X4,c_Finite__Set_OMax(X1,X23),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
fof(f23293,plain,
spl0_2037,
inference(avatar_split_clause,[],[f6,f23291]) ).
fof(f23291,plain,
( spl0_2037
<=> ! [X6,X4,X0,X5,X2,X7] :
( ~ c_in(X4,X0,X5)
| ~ c_lessequals(X0,c_Tarski_Ointerval(X6,X2,X7,X5),tc_set(X5))
| c_in(c_Pair(X4,X7,X5,X5),X6,tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).
fof(f6,axiom,
! [X2,X0,X6,X7,X4,X5] :
( ~ c_in(X4,X0,X5)
| ~ c_lessequals(X0,c_Tarski_Ointerval(X6,X2,X7,X5),tc_set(X5))
| c_in(c_Pair(X4,X7,X5,X5),X6,tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0) ).
fof(f23289,plain,
spl0_2036,
inference(avatar_split_clause,[],[f5,f23287]) ).
fof(f23287,plain,
( spl0_2036
<=> ! [X6,X4,X0,X5,X2,X7] :
( ~ c_in(X4,X0,X5)
| ~ c_lessequals(X0,c_Tarski_Ointerval(X6,X2,X7,X5),tc_set(X5))
| c_in(c_Pair(X2,X4,X5,X5),X6,tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f5,axiom,
! [X2,X0,X6,X7,X4,X5] :
( ~ c_in(X4,X0,X5)
| ~ c_lessequals(X0,c_Tarski_Ointerval(X6,X2,X7,X5),tc_set(X5))
| c_in(c_Pair(X2,X4,X5,X5),X6,tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) ).
fof(f23054,plain,
( spl0_2035
| ~ spl0_1323
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f22885,f22701,f10366,f23051]) ).
fof(f10366,plain,
( spl0_1323
<=> ! [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_1323])]) ).
fof(f22885,plain,
( c_emptyset = c_minus(v_S,v_A,tc_set(t_a))
| ~ spl0_1323
| ~ spl0_2034 ),
inference(resolution,[],[f22703,f10367]) ).
fof(f10367,plain,
( ! [X1,X35,X5] :
( ~ c_lessequals(X1,X35,tc_set(X5))
| c_emptyset = c_minus(X1,X35,tc_set(X5)) )
| ~ spl0_1323 ),
inference(avatar_component_clause,[],[f10366]) ).
fof(f22704,plain,
( ~ spl0_2
| spl0_2034
| ~ spl0_3
| ~ spl0_99
| ~ spl0_2003 ),
inference(avatar_split_clause,[],[f22629,f22487,f3665,f3185,f22701,f3180]) ).
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(f22487,plain,
( spl0_2003
<=> ! [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_2003])]) ).
fof(f22629,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_2003 ),
inference(resolution,[],[f22488,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(f22488,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_2003 ),
inference(avatar_component_clause,[],[f22487]) ).
fof(f22621,plain,
spl0_2033,
inference(avatar_split_clause,[],[f2951,f22619]) ).
fof(f22619,plain,
( spl0_2033
<=> ! [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_2033])]) ).
fof(f2951,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(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(f22617,plain,
spl0_2032,
inference(avatar_split_clause,[],[f2950,f22615]) ).
fof(f22615,plain,
( spl0_2032
<=> ! [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_2032])]) ).
fof(f2950,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(f22613,plain,
spl0_2031,
inference(avatar_split_clause,[],[f2923,f22611]) ).
fof(f22611,plain,
( spl0_2031
<=> ! [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_2031])]) ).
fof(f2923,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(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(f22609,plain,
spl0_2030,
inference(avatar_split_clause,[],[f2813,f22607]) ).
fof(f22607,plain,
( spl0_2030
<=> ! [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_2030])]) ).
fof(f2813,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(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(f22605,plain,
spl0_2029,
inference(avatar_split_clause,[],[f1713,f22603]) ).
fof(f22603,plain,
( spl0_2029
<=> ! [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_2029])]) ).
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(f22601,plain,
spl0_2028,
inference(avatar_split_clause,[],[f1666,f22599]) ).
fof(f22599,plain,
( spl0_2028
<=> ! [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_2028])]) ).
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(f22597,plain,
spl0_2027,
inference(avatar_split_clause,[],[f1427,f22595]) ).
fof(f22595,plain,
( spl0_2027
<=> ! [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_2027])]) ).
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(f22593,plain,
( spl0_2026
| ~ spl0_1707
| ~ spl0_1991 ),
inference(avatar_split_clause,[],[f21662,f21579,f16135,f22591]) ).
fof(f22591,plain,
( spl0_2026
<=> ! [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_2026])]) ).
fof(f16135,plain,
( spl0_1707
<=> ! [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_1707])]) ).
fof(f21579,plain,
( spl0_1991
<=> v_A = c_insert(v_a,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f21662,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_1707
| ~ spl0_1991 ),
inference(superposition,[],[f16136,f21581]) ).
fof(f21581,plain,
( v_A = c_insert(v_a,v_A,t_a)
| ~ spl0_1991 ),
inference(avatar_component_clause,[],[f21579]) ).
fof(f16136,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_1707 ),
inference(avatar_component_clause,[],[f16135]) ).
fof(f22589,plain,
spl0_2025,
inference(avatar_split_clause,[],[f1221,f22587]) ).
fof(f22587,plain,
( spl0_2025
<=> ! [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_2025])]) ).
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(f22585,plain,
spl0_2024,
inference(avatar_split_clause,[],[f1220,f22583]) ).
fof(f22583,plain,
( spl0_2024
<=> ! [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_2024])]) ).
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(f22581,plain,
spl0_2023,
inference(avatar_split_clause,[],[f1216,f22579]) ).
fof(f22579,plain,
( spl0_2023
<=> ! [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_2023])]) ).
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(f22577,plain,
spl0_2022,
inference(avatar_split_clause,[],[f1215,f22575]) ).
fof(f22575,plain,
( spl0_2022
<=> ! [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_2022])]) ).
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(f22573,plain,
spl0_2021,
inference(avatar_split_clause,[],[f1201,f22571]) ).
fof(f22571,plain,
( spl0_2021
<=> ! [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_2021])]) ).
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(f22569,plain,
spl0_2020,
inference(avatar_split_clause,[],[f1198,f22567]) ).
fof(f22567,plain,
( spl0_2020
<=> ! [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_2020])]) ).
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(f22565,plain,
spl0_2019,
inference(avatar_split_clause,[],[f1195,f22563]) ).
fof(f22563,plain,
( spl0_2019
<=> ! [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_2019])]) ).
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(f22561,plain,
spl0_2018,
inference(avatar_split_clause,[],[f1193,f22559]) ).
fof(f22559,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(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(f22557,plain,
spl0_2017,
inference(avatar_split_clause,[],[f1190,f22555]) ).
fof(f22555,plain,
( spl0_2017
<=> ! [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_2017])]) ).
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(f22553,plain,
spl0_2016,
inference(avatar_split_clause,[],[f1184,f22551]) ).
fof(f22551,plain,
( spl0_2016
<=> ! [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_2016])]) ).
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(f22543,plain,
spl0_2015,
inference(avatar_split_clause,[],[f1033,f22541]) ).
fof(f22541,plain,
( spl0_2015
<=> ! [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_2015])]) ).
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(f22539,plain,
spl0_2014,
inference(avatar_split_clause,[],[f973,f22537]) ).
fof(f22537,plain,
( spl0_2014
<=> ! [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_2014])]) ).
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(f22535,plain,
spl0_2013,
inference(avatar_split_clause,[],[f726,f22533]) ).
fof(f22533,plain,
( spl0_2013
<=> ! [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_2013])]) ).
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(f22531,plain,
spl0_2012,
inference(avatar_split_clause,[],[f699,f22529]) ).
fof(f22529,plain,
( spl0_2012
<=> ! [X80,X40] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X80,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_2012])]) ).
fof(f699,axiom,
! [X40,X80] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X40,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X80,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_0) ).
fof(f22527,plain,
spl0_2011,
inference(avatar_split_clause,[],[f690,f22525]) ).
fof(f22525,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_plus(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(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(f22523,plain,
spl0_2010,
inference(avatar_split_clause,[],[f500,f22521]) ).
fof(f22521,plain,
( spl0_2010
<=> ! [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_2010])]) ).
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(f22519,plain,
spl0_2009,
inference(avatar_split_clause,[],[f499,f22517]) ).
fof(f22517,plain,
( spl0_2009
<=> ! [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_2009])]) ).
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(f22515,plain,
spl0_2008,
inference(avatar_split_clause,[],[f220,f22513]) ).
fof(f22513,plain,
( spl0_2008
<=> ! [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_2008])]) ).
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(f22511,plain,
spl0_2007,
inference(avatar_split_clause,[],[f159,f22509]) ).
fof(f22509,plain,
( spl0_2007
<=> ! [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_2007])]) ).
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(f22507,plain,
spl0_2006,
inference(avatar_split_clause,[],[f158,f22505]) ).
fof(f22505,plain,
( spl0_2006
<=> ! [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_2006])]) ).
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(f22497,plain,
spl0_2005,
inference(avatar_split_clause,[],[f87,f22495]) ).
fof(f22495,plain,
( spl0_2005
<=> ! [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_2005])]) ).
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(f22493,plain,
spl0_2004,
inference(avatar_split_clause,[],[f85,f22491]) ).
fof(f22491,plain,
( spl0_2004
<=> ! [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_2004])]) ).
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(f22489,plain,
spl0_2003,
inference(avatar_split_clause,[],[f8,f22487]) ).
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(f21893,plain,
( spl0_2002
| ~ spl0_1334
| ~ spl0_1991 ),
inference(avatar_split_clause,[],[f21656,f21579,f10410,f21891]) ).
fof(f21891,plain,
( spl0_2002
<=> ! [X0] :
( v_A != c_insert(X0,c_emptyset,t_a)
| v_a = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f10410,plain,
( spl0_1334
<=> ! [X7,X5,X2,X1] :
( X2 = X7
| c_insert(X2,X1,X5) != c_insert(X7,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f21656,plain,
( ! [X0] :
( v_A != c_insert(X0,c_emptyset,t_a)
| v_a = X0 )
| ~ spl0_1334
| ~ spl0_1991 ),
inference(superposition,[],[f10411,f21581]) ).
fof(f10411,plain,
( ! [X2,X1,X7,X5] :
( c_insert(X2,X1,X5) != c_insert(X7,c_emptyset,X5)
| X2 = X7 )
| ~ spl0_1334 ),
inference(avatar_component_clause,[],[f10410]) ).
fof(f21889,plain,
( spl0_2001
| ~ spl0_1333
| ~ spl0_1991 ),
inference(avatar_split_clause,[],[f21655,f21579,f10406,f21887]) ).
fof(f21887,plain,
( spl0_2001
<=> ! [X0] :
( ~ c_lessequals(v_A,X0,tc_set(t_a))
| c_in(v_a,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f10406,plain,
( spl0_1333
<=> ! [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_1333])]) ).
fof(f21655,plain,
( ! [X0] :
( ~ c_lessequals(v_A,X0,tc_set(t_a))
| c_in(v_a,X0,t_a) )
| ~ spl0_1333
| ~ spl0_1991 ),
inference(superposition,[],[f10407,f21581]) ).
fof(f10407,plain,
( ! [X1,X4,X5,X35] :
( ~ c_lessequals(c_insert(X4,X1,X5),X35,tc_set(X5))
| c_in(X4,X35,X5) )
| ~ spl0_1333 ),
inference(avatar_component_clause,[],[f10406]) ).
fof(f21885,plain,
( ~ spl0_2000
| ~ spl0_802
| ~ spl0_1991 ),
inference(avatar_split_clause,[],[f21651,f21579,f7303,f21882]) ).
fof(f21882,plain,
( spl0_2000
<=> c_emptyset = v_A ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f7303,plain,
( spl0_802
<=> ! [X2,X5,X1] : c_emptyset != c_insert(X2,X1,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f21651,plain,
( c_emptyset != v_A
| ~ spl0_802
| ~ spl0_1991 ),
inference(superposition,[],[f7304,f21581]) ).
fof(f7304,plain,
( ! [X2,X1,X5] : c_emptyset != c_insert(X2,X1,X5)
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f7303]) ).
fof(f21640,plain,
( spl0_1999
| ~ spl0_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_1998 ),
inference(avatar_split_clause,[],[f21636,f21632,f18906,f7218,f7182,f21638]) ).
fof(f21638,plain,
( spl0_1999
<=> ! [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_1999])]) ).
fof(f21632,plain,
( spl0_1998
<=> ! [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_1998])]) ).
fof(f21636,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_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_1998 ),
inference(forward_demodulation,[],[f21635,f18994]) ).
fof(f21635,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_772
| ~ spl0_781
| ~ spl0_1852
| ~ spl0_1998 ),
inference(forward_demodulation,[],[f21633,f18994]) ).
fof(f21633,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_1998 ),
inference(avatar_component_clause,[],[f21632]) ).
fof(f21634,plain,
spl0_1998,
inference(avatar_split_clause,[],[f3116,f21632]) ).
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(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(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(f21607,plain,
( spl0_1997
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1996 ),
inference(avatar_split_clause,[],[f21603,f21600,f10450,f10135,f6752,f3744,f21605]) ).
fof(f21605,plain,
( spl0_1997
<=> ! [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_1997])]) ).
fof(f21600,plain,
( spl0_1996
<=> ! [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_1996])]) ).
fof(f21603,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1996 ),
inference(forward_demodulation,[],[f21601,f11244]) ).
fof(f21601,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_1996 ),
inference(avatar_component_clause,[],[f21600]) ).
fof(f21602,plain,
spl0_1996,
inference(avatar_split_clause,[],[f3022,f21600]) ).
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,[],[f2847,f2816]) ).
fof(f2847,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(f21598,plain,
spl0_1995,
inference(avatar_split_clause,[],[f2972,f21596]) ).
fof(f21596,plain,
( spl0_1995
<=> ! [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_1995])]) ).
fof(f2972,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(f21594,plain,
spl0_1994,
inference(avatar_split_clause,[],[f2971,f21592]) ).
fof(f21592,plain,
( spl0_1994
<=> ! [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_1994])]) ).
fof(f2971,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(f21590,plain,
spl0_1993,
inference(avatar_split_clause,[],[f2970,f21588]) ).
fof(f21588,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(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_1993])]) ).
fof(f2970,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(f21586,plain,
spl0_1992,
inference(avatar_split_clause,[],[f2969,f21584]) ).
fof(f21584,plain,
( spl0_1992
<=> ! [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_1992])]) ).
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(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(f21582,plain,
( spl0_1991
| ~ spl0_799
| ~ spl0_1915
| ~ spl0_1951 ),
inference(avatar_split_clause,[],[f21438,f21268,f20999,f7291,f21579]) ).
fof(f7291,plain,
( spl0_799
<=> ! [X5,X8] : c_union(X8,X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f20999,plain,
( spl0_1915
<=> ! [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_1915])]) ).
fof(f21268,plain,
( spl0_1951
<=> ! [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_1951])]) ).
fof(f21438,plain,
( v_A = c_insert(v_a,v_A,t_a)
| ~ spl0_799
| ~ spl0_1915
| ~ spl0_1951 ),
inference(forward_demodulation,[],[f21437,f7292]) ).
fof(f7292,plain,
( ! [X8,X5] : c_union(X8,X8,X5) = X8
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7291]) ).
fof(f21437,plain,
( c_insert(v_a,v_A,t_a) = c_union(v_A,v_A,t_a)
| ~ spl0_799
| ~ spl0_1915
| ~ spl0_1951 ),
inference(forward_demodulation,[],[f21415,f21000]) ).
fof(f21000,plain,
( ! [X0] : c_union(c_insert(v_a,X0,t_a),v_A,t_a) = c_union(X0,v_A,t_a)
| ~ spl0_1915 ),
inference(avatar_component_clause,[],[f20999]) ).
fof(f21415,plain,
( c_insert(v_a,v_A,t_a) = c_union(c_insert(v_a,v_A,t_a),v_A,t_a)
| ~ spl0_799
| ~ spl0_1951 ),
inference(superposition,[],[f21269,f7292]) ).
fof(f21269,plain,
( ! [X0] : c_union(X0,v_A,t_a) = c_union(X0,c_insert(v_a,v_A,t_a),t_a)
| ~ spl0_1951 ),
inference(avatar_component_clause,[],[f21268]) ).
fof(f21577,plain,
spl0_1990,
inference(avatar_split_clause,[],[f2949,f21575]) ).
fof(f21575,plain,
( spl0_1990
<=> ! [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_1990])]) ).
fof(f2949,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(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(f21573,plain,
spl0_1989,
inference(avatar_split_clause,[],[f2920,f21571]) ).
fof(f21571,plain,
( spl0_1989
<=> ! [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_1989])]) ).
fof(f2920,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,[],[f1543,f1238,f1238]) ).
fof(f1543,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__1_1) ).
fof(f21569,plain,
spl0_1988,
inference(avatar_split_clause,[],[f2918,f21567]) ).
fof(f21567,plain,
( spl0_1988
<=> ! [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_1988])]) ).
fof(f2918,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(f21493,plain,
( spl0_1987
| ~ spl0_116
| ~ spl0_674
| ~ spl0_766
| ~ spl0_772
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1697
| ~ spl0_1986 ),
inference(avatar_split_clause,[],[f21489,f21485,f16036,f10450,f10135,f7182,f7158,f6752,f3744,f21491]) ).
fof(f21491,plain,
( spl0_1987
<=> ! [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_1987])]) ).
fof(f7158,plain,
( spl0_766
<=> ! [X4,X21] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X4,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f16036,plain,
( spl0_1697
<=> ! [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_1697])]) ).
fof(f21485,plain,
( spl0_1986
<=> ! [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_1986])]) ).
fof(f21489,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_116
| ~ spl0_674
| ~ spl0_766
| ~ spl0_772
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1697
| ~ spl0_1986 ),
inference(forward_demodulation,[],[f21488,f16062]) ).
fof(f16062,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_766
| ~ spl0_772
| ~ spl0_1697 ),
inference(forward_demodulation,[],[f16039,f7183]) ).
fof(f16039,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_766
| ~ spl0_1697 ),
inference(superposition,[],[f16037,f7159]) ).
fof(f7159,plain,
( ! [X21,X4] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X4,X21)
| ~ spl0_766 ),
inference(avatar_component_clause,[],[f7158]) ).
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_1697 ),
inference(avatar_component_clause,[],[f16036]) ).
fof(f21488,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1986 ),
inference(forward_demodulation,[],[f21486,f11244]) ).
fof(f21486,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_1986 ),
inference(avatar_component_clause,[],[f21485]) ).
fof(f21487,plain,
spl0_1986,
inference(avatar_split_clause,[],[f2882,f21485]) ).
fof(f2882,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(f21483,plain,
spl0_1985,
inference(avatar_split_clause,[],[f2849,f21481]) ).
fof(f21481,plain,
( spl0_1985
<=> ! [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_1985])]) ).
fof(f2849,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(f21479,plain,
spl0_1984,
inference(avatar_split_clause,[],[f2848,f21477]) ).
fof(f21477,plain,
( spl0_1984
<=> ! [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_1984])]) ).
fof(f2848,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(f21475,plain,
spl0_1983,
inference(avatar_split_clause,[],[f2842,f21473]) ).
fof(f21473,plain,
( spl0_1983
<=> ! [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_1983])]) ).
fof(f2842,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(f21414,plain,
( spl0_1982
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f21410,f21405,f10450,f10135,f6752,f3744,f21412]) ).
fof(f21412,plain,
( spl0_1982
<=> ! [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_1982])]) ).
fof(f21405,plain,
( spl0_1981
<=> ! [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_1981])]) ).
fof(f21410,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f21409,f11244]) ).
fof(f21409,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f21408,f11244]) ).
fof(f21408,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1981 ),
inference(forward_demodulation,[],[f21406,f11244]) ).
fof(f21406,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_1981 ),
inference(avatar_component_clause,[],[f21405]) ).
fof(f21407,plain,
spl0_1981,
inference(avatar_split_clause,[],[f2818,f21405]) ).
fof(f2818,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(f21389,plain,
( spl0_1980
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1979 ),
inference(avatar_split_clause,[],[f21385,f21380,f10450,f10135,f6752,f3744,f21387]) ).
fof(f21387,plain,
( spl0_1980
<=> ! [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_1980])]) ).
fof(f21380,plain,
( spl0_1979
<=> ! [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_1979])]) ).
fof(f21385,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21384,f11244]) ).
fof(f21384,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21383,f11244]) ).
fof(f21383,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1979 ),
inference(forward_demodulation,[],[f21381,f11244]) ).
fof(f21381,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_1979 ),
inference(avatar_component_clause,[],[f21380]) ).
fof(f21382,plain,
spl0_1979,
inference(avatar_split_clause,[],[f2817,f21380]) ).
fof(f2817,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(f21378,plain,
spl0_1978,
inference(avatar_split_clause,[],[f1671,f21376]) ).
fof(f21376,plain,
( spl0_1978
<=> ! [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_1978])]) ).
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(f21374,plain,
spl0_1977,
inference(avatar_split_clause,[],[f1667,f21372]) ).
fof(f21372,plain,
( spl0_1977
<=> ! [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_1977])]) ).
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(f21370,plain,
spl0_1976,
inference(avatar_split_clause,[],[f1661,f21368]) ).
fof(f21368,plain,
( spl0_1976
<=> ! [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_1976])]) ).
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(f21366,plain,
spl0_1975,
inference(avatar_split_clause,[],[f1652,f21364]) ).
fof(f21364,plain,
( spl0_1975
<=> ! [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_1975])]) ).
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(f21362,plain,
spl0_1974,
inference(avatar_split_clause,[],[f1614,f21360]) ).
fof(f21360,plain,
( spl0_1974
<=> ! [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_1974])]) ).
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(f21358,plain,
( spl0_1973
| ~ spl0_1026
| ~ spl0_1920 ),
inference(avatar_split_clause,[],[f21214,f21108,f8400,f21356]) ).
fof(f21356,plain,
( spl0_1973
<=> ! [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_1973])]) ).
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(f21108,plain,
( spl0_1920
<=> ! [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_1920])]) ).
fof(f21214,plain,
( ! [X0] :
( c_emptyset != c_union(v_A,X0,t_a)
| c_emptyset = c_insert(v_a,X0,t_a) )
| ~ spl0_1026
| ~ spl0_1920 ),
inference(superposition,[],[f8401,f21109]) ).
fof(f21109,plain,
( ! [X0] : c_union(v_A,c_insert(v_a,X0,t_a),t_a) = c_union(v_A,X0,t_a)
| ~ spl0_1920 ),
inference(avatar_component_clause,[],[f21108]) ).
fof(f8401,plain,
( ! [X1,X35,X5] :
( c_emptyset != c_union(X1,X35,X5)
| c_emptyset = X35 )
| ~ spl0_1026 ),
inference(avatar_component_clause,[],[f8400]) ).
fof(f21354,plain,
spl0_1972,
inference(avatar_split_clause,[],[f1613,f21352]) ).
fof(f21352,plain,
( spl0_1972
<=> ! [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_1972])]) ).
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(f21350,plain,
spl0_1971,
inference(avatar_split_clause,[],[f1431,f21348]) ).
fof(f21348,plain,
( spl0_1971
<=> ! [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_1971])]) ).
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(f21346,plain,
spl0_1970,
inference(avatar_split_clause,[],[f1429,f21344]) ).
fof(f21344,plain,
( spl0_1970
<=> ! [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_1970])]) ).
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(f21342,plain,
spl0_1969,
inference(avatar_split_clause,[],[f1428,f21340]) ).
fof(f21340,plain,
( spl0_1969
<=> ! [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_1969])]) ).
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(f21338,plain,
spl0_1968,
inference(avatar_split_clause,[],[f1241,f21336]) ).
fof(f21336,plain,
( spl0_1968
<=> ! [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_1968])]) ).
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(f21334,plain,
spl0_1967,
inference(avatar_split_clause,[],[f1240,f21332]) ).
fof(f21332,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(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(f21330,plain,
spl0_1966,
inference(avatar_split_clause,[],[f1200,f21328]) ).
fof(f21328,plain,
( spl0_1966
<=> ! [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_1966])]) ).
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(f21326,plain,
spl0_1965,
inference(avatar_split_clause,[],[f1183,f21324]) ).
fof(f21324,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_lessequals(c_Nat_Opower(X4,c_Numeral_Onumber__of(X39,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
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(f21322,plain,
spl0_1964,
inference(avatar_split_clause,[],[f1039,f21320]) ).
fof(f21320,plain,
( spl0_1964
<=> ! [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_1964])]) ).
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(f21318,plain,
spl0_1963,
inference(avatar_split_clause,[],[f986,f21316]) ).
fof(f21316,plain,
( spl0_1963
<=> ! [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_1963])]) ).
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(f21314,plain,
( spl0_1962
| ~ spl0_1025
| ~ spl0_1915 ),
inference(avatar_split_clause,[],[f21155,f20999,f8396,f21312]) ).
fof(f21312,plain,
( spl0_1962
<=> ! [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_1962])]) ).
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(f21155,plain,
( ! [X0] :
( c_emptyset != c_union(X0,v_A,t_a)
| c_emptyset = c_insert(v_a,X0,t_a) )
| ~ spl0_1025
| ~ spl0_1915 ),
inference(superposition,[],[f8397,f21000]) ).
fof(f8397,plain,
( ! [X1,X35,X5] :
( c_emptyset != c_union(X1,X35,X5)
| c_emptyset = X1 )
| ~ spl0_1025 ),
inference(avatar_component_clause,[],[f8396]) ).
fof(f21310,plain,
spl0_1961,
inference(avatar_split_clause,[],[f675,f21308]) ).
fof(f21308,plain,
( spl0_1961
<=> ! [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_1961])]) ).
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(f21306,plain,
spl0_1960,
inference(avatar_split_clause,[],[f537,f21304]) ).
fof(f21304,plain,
( spl0_1960
<=> ! [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_1960])]) ).
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(f21302,plain,
spl0_1959,
inference(avatar_split_clause,[],[f536,f21300]) ).
fof(f21300,plain,
( spl0_1959
<=> ! [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_1959])]) ).
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(f21298,plain,
spl0_1958,
inference(avatar_split_clause,[],[f535,f21296]) ).
fof(f21296,plain,
( spl0_1958
<=> ! [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_1958])]) ).
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(f21294,plain,
spl0_1957,
inference(avatar_split_clause,[],[f534,f21292]) ).
fof(f21292,plain,
( spl0_1957
<=> ! [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_1957])]) ).
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(f21290,plain,
spl0_1956,
inference(avatar_split_clause,[],[f533,f21288]) ).
fof(f21288,plain,
( spl0_1956
<=> ! [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_1956])]) ).
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(f21286,plain,
spl0_1955,
inference(avatar_split_clause,[],[f532,f21284]) ).
fof(f21284,plain,
( spl0_1955
<=> ! [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_1955])]) ).
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(f21282,plain,
spl0_1954,
inference(avatar_split_clause,[],[f531,f21280]) ).
fof(f21280,plain,
( spl0_1954
<=> ! [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_1954])]) ).
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(f21278,plain,
spl0_1953,
inference(avatar_split_clause,[],[f530,f21276]) ).
fof(f21276,plain,
( spl0_1953
<=> ! [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_1953])]) ).
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(f21274,plain,
spl0_1952,
inference(avatar_split_clause,[],[f529,f21272]) ).
fof(f21272,plain,
( spl0_1952
<=> ! [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_1952])]) ).
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(f21270,plain,
( spl0_1951
| ~ spl0_1615
| ~ spl0_1915 ),
inference(avatar_split_clause,[],[f21154,f20999,f14492,f21268]) ).
fof(f14492,plain,
( spl0_1615
<=> ! [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_1615])]) ).
fof(f21154,plain,
( ! [X0] : c_union(X0,v_A,t_a) = c_union(X0,c_insert(v_a,v_A,t_a),t_a)
| ~ spl0_1615
| ~ spl0_1915 ),
inference(superposition,[],[f21000,f14493]) ).
fof(f14493,plain,
( ! [X2,X83,X35,X5] : c_union(c_insert(X2,X35,X5),X83,X5) = c_union(X35,c_insert(X2,X83,X5),X5)
| ~ spl0_1615 ),
inference(avatar_component_clause,[],[f14492]) ).
fof(f21266,plain,
spl0_1950,
inference(avatar_split_clause,[],[f528,f21264]) ).
fof(f21264,plain,
( spl0_1950
<=> ! [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_1950])]) ).
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(f21262,plain,
spl0_1949,
inference(avatar_split_clause,[],[f527,f21260]) ).
fof(f21260,plain,
( spl0_1949
<=> ! [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_1949])]) ).
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(f21258,plain,
spl0_1948,
inference(avatar_split_clause,[],[f526,f21256]) ).
fof(f21256,plain,
( spl0_1948
<=> ! [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_1948])]) ).
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(f21254,plain,
spl0_1947,
inference(avatar_split_clause,[],[f525,f21252]) ).
fof(f21252,plain,
( spl0_1947
<=> ! [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_1947])]) ).
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(f21250,plain,
spl0_1946,
inference(avatar_split_clause,[],[f524,f21248]) ).
fof(f21248,plain,
( spl0_1946
<=> ! [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_1946])]) ).
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(f21246,plain,
spl0_1945,
inference(avatar_split_clause,[],[f523,f21244]) ).
fof(f21244,plain,
( spl0_1945
<=> ! [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_1945])]) ).
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(f21242,plain,
spl0_1944,
inference(avatar_split_clause,[],[f522,f21240]) ).
fof(f21240,plain,
( spl0_1944
<=> ! [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_1944])]) ).
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(f21238,plain,
spl0_1943,
inference(avatar_split_clause,[],[f521,f21236]) ).
fof(f21236,plain,
( spl0_1943
<=> ! [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_1943])]) ).
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(f21234,plain,
spl0_1942,
inference(avatar_split_clause,[],[f520,f21232]) ).
fof(f21232,plain,
( spl0_1942
<=> ! [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_1942])]) ).
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(f21230,plain,
spl0_1941,
inference(avatar_split_clause,[],[f519,f21228]) ).
fof(f21228,plain,
( spl0_1941
<=> ! [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_1941])]) ).
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(f21209,plain,
spl0_1940,
inference(avatar_split_clause,[],[f518,f21207]) ).
fof(f21207,plain,
( spl0_1940
<=> ! [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_1940])]) ).
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(f21205,plain,
spl0_1939,
inference(avatar_split_clause,[],[f517,f21203]) ).
fof(f21203,plain,
( spl0_1939
<=> ! [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_1939])]) ).
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(f21201,plain,
spl0_1938,
inference(avatar_split_clause,[],[f516,f21199]) ).
fof(f21199,plain,
( spl0_1938
<=> ! [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_1938])]) ).
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(f21197,plain,
spl0_1937,
inference(avatar_split_clause,[],[f515,f21195]) ).
fof(f21195,plain,
( spl0_1937
<=> ! [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_1937])]) ).
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(f21193,plain,
spl0_1936,
inference(avatar_split_clause,[],[f514,f21191]) ).
fof(f21191,plain,
( spl0_1936
<=> ! [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_1936])]) ).
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(f21189,plain,
spl0_1935,
inference(avatar_split_clause,[],[f513,f21187]) ).
fof(f21187,plain,
( spl0_1935
<=> ! [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_1935])]) ).
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(f21185,plain,
spl0_1934,
inference(avatar_split_clause,[],[f512,f21183]) ).
fof(f21183,plain,
( spl0_1934
<=> ! [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_1934])]) ).
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(f21181,plain,
spl0_1933,
inference(avatar_split_clause,[],[f511,f21179]) ).
fof(f21179,plain,
( spl0_1933
<=> ! [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_1933])]) ).
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(f21177,plain,
spl0_1932,
inference(avatar_split_clause,[],[f510,f21175]) ).
fof(f21175,plain,
( spl0_1932
<=> ! [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_1932])]) ).
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(f21173,plain,
spl0_1931,
inference(avatar_split_clause,[],[f509,f21171]) ).
fof(f21171,plain,
( spl0_1931
<=> ! [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_1931])]) ).
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(f21150,plain,
spl0_1930,
inference(avatar_split_clause,[],[f508,f21148]) ).
fof(f21148,plain,
( spl0_1930
<=> ! [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_1930])]) ).
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(f21146,plain,
spl0_1929,
inference(avatar_split_clause,[],[f507,f21144]) ).
fof(f21144,plain,
( spl0_1929
<=> ! [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_1929])]) ).
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(f21142,plain,
spl0_1928,
inference(avatar_split_clause,[],[f506,f21140]) ).
fof(f21140,plain,
( spl0_1928
<=> ! [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_1928])]) ).
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(f21138,plain,
spl0_1927,
inference(avatar_split_clause,[],[f494,f21136]) ).
fof(f21136,plain,
( spl0_1927
<=> ! [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_1927])]) ).
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(f21134,plain,
spl0_1926,
inference(avatar_split_clause,[],[f479,f21132]) ).
fof(f21132,plain,
( spl0_1926
<=> ! [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_1926])]) ).
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(f21130,plain,
spl0_1925,
inference(avatar_split_clause,[],[f388,f21128]) ).
fof(f21128,plain,
( spl0_1925
<=> ! [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_1925])]) ).
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(f21126,plain,
spl0_1924,
inference(avatar_split_clause,[],[f387,f21124]) ).
fof(f21124,plain,
( spl0_1924
<=> ! [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_1924])]) ).
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(f21122,plain,
spl0_1923,
inference(avatar_split_clause,[],[f386,f21120]) ).
fof(f21120,plain,
( spl0_1923
<=> ! [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_1923])]) ).
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(f21118,plain,
spl0_1922,
inference(avatar_split_clause,[],[f385,f21116]) ).
fof(f21116,plain,
( spl0_1922
<=> ! [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_1922])]) ).
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(f21114,plain,
spl0_1921,
inference(avatar_split_clause,[],[f333,f21112]) ).
fof(f21112,plain,
( spl0_1921
<=> ! [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_1921])]) ).
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(f21110,plain,
( spl0_1920
| ~ spl0_1433
| ~ spl0_1883 ),
inference(avatar_split_clause,[],[f20868,f20510,f11631,f21108]) ).
fof(f20510,plain,
( spl0_1883
<=> ! [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_1883])]) ).
fof(f20868,plain,
( ! [X0] : c_union(v_A,c_insert(v_a,X0,t_a),t_a) = c_union(v_A,X0,t_a)
| ~ spl0_1433
| ~ spl0_1883 ),
inference(forward_demodulation,[],[f20854,f11632]) ).
fof(f20854,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_1433
| ~ spl0_1883 ),
inference(superposition,[],[f11632,f20511]) ).
fof(f20511,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_1883 ),
inference(avatar_component_clause,[],[f20510]) ).
fof(f21106,plain,
spl0_1919,
inference(avatar_split_clause,[],[f148,f21104]) ).
fof(f21104,plain,
( spl0_1919
<=> ! [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_1919])]) ).
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(f21102,plain,
spl0_1918,
inference(avatar_split_clause,[],[f147,f21100]) ).
fof(f21100,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(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(f21009,plain,
( spl0_1917
| ~ spl0_58
| ~ spl0_1453
| ~ spl0_1898 ),
inference(avatar_split_clause,[],[f20574,f20571,f11734,f3460,f21007]) ).
fof(f21007,plain,
( spl0_1917
<=> ! [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_1917])]) ).
fof(f20571,plain,
( spl0_1898
<=> ! [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_1898])]) ).
fof(f20574,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_1453
| ~ spl0_1898 ),
inference(forward_demodulation,[],[f20572,f12822]) ).
fof(f20572,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_1898 ),
inference(avatar_component_clause,[],[f20571]) ).
fof(f21005,plain,
( spl0_1916
| ~ spl0_58
| ~ spl0_1453
| ~ spl0_1897 ),
inference(avatar_split_clause,[],[f20569,f20566,f11734,f3460,f21003]) ).
fof(f21003,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(f20566,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(f20569,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_1453
| ~ spl0_1897 ),
inference(forward_demodulation,[],[f20567,f12822]) ).
fof(f20567,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,[],[f20566]) ).
fof(f21001,plain,
( spl0_1915
| ~ spl0_1432
| ~ spl0_1883 ),
inference(avatar_split_clause,[],[f20867,f20510,f11627,f20999]) ).
fof(f20867,plain,
( ! [X0] : c_union(c_insert(v_a,X0,t_a),v_A,t_a) = c_union(X0,v_A,t_a)
| ~ spl0_1432
| ~ spl0_1883 ),
inference(forward_demodulation,[],[f20853,f11628]) ).
fof(f20853,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_1432
| ~ spl0_1883 ),
inference(superposition,[],[f11628,f20511]) ).
fof(f20701,plain,
( spl0_1914
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1913 ),
inference(avatar_split_clause,[],[f20697,f20694,f11792,f7584,f7226,f6999,f6895,f6885,f20699]) ).
fof(f20699,plain,
( spl0_1914
<=> ! [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_1914])]) ).
fof(f6885,plain,
( spl0_703
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f6895,plain,
( spl0_705
<=> ! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f6999,plain,
( spl0_730
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f7226,plain,
( spl0_783
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f7584,plain,
( spl0_871
<=> ! [X39] : c_Numeral_Obin__add(c_Numeral_OMin,X39) = c_Numeral_Obin__add(X39,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f11792,plain,
( spl0_1458
<=> ! [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_1458])]) ).
fof(f20694,plain,
( spl0_1913
<=> ! [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_1913])]) ).
fof(f20697,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_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1913 ),
inference(forward_demodulation,[],[f20695,f12846]) ).
fof(f12846,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458 ),
inference(forward_demodulation,[],[f12845,f6887]) ).
fof(f6887,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_703 ),
inference(avatar_component_clause,[],[f6885]) ).
fof(f12845,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_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458 ),
inference(forward_demodulation,[],[f12844,f7228]) ).
fof(f7228,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_783 ),
inference(avatar_component_clause,[],[f7226]) ).
fof(f12844,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_705
| ~ spl0_730
| ~ spl0_871
| ~ spl0_1458 ),
inference(forward_demodulation,[],[f12843,f6896]) ).
fof(f6896,plain,
( ! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8
| ~ spl0_705 ),
inference(avatar_component_clause,[],[f6895]) ).
fof(f12843,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_730
| ~ spl0_871
| ~ spl0_1458 ),
inference(forward_demodulation,[],[f12837,f7585]) ).
fof(f7585,plain,
( ! [X39] : c_Numeral_Obin__add(c_Numeral_OMin,X39) = c_Numeral_Obin__add(X39,c_Numeral_OMin)
| ~ spl0_871 ),
inference(avatar_component_clause,[],[f7584]) ).
fof(f12837,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_730
| ~ spl0_1458 ),
inference(superposition,[],[f11793,f7001]) ).
fof(f7001,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_730 ),
inference(avatar_component_clause,[],[f6999]) ).
fof(f11793,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_1458 ),
inference(avatar_component_clause,[],[f11792]) ).
fof(f20695,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_1913 ),
inference(avatar_component_clause,[],[f20694]) ).
fof(f20696,plain,
spl0_1913,
inference(avatar_split_clause,[],[f3169,f20694]) ).
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,[],[f2967,f1021]) ).
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_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(f20692,plain,
( spl0_1912
| ~ spl0_5
| ~ spl0_1856 ),
inference(avatar_split_clause,[],[f19986,f19903,f3195,f20690]) ).
fof(f3195,plain,
( spl0_5
<=> c_Tarski_OisLub(v_S,v_cl,v_L,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f19903,plain,
( spl0_1856
<=> ! [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_1856])]) ).
fof(f19986,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_5
| ~ spl0_1856 ),
inference(resolution,[],[f19904,f3197]) ).
fof(f3197,plain,
( c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f3195]) ).
fof(f19904,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_1856 ),
inference(avatar_component_clause,[],[f19903]) ).
fof(f20688,plain,
spl0_1911,
inference(avatar_split_clause,[],[f3167,f20686]) ).
fof(f20686,plain,
( spl0_1911
<=> ! [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_1911])]) ).
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,[],[f2965,f1021]) ).
fof(f2965,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(f20684,plain,
spl0_1910,
inference(avatar_split_clause,[],[f3165,f20682]) ).
fof(f20682,plain,
( spl0_1910
<=> ! [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_1910])]) ).
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,[],[f2963,f1021]) ).
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_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(f20664,plain,
( spl0_1909
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1908 ),
inference(avatar_split_clause,[],[f20660,f20657,f11792,f7584,f7226,f6999,f6895,f6885,f20662]) ).
fof(f20662,plain,
( spl0_1909
<=> ! [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_1909])]) ).
fof(f20657,plain,
( spl0_1908
<=> ! [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_1908])]) ).
fof(f20660,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_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1908 ),
inference(forward_demodulation,[],[f20658,f12846]) ).
fof(f20658,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_1908 ),
inference(avatar_component_clause,[],[f20657]) ).
fof(f20659,plain,
spl0_1908,
inference(avatar_split_clause,[],[f3162,f20657]) ).
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,[],[f2961,f1021]) ).
fof(f2961,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(f20639,plain,
( spl0_1907
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1906 ),
inference(avatar_split_clause,[],[f20635,f20632,f11792,f7584,f7226,f6999,f6895,f6885,f20637]) ).
fof(f20637,plain,
( spl0_1907
<=> ! [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_1907])]) ).
fof(f20632,plain,
( spl0_1906
<=> ! [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_1906])]) ).
fof(f20635,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_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1906 ),
inference(forward_demodulation,[],[f20633,f12846]) ).
fof(f20633,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_1906 ),
inference(avatar_component_clause,[],[f20632]) ).
fof(f20634,plain,
spl0_1906,
inference(avatar_split_clause,[],[f3159,f20632]) ).
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,[],[f2959,f1021]) ).
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_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(f20630,plain,
spl0_1905,
inference(avatar_split_clause,[],[f3157,f20628]) ).
fof(f20628,plain,
( spl0_1905
<=> ! [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_1905])]) ).
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,[],[f2957,f1021]) ).
fof(f2957,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(f20626,plain,
spl0_1904,
inference(avatar_split_clause,[],[f3155,f20624]) ).
fof(f20624,plain,
( spl0_1904
<=> ! [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_1904])]) ).
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,[],[f2955,f1021]) ).
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_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(f20622,plain,
( spl0_1903
| ~ spl0_4
| ~ spl0_1845 ),
inference(avatar_split_clause,[],[f19751,f18876,f3190,f20620]) ).
fof(f20620,plain,
( spl0_1903
<=> ! [X0] : c_minus(X0,v_S,tc_set(t_a)) = c_minus(c_insert(v_x,X0,t_a),v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f18876,plain,
( spl0_1845
<=> ! [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_1845])]) ).
fof(f19751,plain,
( ! [X0] : c_minus(X0,v_S,tc_set(t_a)) = c_minus(c_insert(v_x,X0,t_a),v_S,tc_set(t_a))
| ~ spl0_4
| ~ spl0_1845 ),
inference(resolution,[],[f18877,f3192]) ).
fof(f18877,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_1845 ),
inference(avatar_component_clause,[],[f18876]) ).
fof(f20610,plain,
( spl0_1902
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1901 ),
inference(avatar_split_clause,[],[f20606,f20603,f11792,f7584,f7226,f6999,f6895,f6885,f20608]) ).
fof(f20608,plain,
( spl0_1902
<=> ! [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_1902])]) ).
fof(f20603,plain,
( spl0_1901
<=> ! [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_1901])]) ).
fof(f20606,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_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1901 ),
inference(forward_demodulation,[],[f20604,f12846]) ).
fof(f20604,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_1901 ),
inference(avatar_component_clause,[],[f20603]) ).
fof(f20605,plain,
spl0_1901,
inference(avatar_split_clause,[],[f3152,f20603]) ).
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,[],[f2953,f1021]) ).
fof(f2953,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(f20584,plain,
( spl0_1900
| ~ spl0_58
| ~ spl0_1348
| ~ spl0_1899 ),
inference(avatar_split_clause,[],[f20580,f20576,f10466,f3460,f20582]) ).
fof(f20582,plain,
( spl0_1900
<=> ! [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_1900])]) ).
fof(f10466,plain,
( spl0_1348
<=> ! [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_1348])]) ).
fof(f20576,plain,
( spl0_1899
<=> ! [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_1899])]) ).
fof(f20580,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_1348
| ~ spl0_1899 ),
inference(forward_demodulation,[],[f20579,f11316]) ).
fof(f11316,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_1348 ),
inference(resolution,[],[f10467,f3462]) ).
fof(f10467,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_1348 ),
inference(avatar_component_clause,[],[f10466]) ).
fof(f20579,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_1348
| ~ spl0_1899 ),
inference(forward_demodulation,[],[f20577,f11316]) ).
fof(f20577,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_1899 ),
inference(avatar_component_clause,[],[f20576]) ).
fof(f20578,plain,
spl0_1899,
inference(avatar_split_clause,[],[f3110,f20576]) ).
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(f20573,plain,
spl0_1898,
inference(avatar_split_clause,[],[f2948,f20571]) ).
fof(f2948,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(f20568,plain,
spl0_1897,
inference(avatar_split_clause,[],[f2947,f20566]) ).
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,[],[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(f20564,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1625,f20562]) ).
fof(f20562,plain,
( spl0_1896
<=> ! [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_1896])]) ).
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(f20560,plain,
spl0_1895,
inference(avatar_split_clause,[],[f1624,f20558]) ).
fof(f20558,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),X1,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(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(f20556,plain,
( spl0_1894
| ~ spl0_3
| ~ spl0_1845 ),
inference(avatar_split_clause,[],[f19749,f18876,f3185,f20554]) ).
fof(f20554,plain,
( spl0_1894
<=> ! [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_1894])]) ).
fof(f19749,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_1845 ),
inference(resolution,[],[f18877,f3187]) ).
fof(f20552,plain,
spl0_1893,
inference(avatar_split_clause,[],[f1217,f20550]) ).
fof(f20550,plain,
( spl0_1893
<=> ! [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_1893])]) ).
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(f20548,plain,
spl0_1892,
inference(avatar_split_clause,[],[f1192,f20546]) ).
fof(f20546,plain,
( spl0_1892
<=> ! [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_1892])]) ).
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(f20544,plain,
spl0_1891,
inference(avatar_split_clause,[],[f1185,f20542]) ).
fof(f20542,plain,
( spl0_1891
<=> ! [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_1891])]) ).
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(f20540,plain,
spl0_1890,
inference(avatar_split_clause,[],[f838,f20538]) ).
fof(f20538,plain,
( spl0_1890
<=> ! [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_1890])]) ).
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(f20536,plain,
spl0_1889,
inference(avatar_split_clause,[],[f837,f20534]) ).
fof(f20534,plain,
( spl0_1889
<=> ! [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_1889])]) ).
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(f20532,plain,
spl0_1888,
inference(avatar_split_clause,[],[f834,f20530]) ).
fof(f20530,plain,
( spl0_1888
<=> ! [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_1888])]) ).
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(f20528,plain,
spl0_1887,
inference(avatar_split_clause,[],[f833,f20526]) ).
fof(f20526,plain,
( spl0_1887
<=> ! [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_1887])]) ).
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(f20524,plain,
spl0_1886,
inference(avatar_split_clause,[],[f827,f20522]) ).
fof(f20522,plain,
( spl0_1886
<=> ! [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_1886])]) ).
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(f20520,plain,
spl0_1885,
inference(avatar_split_clause,[],[f826,f20518]) ).
fof(f20518,plain,
( spl0_1885
<=> ! [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_1885])]) ).
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(f20516,plain,
spl0_1884,
inference(avatar_split_clause,[],[f811,f20514]) ).
fof(f20514,plain,
( spl0_1884
<=> ! [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_1884])]) ).
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(f20512,plain,
( spl0_1883
| ~ spl0_2
| ~ spl0_1845 ),
inference(avatar_split_clause,[],[f19748,f18876,f3180,f20510]) ).
fof(f19748,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_1845 ),
inference(resolution,[],[f18877,f3182]) ).
fof(f20508,plain,
spl0_1882,
inference(avatar_split_clause,[],[f810,f20506]) ).
fof(f20506,plain,
( spl0_1882
<=> ! [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_1882])]) ).
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(f20504,plain,
spl0_1881,
inference(avatar_split_clause,[],[f741,f20502]) ).
fof(f20502,plain,
( spl0_1881
<=> ! [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_1881])]) ).
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(f20500,plain,
spl0_1880,
inference(avatar_split_clause,[],[f620,f20498]) ).
fof(f20498,plain,
( spl0_1880
<=> ! [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_1880])]) ).
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(f20496,plain,
spl0_1879,
inference(avatar_split_clause,[],[f139,f20494]) ).
fof(f20494,plain,
( spl0_1879
<=> ! [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_1879])]) ).
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(f20492,plain,
spl0_1878,
inference(avatar_split_clause,[],[f121,f20490]) ).
fof(f20490,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(X4,c_Finite__Set_OMax(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
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(f20078,plain,
( spl0_1877
| ~ spl0_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1863 ),
inference(avatar_split_clause,[],[f19935,f19932,f16036,f7182,f7158,f20076]) ).
fof(f20076,plain,
( spl0_1877
<=> ! [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_1877])]) ).
fof(f19932,plain,
( spl0_1863
<=> ! [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_1863])]) ).
fof(f19935,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_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1863 ),
inference(forward_demodulation,[],[f19933,f16062]) ).
fof(f19933,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_1863 ),
inference(avatar_component_clause,[],[f19932]) ).
fof(f20046,plain,
( spl0_1876
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_1859 ),
inference(avatar_split_clause,[],[f19918,f19915,f8336,f3460,f20044]) ).
fof(f20044,plain,
( spl0_1876
<=> ! [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_1876])]) ).
fof(f19915,plain,
( spl0_1859
<=> ! [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_1859])]) ).
fof(f19918,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_1010
| ~ spl0_1859 ),
inference(forward_demodulation,[],[f19916,f8622]) ).
fof(f19916,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_1859 ),
inference(avatar_component_clause,[],[f19915]) ).
fof(f19985,plain,
spl0_1875,
inference(avatar_split_clause,[],[f3085,f19983]) ).
fof(f19983,plain,
( spl0_1875
<=> ! [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_1875])]) ).
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,[],[f2911,f2764]) ).
fof(f2764,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(f2911,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(f19981,plain,
spl0_1874,
inference(avatar_split_clause,[],[f2917,f19979]) ).
fof(f19979,plain,
( spl0_1874
<=> ! [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_1874])]) ).
fof(f2917,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(f19977,plain,
spl0_1873,
inference(avatar_split_clause,[],[f2915,f19975]) ).
fof(f19975,plain,
( spl0_1873
<=> ! [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_1873])]) ).
fof(f2915,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(f19973,plain,
spl0_1872,
inference(avatar_split_clause,[],[f2866,f19971]) ).
fof(f19971,plain,
( spl0_1872
<=> ! [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_1872])]) ).
fof(f2866,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(f19967,plain,
spl0_1871,
inference(avatar_split_clause,[],[f2840,f19965]) ).
fof(f19965,plain,
( spl0_1871
<=> ! [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_1871])]) ).
fof(f2840,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(f19963,plain,
spl0_1870,
inference(avatar_split_clause,[],[f1649,f19961]) ).
fof(f19961,plain,
( spl0_1870
<=> ! [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_1870])]) ).
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(f19959,plain,
spl0_1869,
inference(avatar_split_clause,[],[f1648,f19957]) ).
fof(f19957,plain,
( spl0_1869
<=> ! [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_1869])]) ).
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(f19955,plain,
spl0_1868,
inference(avatar_split_clause,[],[f987,f19953]) ).
fof(f19953,plain,
( spl0_1868
<=> ! [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_1868])]) ).
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(f19951,plain,
spl0_1867,
inference(avatar_split_clause,[],[f729,f19949]) ).
fof(f19949,plain,
( spl0_1867
<=> ! [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_1867])]) ).
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(f19947,plain,
spl0_1866,
inference(avatar_split_clause,[],[f665,f19945]) ).
fof(f19945,plain,
( spl0_1866
<=> ! [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_1866])]) ).
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(f19943,plain,
spl0_1865,
inference(avatar_split_clause,[],[f661,f19941]) ).
fof(f19941,plain,
( spl0_1865
<=> ! [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_1865])]) ).
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(f19939,plain,
spl0_1864,
inference(avatar_split_clause,[],[f660,f19937]) ).
fof(f19937,plain,
( spl0_1864
<=> ! [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_1864])]) ).
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(f19934,plain,
spl0_1863,
inference(avatar_split_clause,[],[f591,f19932]) ).
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(f19930,plain,
spl0_1862,
inference(avatar_split_clause,[],[f579,f19928]) ).
fof(f19928,plain,
( spl0_1862
<=> ! [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_1862])]) ).
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(f19926,plain,
( spl0_1861
| ~ spl0_1066
| ~ spl0_1818 ),
inference(avatar_split_clause,[],[f19844,f18470,f8760,f19924]) ).
fof(f19924,plain,
( spl0_1861
<=> ! [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_1861])]) ).
fof(f8760,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(f18470,plain,
( spl0_1818
<=> ! [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_1818])]) ).
fof(f19844,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_1818 ),
inference(resolution,[],[f18471,f8761]) ).
fof(f8761,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,[],[f8760]) ).
fof(f18471,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_1818 ),
inference(avatar_component_clause,[],[f18470]) ).
fof(f19922,plain,
spl0_1860,
inference(avatar_split_clause,[],[f482,f19920]) ).
fof(f19920,plain,
( spl0_1860
<=> ! [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_1860])]) ).
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(f19917,plain,
spl0_1859,
inference(avatar_split_clause,[],[f318,f19915]) ).
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(f19913,plain,
spl0_1858,
inference(avatar_split_clause,[],[f84,f19911]) ).
fof(f19911,plain,
( spl0_1858
<=> ! [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_1858])]) ).
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(f19909,plain,
spl0_1857,
inference(avatar_split_clause,[],[f83,f19907]) ).
fof(f19907,plain,
( spl0_1857
<=> ! [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_1857])]) ).
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(f19905,plain,
spl0_1856,
inference(avatar_split_clause,[],[f9,f19903]) ).
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(f19237,plain,
( spl0_1855
| ~ spl0_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1826 ),
inference(avatar_split_clause,[],[f18800,f18796,f16036,f7182,f7158,f19235]) ).
fof(f19235,plain,
( spl0_1855
<=> ! [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_1855])]) ).
fof(f18796,plain,
( spl0_1826
<=> ! [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_1826])]) ).
fof(f18800,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_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1826 ),
inference(forward_demodulation,[],[f18799,f16062]) ).
fof(f18799,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_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1826 ),
inference(forward_demodulation,[],[f18797,f16062]) ).
fof(f18797,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_1826 ),
inference(avatar_component_clause,[],[f18796]) ).
fof(f19233,plain,
( spl0_1854
| ~ spl0_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1825 ),
inference(avatar_split_clause,[],[f18794,f18790,f16036,f7182,f7158,f19231]) ).
fof(f19231,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)
| X44 = X45 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f18790,plain,
( spl0_1825
<=> ! [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_1825])]) ).
fof(f18794,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_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1825 ),
inference(forward_demodulation,[],[f18793,f16062]) ).
fof(f18793,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_766
| ~ spl0_772
| ~ spl0_1697
| ~ spl0_1825 ),
inference(forward_demodulation,[],[f18791,f16062]) ).
fof(f18791,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_1825 ),
inference(avatar_component_clause,[],[f18790]) ).
fof(f18912,plain,
( spl0_1853
| ~ spl0_1341
| ~ spl0_1632 ),
inference(avatar_split_clause,[],[f18866,f15493,f10438,f18910]) ).
fof(f18910,plain,
( spl0_1853
<=> ! [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_1853])]) ).
fof(f10438,plain,
( spl0_1341
<=> ! [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_1341])]) ).
fof(f15493,plain,
( spl0_1632
<=> ! [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_1632])]) ).
fof(f18866,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_1341
| ~ spl0_1632 ),
inference(resolution,[],[f15494,f10439]) ).
fof(f10439,plain,
( ! [X1,X35,X5] :
( ~ c_in(c_Main_OsubsetI__1(X1,X35,X5),X35,X5)
| c_lessequals(X1,X35,tc_set(X5)) )
| ~ spl0_1341 ),
inference(avatar_component_clause,[],[f10438]) ).
fof(f15494,plain,
( ! [X0] :
( c_in(X0,c_Union(c_Finite__Set_OFinites,t_a),t_a)
| ~ c_in(X0,v_S,t_a) )
| ~ spl0_1632 ),
inference(avatar_component_clause,[],[f15493]) ).
fof(f18908,plain,
( spl0_1852
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1851 ),
inference(avatar_split_clause,[],[f18904,f18900,f10450,f10135,f6752,f3744,f18906]) ).
fof(f18900,plain,
( spl0_1851
<=> ! [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_1851])]) ).
fof(f18904,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f18903,f11244]) ).
fof(f18903,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f18901,f11244]) ).
fof(f18901,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_1851 ),
inference(avatar_component_clause,[],[f18900]) ).
fof(f18902,plain,
spl0_1851,
inference(avatar_split_clause,[],[f3010,f18900]) ).
fof(f18898,plain,
spl0_1850,
inference(avatar_split_clause,[],[f2941,f18896]) ).
fof(f18896,plain,
( spl0_1850
<=> ! [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_1850])]) ).
fof(f2941,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(f18894,plain,
spl0_1849,
inference(avatar_split_clause,[],[f2936,f18892]) ).
fof(f18892,plain,
( spl0_1849
<=> ! [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_1849])]) ).
fof(f2936,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(f18890,plain,
spl0_1848,
inference(avatar_split_clause,[],[f2935,f18888]) ).
fof(f18888,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,[],[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(f18886,plain,
spl0_1847,
inference(avatar_split_clause,[],[f2887,f18884]) ).
fof(f18884,plain,
( spl0_1847
<=> ! [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_1847])]) ).
fof(f2887,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(f18882,plain,
spl0_1846,
inference(avatar_split_clause,[],[f2863,f18880]) ).
fof(f18880,plain,
( spl0_1846
<=> ! [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_1846])]) ).
fof(f2863,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(f18878,plain,
spl0_1845,
inference(avatar_split_clause,[],[f1539,f18876]) ).
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(f18874,plain,
spl0_1844,
inference(avatar_split_clause,[],[f1512,f18872]) ).
fof(f18872,plain,
( spl0_1844
<=> ! [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_1844])]) ).
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(f18870,plain,
spl0_1843,
inference(avatar_split_clause,[],[f1462,f18868]) ).
fof(f18868,plain,
( spl0_1843
<=> ! [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_1843])]) ).
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(f18864,plain,
spl0_1842,
inference(avatar_split_clause,[],[f1202,f18862]) ).
fof(f18862,plain,
( spl0_1842
<=> ! [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_1842])]) ).
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(f18860,plain,
spl0_1841,
inference(avatar_split_clause,[],[f1194,f18858]) ).
fof(f18858,plain,
( spl0_1841
<=> ! [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_1841])]) ).
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(f18856,plain,
spl0_1840,
inference(avatar_split_clause,[],[f1191,f18854]) ).
fof(f18854,plain,
( spl0_1840
<=> ! [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_1840])]) ).
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(f18852,plain,
spl0_1839,
inference(avatar_split_clause,[],[f1188,f18850]) ).
fof(f18850,plain,
( spl0_1839
<=> ! [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_1839])]) ).
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(f18848,plain,
spl0_1838,
inference(avatar_split_clause,[],[f942,f18846]) ).
fof(f18846,plain,
( spl0_1838
<=> ! [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_1838])]) ).
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(f18844,plain,
spl0_1837,
inference(avatar_split_clause,[],[f939,f18842]) ).
fof(f18842,plain,
( spl0_1837
<=> ! [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_1837])]) ).
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(f18840,plain,
spl0_1836,
inference(avatar_split_clause,[],[f934,f18838]) ).
fof(f18838,plain,
( spl0_1836
<=> ! [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_1836])]) ).
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(f18836,plain,
spl0_1835,
inference(avatar_split_clause,[],[f931,f18834]) ).
fof(f18834,plain,
( spl0_1835
<=> ! [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_1835])]) ).
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(f18832,plain,
spl0_1834,
inference(avatar_split_clause,[],[f794,f18830]) ).
fof(f18830,plain,
( spl0_1834
<=> ! [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_1834])]) ).
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(f18828,plain,
spl0_1833,
inference(avatar_split_clause,[],[f695,f18826]) ).
fof(f18826,plain,
( spl0_1833
<=> ! [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_1833])]) ).
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(f18824,plain,
spl0_1832,
inference(avatar_split_clause,[],[f694,f18822]) ).
fof(f18822,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(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(f18820,plain,
spl0_1831,
inference(avatar_split_clause,[],[f586,f18818]) ).
fof(f18818,plain,
( spl0_1831
<=> ! [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_1831])]) ).
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(f18816,plain,
spl0_1830,
inference(avatar_split_clause,[],[f569,f18814]) ).
fof(f18814,plain,
( spl0_1830
<=> ! [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_1830])]) ).
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(f18812,plain,
spl0_1829,
inference(avatar_split_clause,[],[f562,f18810]) ).
fof(f18810,plain,
( spl0_1829
<=> ! [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_1829])]) ).
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(f18808,plain,
spl0_1828,
inference(avatar_split_clause,[],[f495,f18806]) ).
fof(f18806,plain,
( spl0_1828
<=> ! [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_1828])]) ).
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(f18804,plain,
spl0_1827,
inference(avatar_split_clause,[],[f464,f18802]) ).
fof(f18802,plain,
( spl0_1827
<=> ! [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_1827])]) ).
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(f18798,plain,
spl0_1826,
inference(avatar_split_clause,[],[f382,f18796]) ).
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(f18792,plain,
spl0_1825,
inference(avatar_split_clause,[],[f381,f18790]) ).
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(f18788,plain,
spl0_1824,
inference(avatar_split_clause,[],[f346,f18786]) ).
fof(f18786,plain,
( spl0_1824
<=> ! [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_1824])]) ).
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(f18784,plain,
spl0_1823,
inference(avatar_split_clause,[],[f345,f18782]) ).
fof(f18782,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(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(f18780,plain,
( ~ spl0_1547
| spl0_1
| ~ spl0_1359
| ~ spl0_1549 ),
inference(avatar_split_clause,[],[f15579,f13633,f11333,f3175,f13342]) ).
fof(f13342,plain,
( spl0_1547
<=> c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f11333,plain,
( spl0_1359
<=> ! [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_1359])]) ).
fof(f13633,plain,
( spl0_1549
<=> c_0 = c_Finite__Set_Ocard(v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f15579,plain,
( c_emptyset = v_S
| ~ c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1359
| ~ spl0_1549 ),
inference(trivial_inequality_removal,[],[f15578]) ).
fof(f15578,plain,
( c_0 != c_0
| c_emptyset = v_S
| ~ c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1359
| ~ spl0_1549 ),
inference(superposition,[],[f11334,f13635]) ).
fof(f13635,plain,
( c_0 = c_Finite__Set_Ocard(v_S,t_a)
| ~ spl0_1549 ),
inference(avatar_component_clause,[],[f13633]) ).
fof(f11334,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_1359 ),
inference(avatar_component_clause,[],[f11333]) ).
fof(f18779,plain,
spl0_1822,
inference(avatar_split_clause,[],[f338,f18777]) ).
fof(f18777,plain,
( spl0_1822
<=> ! [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_1822])]) ).
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(f18775,plain,
spl0_1821,
inference(avatar_split_clause,[],[f337,f18773]) ).
fof(f18773,plain,
( spl0_1821
<=> ! [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_1821])]) ).
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(f18771,plain,
spl0_1820,
inference(avatar_split_clause,[],[f157,f18769]) ).
fof(f18769,plain,
( spl0_1820
<=> ! [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_1820])]) ).
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(f18767,plain,
spl0_1819,
inference(avatar_split_clause,[],[f153,f18765]) ).
fof(f18765,plain,
( spl0_1819
<=> ! [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_1819])]) ).
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(f18472,plain,
( spl0_1547
| spl0_1818
| ~ spl0_1362
| ~ spl0_1814 ),
inference(avatar_split_clause,[],[f18102,f17908,f11345,f18470,f13342]) ).
fof(f11345,plain,
( spl0_1362
<=> ! [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_1362])]) ).
fof(f17908,plain,
( spl0_1814
<=> ! [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_1814])]) ).
fof(f18102,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_1362
| ~ spl0_1814 ),
inference(superposition,[],[f11346,f17909]) ).
fof(f17909,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_1814 ),
inference(avatar_component_clause,[],[f17908]) ).
fof(f11346,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_1362 ),
inference(avatar_component_clause,[],[f11345]) ).
fof(f18196,plain,
( spl0_1817
| ~ spl0_1202
| ~ spl0_1814 ),
inference(avatar_split_clause,[],[f18100,f17908,f9507,f18194]) ).
fof(f18194,plain,
( spl0_1817
<=> ! [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_1817])]) ).
fof(f9507,plain,
( spl0_1202
<=> ! [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_1202])]) ).
fof(f18100,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_1202
| ~ spl0_1814 ),
inference(superposition,[],[f9508,f17909]) ).
fof(f9508,plain,
( ! [X31,X1,X35,X5] :
( c_in(X31,c_union(X1,X35,X5),X5)
| ~ c_in(X31,X1,X5) )
| ~ spl0_1202 ),
inference(avatar_component_clause,[],[f9507]) ).
fof(f17992,plain,
( spl0_1816
| ~ spl0_1528
| ~ spl0_1601 ),
inference(avatar_split_clause,[],[f15210,f14371,f13130,f17990]) ).
fof(f17990,plain,
( spl0_1816
<=> ! [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_1816])]) ).
fof(f13130,plain,
( spl0_1528
<=> 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_1528])]) ).
fof(f15210,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_1528
| ~ spl0_1601 ),
inference(superposition,[],[f14372,f13132]) ).
fof(f13132,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_1528 ),
inference(avatar_component_clause,[],[f13130]) ).
fof(f17914,plain,
spl0_1815,
inference(avatar_split_clause,[],[f3168,f17912]) ).
fof(f17912,plain,
( spl0_1815
<=> ! [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_1815])]) ).
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,[],[f2966,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(f2966,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(f17910,plain,
( spl0_1814
| ~ spl0_1517
| ~ spl0_1601 ),
inference(avatar_split_clause,[],[f15209,f14371,f13085,f17908]) ).
fof(f13085,plain,
( spl0_1517
<=> 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_1517])]) ).
fof(f15209,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_1517
| ~ spl0_1601 ),
inference(superposition,[],[f14372,f13087]) ).
fof(f13087,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_1517 ),
inference(avatar_component_clause,[],[f13085]) ).
fof(f17906,plain,
spl0_1813,
inference(avatar_split_clause,[],[f3166,f17904]) ).
fof(f17904,plain,
( spl0_1813
<=> ! [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_1813])]) ).
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,[],[f2964,f979]) ).
fof(f2964,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(f17902,plain,
spl0_1812,
inference(avatar_split_clause,[],[f3158,f17900]) ).
fof(f17900,plain,
( spl0_1812
<=> ! [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_1812])]) ).
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,[],[f2958,f979]) ).
fof(f2958,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(f17898,plain,
spl0_1811,
inference(avatar_split_clause,[],[f3156,f17896]) ).
fof(f17896,plain,
( spl0_1811
<=> ! [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_1811])]) ).
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,[],[f2956,f979]) ).
fof(f2956,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(f17894,plain,
spl0_1810,
inference(avatar_split_clause,[],[f3124,f17892]) ).
fof(f17892,plain,
( spl0_1810
<=> ! [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_1810])]) ).
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,[],[f2932,f1021]) ).
fof(f2932,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(f17886,plain,
( spl0_1809
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1808 ),
inference(avatar_split_clause,[],[f17882,f17879,f11792,f7584,f7226,f6999,f6895,f6885,f17884]) ).
fof(f17884,plain,
( spl0_1809
<=> ! [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_1809])]) ).
fof(f17879,plain,
( spl0_1808
<=> ! [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_1808])]) ).
fof(f17882,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_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1808 ),
inference(forward_demodulation,[],[f17880,f12846]) ).
fof(f17880,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_1808 ),
inference(avatar_component_clause,[],[f17879]) ).
fof(f17881,plain,
spl0_1808,
inference(avatar_split_clause,[],[f3123,f17879]) ).
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,[],[f2931,f1021]) ).
fof(f2931,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(f17877,plain,
spl0_1807,
inference(avatar_split_clause,[],[f3118,f17875]) ).
fof(f17875,plain,
( spl0_1807
<=> ! [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_1807])]) ).
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,[],[f2928,f1021]) ).
fof(f2928,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(f17869,plain,
( spl0_1806
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1805 ),
inference(avatar_split_clause,[],[f17863,f17860,f11792,f7584,f7226,f6999,f6895,f6885,f17867]) ).
fof(f17867,plain,
( spl0_1806
<=> ! [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_1806])]) ).
fof(f17860,plain,
( spl0_1805
<=> ! [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_1805])]) ).
fof(f17863,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_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1805 ),
inference(forward_demodulation,[],[f17861,f12846]) ).
fof(f17861,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_1805 ),
inference(avatar_component_clause,[],[f17860]) ).
fof(f17862,plain,
spl0_1805,
inference(avatar_split_clause,[],[f3117,f17860]) ).
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,[],[f2927,f1021]) ).
fof(f2927,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(f17857,plain,
( spl0_1804
| ~ spl0_58
| ~ spl0_1348
| ~ spl0_1803 ),
inference(avatar_split_clause,[],[f17853,f17850,f10466,f3460,f17855]) ).
fof(f17855,plain,
( spl0_1804
<=> ! [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_1804])]) ).
fof(f17850,plain,
( spl0_1803
<=> ! [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_1803])]) ).
fof(f17853,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_1348
| ~ spl0_1803 ),
inference(forward_demodulation,[],[f17851,f11316]) ).
fof(f17851,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_1803 ),
inference(avatar_component_clause,[],[f17850]) ).
fof(f17852,plain,
spl0_1803,
inference(avatar_split_clause,[],[f3088,f17850]) ).
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(f17847,plain,
( spl0_1802
| ~ spl0_58
| ~ spl0_1348
| ~ spl0_1801 ),
inference(avatar_split_clause,[],[f17843,f17840,f10466,f3460,f17845]) ).
fof(f17845,plain,
( spl0_1802
<=> ! [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_1802])]) ).
fof(f17840,plain,
( spl0_1801
<=> ! [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_1801])]) ).
fof(f17843,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_1348
| ~ spl0_1801 ),
inference(forward_demodulation,[],[f17841,f11316]) ).
fof(f17841,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_1801 ),
inference(avatar_component_clause,[],[f17840]) ).
fof(f17842,plain,
spl0_1801,
inference(avatar_split_clause,[],[f3084,f17840]) ).
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(f17837,plain,
( spl0_1800
| ~ spl0_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1799 ),
inference(avatar_split_clause,[],[f17833,f17830,f11792,f7584,f7226,f6999,f6895,f6885,f17835]) ).
fof(f17835,plain,
( spl0_1800
<=> ! [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_1800])]) ).
fof(f17830,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_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_1799])]) ).
fof(f17833,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_703
| ~ spl0_705
| ~ spl0_730
| ~ spl0_783
| ~ spl0_871
| ~ spl0_1458
| ~ spl0_1799 ),
inference(forward_demodulation,[],[f17831,f12846]) ).
fof(f17831,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_1799 ),
inference(avatar_component_clause,[],[f17830]) ).
fof(f17832,plain,
spl0_1799,
inference(avatar_split_clause,[],[f3053,f17830]) ).
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,[],[f2865,f1021]) ).
fof(f2865,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(f17828,plain,
( spl0_1798
| ~ spl0_1341
| ~ spl0_1466 ),
inference(avatar_split_clause,[],[f12870,f12771,f10438,f17826]) ).
fof(f17826,plain,
( spl0_1798
<=> ! [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_1798])]) ).
fof(f12771,plain,
( spl0_1466
<=> ! [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_1466])]) ).
fof(f12870,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_1341
| ~ spl0_1466 ),
inference(resolution,[],[f12772,f10439]) ).
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_1466 ),
inference(avatar_component_clause,[],[f12771]) ).
fof(f17824,plain,
spl0_1797,
inference(avatar_split_clause,[],[f3052,f17822]) ).
fof(f17822,plain,
( spl0_1797
<=> ! [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_1797])]) ).
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,[],[f2864,f1021]) ).
fof(f2864,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(f17820,plain,
spl0_1796,
inference(avatar_split_clause,[],[f3014,f17818]) ).
fof(f17818,plain,
( spl0_1796
<=> ! [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_1796])]) ).
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,[],[f2836,f3010]) ).
fof(f2836,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(f17800,plain,
( spl0_1795
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1794 ),
inference(avatar_split_clause,[],[f17796,f17793,f10450,f10135,f6752,f3744,f17798]) ).
fof(f17798,plain,
( spl0_1795
<=> ! [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_1795])]) ).
fof(f17793,plain,
( spl0_1794
<=> ! [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_1794])]) ).
fof(f17796,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1794 ),
inference(forward_demodulation,[],[f17794,f11244]) ).
fof(f17794,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_1794 ),
inference(avatar_component_clause,[],[f17793]) ).
fof(f17795,plain,
spl0_1794,
inference(avatar_split_clause,[],[f2910,f17793]) ).
fof(f2910,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(f17791,plain,
spl0_1793,
inference(avatar_split_clause,[],[f2841,f17789]) ).
fof(f17789,plain,
( spl0_1793
<=> ! [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_1793])]) ).
fof(f2841,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(f17787,plain,
spl0_1792,
inference(avatar_split_clause,[],[f2839,f17785]) ).
fof(f17785,plain,
( spl0_1792
<=> ! [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_1792])]) ).
fof(f2839,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(f17783,plain,
spl0_1791,
inference(avatar_split_clause,[],[f2835,f17781]) ).
fof(f17781,plain,
( spl0_1791
<=> ! [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_1791])]) ).
fof(f2835,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(f17778,plain,
( spl0_1790
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1789 ),
inference(avatar_split_clause,[],[f17762,f17759,f10450,f10135,f6752,f3744,f17776]) ).
fof(f17776,plain,
( spl0_1790
<=> ! [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_1790])]) ).
fof(f17759,plain,
( spl0_1789
<=> ! [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_1789])]) ).
fof(f17762,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1789 ),
inference(forward_demodulation,[],[f17760,f11244]) ).
fof(f17760,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_1789 ),
inference(avatar_component_clause,[],[f17759]) ).
fof(f17761,plain,
spl0_1789,
inference(avatar_split_clause,[],[f2834,f17759]) ).
fof(f2834,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(f17756,plain,
( spl0_1788
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1787 ),
inference(avatar_split_clause,[],[f17752,f17749,f10450,f10135,f6752,f3744,f17754]) ).
fof(f17754,plain,
( spl0_1788
<=> ! [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_1788])]) ).
fof(f17749,plain,
( spl0_1787
<=> ! [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_1787])]) ).
fof(f17752,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1787 ),
inference(forward_demodulation,[],[f17750,f11244]) ).
fof(f17750,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_1787 ),
inference(avatar_component_clause,[],[f17749]) ).
fof(f17751,plain,
spl0_1787,
inference(avatar_split_clause,[],[f2833,f17749]) ).
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(f17746,plain,
( spl0_1786
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1785 ),
inference(avatar_split_clause,[],[f17742,f17739,f10450,f10135,f6752,f3744,f17744]) ).
fof(f17744,plain,
( spl0_1786
<=> ! [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_1786])]) ).
fof(f17739,plain,
( spl0_1785
<=> ! [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_1785])]) ).
fof(f17742,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1785 ),
inference(forward_demodulation,[],[f17740,f11244]) ).
fof(f17740,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_1785 ),
inference(avatar_component_clause,[],[f17739]) ).
fof(f17741,plain,
spl0_1785,
inference(avatar_split_clause,[],[f2832,f17739]) ).
fof(f2832,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(f17737,plain,
spl0_1784,
inference(avatar_split_clause,[],[f2821,f17735]) ).
fof(f17735,plain,
( spl0_1784
<=> ! [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_1784])]) ).
fof(f2821,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(f17733,plain,
spl0_1783,
inference(avatar_split_clause,[],[f2819,f17731]) ).
fof(f17731,plain,
( spl0_1783
<=> ! [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_1783])]) ).
fof(f2819,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(f17710,plain,
( spl0_1782
| ~ spl0_797
| ~ spl0_1601
| ~ spl0_1742 ),
inference(avatar_split_clause,[],[f17480,f17427,f14371,f7283,f17708]) ).
fof(f17708,plain,
( spl0_1782
<=> ! [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_1782])]) ).
fof(f7283,plain,
( spl0_797
<=> ! [X5,X35] : c_UNIV = c_union(c_UNIV,X35,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f17427,plain,
( spl0_1742
<=> ! [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_1742])]) ).
fof(f17480,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_797
| ~ spl0_1601
| ~ spl0_1742 ),
inference(forward_demodulation,[],[f17479,f15222]) ).
fof(f15222,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_797
| ~ spl0_1601 ),
inference(forward_demodulation,[],[f15205,f7284]) ).
fof(f7284,plain,
( ! [X35,X5] : c_UNIV = c_union(c_UNIV,X35,X5)
| ~ spl0_797 ),
inference(avatar_component_clause,[],[f7283]) ).
fof(f15205,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_797
| ~ spl0_1601 ),
inference(superposition,[],[f14372,f7284]) ).
fof(f17479,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_1601
| ~ spl0_1742 ),
inference(superposition,[],[f14372,f17428]) ).
fof(f17428,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_1742 ),
inference(avatar_component_clause,[],[f17427]) ).
fof(f17706,plain,
( spl0_1781
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1780 ),
inference(avatar_split_clause,[],[f17702,f17699,f10450,f10135,f6752,f3744,f17704]) ).
fof(f17704,plain,
( spl0_1781
<=> ! [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_1781])]) ).
fof(f17699,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_Finite__Set_Ocard(c_SetInterval_OatMost(X19,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f17702,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1780 ),
inference(forward_demodulation,[],[f17700,f11244]) ).
fof(f17700,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_1780 ),
inference(avatar_component_clause,[],[f17699]) ).
fof(f17701,plain,
spl0_1780,
inference(avatar_split_clause,[],[f2812,f17699]) ).
fof(f2812,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(f17616,plain,
( spl0_1779
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1778 ),
inference(avatar_split_clause,[],[f17612,f17608,f10450,f10135,f6752,f3744,f17614]) ).
fof(f17614,plain,
( spl0_1779
<=> ! [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_1779])]) ).
fof(f17608,plain,
( spl0_1778
<=> ! [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_1778])]) ).
fof(f17612,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1778 ),
inference(forward_demodulation,[],[f17611,f11244]) ).
fof(f17611,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1778 ),
inference(forward_demodulation,[],[f17609,f11244]) ).
fof(f17609,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_1778 ),
inference(avatar_component_clause,[],[f17608]) ).
fof(f17610,plain,
spl0_1778,
inference(avatar_split_clause,[],[f2811,f17608]) ).
fof(f17584,plain,
( spl0_1777
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1776 ),
inference(avatar_split_clause,[],[f17580,f17576,f10450,f10135,f6752,f3744,f17582]) ).
fof(f17582,plain,
( spl0_1777
<=> ! [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_1777])]) ).
fof(f17576,plain,
( spl0_1776
<=> ! [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_1776])]) ).
fof(f17580,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1776 ),
inference(forward_demodulation,[],[f17579,f11244]) ).
fof(f17579,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1776 ),
inference(forward_demodulation,[],[f17577,f11244]) ).
fof(f17577,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_1776 ),
inference(avatar_component_clause,[],[f17576]) ).
fof(f17578,plain,
spl0_1776,
inference(avatar_split_clause,[],[f2810,f17576]) ).
fof(f2810,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(f17574,plain,
spl0_1775,
inference(avatar_split_clause,[],[f1706,f17572]) ).
fof(f17572,plain,
( spl0_1775
<=> ! [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_1775])]) ).
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(f17570,plain,
spl0_1774,
inference(avatar_split_clause,[],[f1705,f17568]) ).
fof(f17568,plain,
( spl0_1774
<=> ! [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_1774])]) ).
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(f17564,plain,
spl0_1773,
inference(avatar_split_clause,[],[f1668,f17562]) ).
fof(f17562,plain,
( spl0_1773
<=> ! [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_1773])]) ).
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(f17560,plain,
spl0_1772,
inference(avatar_split_clause,[],[f1664,f17558]) ).
fof(f17558,plain,
( spl0_1772
<=> ! [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_1772])]) ).
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(f17556,plain,
spl0_1771,
inference(avatar_split_clause,[],[f1663,f17554]) ).
fof(f17554,plain,
( spl0_1771
<=> ! [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_1771])]) ).
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(f17552,plain,
spl0_1770,
inference(avatar_split_clause,[],[f1662,f17550]) ).
fof(f17550,plain,
( spl0_1770
<=> ! [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_1770])]) ).
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(f17548,plain,
spl0_1769,
inference(avatar_split_clause,[],[f1650,f17546]) ).
fof(f17546,plain,
( spl0_1769
<=> ! [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_1769])]) ).
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(f17544,plain,
spl0_1768,
inference(avatar_split_clause,[],[f1638,f17542]) ).
fof(f17542,plain,
( spl0_1768
<=> ! [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_1768])]) ).
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(f17540,plain,
spl0_1767,
inference(avatar_split_clause,[],[f1559,f17538]) ).
fof(f17538,plain,
( spl0_1767
<=> ! [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_1767])]) ).
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(f17536,plain,
spl0_1766,
inference(avatar_split_clause,[],[f1558,f17534]) ).
fof(f17534,plain,
( spl0_1766
<=> ! [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_1766])]) ).
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(f17532,plain,
spl0_1765,
inference(avatar_split_clause,[],[f1555,f17530]) ).
fof(f17530,plain,
( spl0_1765
<=> ! [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_1765])]) ).
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(f17528,plain,
spl0_1764,
inference(avatar_split_clause,[],[f1438,f17526]) ).
fof(f17526,plain,
( spl0_1764
<=> ! [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_1764])]) ).
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(f17524,plain,
( spl0_1763
| ~ spl0_1600
| ~ spl0_1721 ),
inference(avatar_split_clause,[],[f17383,f17331,f14367,f17522]) ).
fof(f17522,plain,
( spl0_1763
<=> ! [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_1763])]) ).
fof(f14367,plain,
( spl0_1600
<=> ! [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_1600])]) ).
fof(f17331,plain,
( spl0_1721
<=> 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_1721])]) ).
fof(f17383,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_1600
| ~ spl0_1721 ),
inference(superposition,[],[f14368,f17333]) ).
fof(f17333,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_1721 ),
inference(avatar_component_clause,[],[f17331]) ).
fof(f14368,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_1600 ),
inference(avatar_component_clause,[],[f14367]) ).
fof(f17520,plain,
spl0_1762,
inference(avatar_split_clause,[],[f1430,f17518]) ).
fof(f17518,plain,
( spl0_1762
<=> ! [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_1762])]) ).
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(f17516,plain,
spl0_1761,
inference(avatar_split_clause,[],[f1421,f17514]) ).
fof(f17514,plain,
( spl0_1761
<=> ! [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_1761])]) ).
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(f17512,plain,
spl0_1760,
inference(avatar_split_clause,[],[f1418,f17510]) ).
fof(f17510,plain,
( spl0_1760
<=> ! [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_1760])]) ).
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(f17508,plain,
spl0_1759,
inference(avatar_split_clause,[],[f1391,f17506]) ).
fof(f17506,plain,
( spl0_1759
<=> ! [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_1759])]) ).
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(f17504,plain,
spl0_1758,
inference(avatar_split_clause,[],[f1386,f17502]) ).
fof(f17502,plain,
( spl0_1758
<=> ! [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_1758])]) ).
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(f17500,plain,
spl0_1757,
inference(avatar_split_clause,[],[f1189,f17498]) ).
fof(f17498,plain,
( spl0_1757
<=> ! [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_1757])]) ).
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(f17496,plain,
spl0_1756,
inference(avatar_split_clause,[],[f1172,f17494]) ).
fof(f17494,plain,
( spl0_1756
<=> ! [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_1756])]) ).
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(f17492,plain,
spl0_1755,
inference(avatar_split_clause,[],[f1170,f17490]) ).
fof(f17490,plain,
( spl0_1755
<=> ! [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_1755])]) ).
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(f17488,plain,
spl0_1754,
inference(avatar_split_clause,[],[f1131,f17486]) ).
fof(f17486,plain,
( spl0_1754
<=> ! [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_1754])]) ).
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(f17484,plain,
spl0_1753,
inference(avatar_split_clause,[],[f1126,f17482]) ).
fof(f17482,plain,
( spl0_1753
<=> ! [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_1753])]) ).
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(f17469,plain,
spl0_1752,
inference(avatar_split_clause,[],[f1123,f17467]) ).
fof(f17467,plain,
( spl0_1752
<=> ! [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_1752])]) ).
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(f17465,plain,
spl0_1751,
inference(avatar_split_clause,[],[f1120,f17463]) ).
fof(f17463,plain,
( spl0_1751
<=> ! [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_1751])]) ).
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(f17461,plain,
spl0_1750,
inference(avatar_split_clause,[],[f1102,f17459]) ).
fof(f17459,plain,
( spl0_1750
<=> ! [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_1750])]) ).
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(f17457,plain,
spl0_1749,
inference(avatar_split_clause,[],[f1093,f17455]) ).
fof(f17455,plain,
( spl0_1749
<=> ! [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_1749])]) ).
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(f17453,plain,
spl0_1748,
inference(avatar_split_clause,[],[f1079,f17451]) ).
fof(f17451,plain,
( spl0_1748
<=> ! [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_1748])]) ).
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(f17449,plain,
spl0_1747,
inference(avatar_split_clause,[],[f708,f17447]) ).
fof(f17447,plain,
( spl0_1747
<=> ! [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_1747])]) ).
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(f17445,plain,
spl0_1746,
inference(avatar_split_clause,[],[f701,f17443]) ).
fof(f17443,plain,
( spl0_1746
<=> ! [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_1746])]) ).
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(f17441,plain,
spl0_1745,
inference(avatar_split_clause,[],[f689,f17439]) ).
fof(f17439,plain,
( spl0_1745
<=> ! [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_1745])]) ).
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(f17437,plain,
spl0_1744,
inference(avatar_split_clause,[],[f686,f17435]) ).
fof(f17435,plain,
( spl0_1744
<=> ! [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_1744])]) ).
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(f17433,plain,
spl0_1743,
inference(avatar_split_clause,[],[f674,f17431]) ).
fof(f17431,plain,
( spl0_1743
<=> ! [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_1743])]) ).
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(f17429,plain,
( spl0_1742
| ~ spl0_797
| ~ spl0_1601
| ~ spl0_1721 ),
inference(avatar_split_clause,[],[f17385,f17331,f14371,f7283,f17427]) ).
fof(f17385,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_797
| ~ spl0_1601
| ~ spl0_1721 ),
inference(forward_demodulation,[],[f17384,f15222]) ).
fof(f17384,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_1601
| ~ spl0_1721 ),
inference(superposition,[],[f14372,f17333]) ).
fof(f17425,plain,
spl0_1741,
inference(avatar_split_clause,[],[f646,f17423]) ).
fof(f17423,plain,
( spl0_1741
<=> ! [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_1741])]) ).
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(f17421,plain,
spl0_1740,
inference(avatar_split_clause,[],[f564,f17419]) ).
fof(f17419,plain,
( spl0_1740
<=> ! [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_1740])]) ).
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(f17417,plain,
spl0_1739,
inference(avatar_split_clause,[],[f498,f17415]) ).
fof(f17415,plain,
( spl0_1739
<=> ! [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_1739])]) ).
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(f17413,plain,
spl0_1738,
inference(avatar_split_clause,[],[f457,f17411]) ).
fof(f17411,plain,
( spl0_1738
<=> ! [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_1738])]) ).
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(f17409,plain,
spl0_1737,
inference(avatar_split_clause,[],[f390,f17407]) ).
fof(f17407,plain,
( spl0_1737
<=> ! [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_1737])]) ).
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(f17405,plain,
spl0_1736,
inference(avatar_split_clause,[],[f389,f17403]) ).
fof(f17403,plain,
( spl0_1736
<=> ! [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_1736])]) ).
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(f17401,plain,
spl0_1735,
inference(avatar_split_clause,[],[f282,f17399]) ).
fof(f17399,plain,
( spl0_1735
<=> ! [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_1735])]) ).
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(f17397,plain,
spl0_1734,
inference(avatar_split_clause,[],[f268,f17395]) ).
fof(f17395,plain,
( spl0_1734
<=> ! [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_1734])]) ).
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(f17393,plain,
spl0_1733,
inference(avatar_split_clause,[],[f267,f17391]) ).
fof(f17391,plain,
( spl0_1733
<=> ! [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_1733])]) ).
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(f17389,plain,
spl0_1732,
inference(avatar_split_clause,[],[f231,f17387]) ).
fof(f17387,plain,
( spl0_1732
<=> ! [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_1732])]) ).
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(f17374,plain,
spl0_1731,
inference(avatar_split_clause,[],[f230,f17372]) ).
fof(f17372,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_plus(X2,X7,X5),c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
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(f17370,plain,
spl0_1730,
inference(avatar_split_clause,[],[f227,f17368]) ).
fof(f17368,plain,
( spl0_1730
<=> ! [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_1730])]) ).
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(f17366,plain,
spl0_1729,
inference(avatar_split_clause,[],[f225,f17364]) ).
fof(f17364,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_minus(X2,X7,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
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(f17362,plain,
spl0_1728,
inference(avatar_split_clause,[],[f224,f17360]) ).
fof(f17360,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_plus(X2,X7,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
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(f17358,plain,
spl0_1727,
inference(avatar_split_clause,[],[f171,f17356]) ).
fof(f17356,plain,
( spl0_1727
<=> ! [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_1727])]) ).
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(f17354,plain,
spl0_1726,
inference(avatar_split_clause,[],[f155,f17352]) ).
fof(f17352,plain,
( spl0_1726
<=> ! [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_1726])]) ).
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(f17350,plain,
spl0_1725,
inference(avatar_split_clause,[],[f154,f17348]) ).
fof(f17348,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(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(f17346,plain,
spl0_1724,
inference(avatar_split_clause,[],[f24,f17344]) ).
fof(f17344,plain,
( spl0_1724
<=> ! [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_1724])]) ).
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(f17342,plain,
spl0_1723,
inference(avatar_split_clause,[],[f23,f17340]) ).
fof(f17340,plain,
( spl0_1723
<=> ! [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_1723])]) ).
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(f17338,plain,
spl0_1722,
inference(avatar_split_clause,[],[f22,f17336]) ).
fof(f17336,plain,
( spl0_1722
<=> ! [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_1722])]) ).
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(f17334,plain,
( spl0_1721
| ~ spl0_796
| ~ spl0_1356
| ~ spl0_1678 ),
inference(avatar_split_clause,[],[f17086,f15684,f11146,f7279,f17331]) ).
fof(f11146,plain,
( spl0_1356
<=> 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_1356])]) ).
fof(f17086,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_796
| ~ spl0_1356
| ~ spl0_1678 ),
inference(forward_demodulation,[],[f17047,f7280]) ).
fof(f17047,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_1356
| ~ spl0_1678 ),
inference(superposition,[],[f15685,f11148]) ).
fof(f11148,plain,
( c_emptyset = c_minus(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ spl0_1356 ),
inference(avatar_component_clause,[],[f11146]) ).
fof(f16237,plain,
( spl0_1718
| spl0_1720 ),
inference(avatar_split_clause,[],[f3173,f16235,f16214]) ).
fof(f16214,plain,
( spl0_1718
<=> ! [X39] : c_0 != c_Numeral_Onumber__of(X39,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f16235,plain,
( spl0_1720
<=> ! [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_1720])]) ).
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(f16223,plain,
( ~ spl0_702
| ~ spl0_1718 ),
inference(avatar_contradiction_clause,[],[f16222]) ).
fof(f16222,plain,
( $false
| ~ spl0_702
| ~ spl0_1718 ),
inference(trivial_inequality_removal,[],[f16220]) ).
fof(f16220,plain,
( c_0 != c_0
| ~ spl0_702
| ~ spl0_1718 ),
inference(superposition,[],[f16215,f6882]) ).
fof(f6882,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f6880]) ).
fof(f6880,plain,
( spl0_702
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f16215,plain,
( ! [X39] : c_0 != c_Numeral_Onumber__of(X39,tc_nat)
| ~ spl0_1718 ),
inference(avatar_component_clause,[],[f16214]) ).
fof(f16219,plain,
( spl0_1718
| spl0_1719 ),
inference(avatar_split_clause,[],[f3172,f16217,f16214]) ).
fof(f16217,plain,
( spl0_1719
<=> ! [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_1719])]) ).
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(f16184,plain,
( spl0_1717
| ~ spl0_1365
| ~ spl0_1407 ),
inference(avatar_split_clause,[],[f14407,f11526,f11357,f16181]) ).
fof(f16181,plain,
( spl0_1717
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f11357,plain,
( spl0_1365
<=> v_S = c_Tarski_Ointerval(v_r,v_a,v_b,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f11526,plain,
( spl0_1407
<=> 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_1407])]) ).
fof(f14407,plain,
( c_emptyset = c_SetInterval_OgreaterThanAtMost(v_S,v_S,tc_set(t_a))
| ~ spl0_1365
| ~ spl0_1407 ),
inference(superposition,[],[f11528,f11359]) ).
fof(f11359,plain,
( v_S = c_Tarski_Ointerval(v_r,v_a,v_b,t_a)
| ~ spl0_1365 ),
inference(avatar_component_clause,[],[f11357]) ).
fof(f11528,plain,
( c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_1407 ),
inference(avatar_component_clause,[],[f11526]) ).
fof(f16179,plain,
( spl0_1716
| ~ spl0_116
| ~ spl0_674
| ~ spl0_772
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1611
| ~ spl0_1715 ),
inference(avatar_split_clause,[],[f16175,f16171,f14445,f10450,f10135,f7182,f6752,f3744,f16177]) ).
fof(f16177,plain,
( spl0_1716
<=> ! [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_1716])]) ).
fof(f14445,plain,
( spl0_1611
<=> ! [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_1611])]) ).
fof(f16171,plain,
( spl0_1715
<=> ! [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_1715])]) ).
fof(f16175,plain,
( ! [X8] :
( c_plus(c_1,c_minus(X8,c_1,tc_nat),tc_nat) = X8
| ~ c_less(c_0,X8,tc_nat) )
| ~ spl0_116
| ~ spl0_674
| ~ spl0_772
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1611
| ~ spl0_1715 ),
inference(forward_demodulation,[],[f16174,f14448]) ).
fof(f14448,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_772
| ~ spl0_1611 ),
inference(superposition,[],[f14446,f7183]) ).
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_1611 ),
inference(avatar_component_clause,[],[f14445]) ).
fof(f16174,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1715 ),
inference(forward_demodulation,[],[f16172,f11244]) ).
fof(f16172,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_1715 ),
inference(avatar_component_clause,[],[f16171]) ).
fof(f16173,plain,
spl0_1715,
inference(avatar_split_clause,[],[f3068,f16171]) ).
fof(f3068,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,[],[f2889,f2815]) ).
fof(f2889,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(f16169,plain,
spl0_1714,
inference(avatar_split_clause,[],[f2913,f16167]) ).
fof(f16167,plain,
( spl0_1714
<=> ! [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_1714])]) ).
fof(f2913,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(f16165,plain,
spl0_1713,
inference(avatar_split_clause,[],[f2912,f16163]) ).
fof(f16163,plain,
( spl0_1713
<=> ! [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_1713])]) ).
fof(f2912,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(f16161,plain,
spl0_1712,
inference(avatar_split_clause,[],[f2908,f16159]) ).
fof(f16159,plain,
( spl0_1712
<=> ! [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_1712])]) ).
fof(f2908,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(f16157,plain,
spl0_1711,
inference(avatar_split_clause,[],[f2907,f16155]) ).
fof(f16155,plain,
( spl0_1711
<=> ! [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_1711])]) ).
fof(f2907,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(f16151,plain,
spl0_1710,
inference(avatar_split_clause,[],[f2900,f16149]) ).
fof(f16149,plain,
( spl0_1710
<=> ! [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_1710])]) ).
fof(f2900,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(f16145,plain,
spl0_1709,
inference(avatar_split_clause,[],[f2898,f16143]) ).
fof(f16143,plain,
( spl0_1709
<=> ! [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_1709])]) ).
fof(f2898,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(f16141,plain,
spl0_1708,
inference(avatar_split_clause,[],[f2893,f16139]) ).
fof(f16139,plain,
( spl0_1708
<=> ! [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_1708])]) ).
fof(f2893,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(f16137,plain,
spl0_1707,
inference(avatar_split_clause,[],[f2891,f16135]) ).
fof(f2891,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(f16132,plain,
( ~ spl0_727
| spl0_1699 ),
inference(avatar_contradiction_clause,[],[f16130]) ).
fof(f16130,plain,
( $false
| ~ spl0_727
| spl0_1699 ),
inference(resolution,[],[f16073,f6988]) ).
fof(f6988,plain,
( ! [X1,X5] : c_lessequals(X1,X1,tc_set(X5))
| ~ spl0_727 ),
inference(avatar_component_clause,[],[f6987]) ).
fof(f6987,plain,
( spl0_727
<=> ! [X5,X1] : c_lessequals(X1,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f16073,plain,
( ~ c_lessequals(v_S,v_S,tc_set(t_a))
| spl0_1699 ),
inference(avatar_component_clause,[],[f16071]) ).
fof(f16071,plain,
( spl0_1699
<=> c_lessequals(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f16127,plain,
spl0_1706,
inference(avatar_split_clause,[],[f2886,f16125]) ).
fof(f16125,plain,
( spl0_1706
<=> ! [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_1706])]) ).
fof(f2886,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(f16121,plain,
spl0_1705,
inference(avatar_split_clause,[],[f2881,f16119]) ).
fof(f16119,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(f2881,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(f16113,plain,
( spl0_1704
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1703 ),
inference(avatar_split_clause,[],[f16109,f16106,f10450,f10135,f6752,f3744,f16111]) ).
fof(f16111,plain,
( spl0_1704
<=> ! [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_1704])]) ).
fof(f16106,plain,
( spl0_1703
<=> ! [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_1703])]) ).
fof(f16109,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1703 ),
inference(forward_demodulation,[],[f16107,f11244]) ).
fof(f16107,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_1703 ),
inference(avatar_component_clause,[],[f16106]) ).
fof(f16108,plain,
spl0_1703,
inference(avatar_split_clause,[],[f2869,f16106]) ).
fof(f2869,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(f16100,plain,
( spl0_1702
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1701 ),
inference(avatar_split_clause,[],[f16096,f16093,f10450,f10135,f6752,f3744,f16098]) ).
fof(f16098,plain,
( spl0_1702
<=> ! [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_1702])]) ).
fof(f16093,plain,
( spl0_1701
<=> ! [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_1701])]) ).
fof(f16096,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1701 ),
inference(forward_demodulation,[],[f16094,f11244]) ).
fof(f16094,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_1701 ),
inference(avatar_component_clause,[],[f16093]) ).
fof(f16095,plain,
spl0_1701,
inference(avatar_split_clause,[],[f2829,f16093]) ).
fof(f2829,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(f16078,plain,
( spl0_1700
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1698 ),
inference(avatar_split_clause,[],[f16069,f16066,f10450,f10135,f6752,f3744,f16076]) ).
fof(f16076,plain,
( spl0_1700
<=> ! [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_1700])]) ).
fof(f16066,plain,
( spl0_1698
<=> ! [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_1698])]) ).
fof(f16069,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1698 ),
inference(forward_demodulation,[],[f16067,f11244]) ).
fof(f16067,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_1698 ),
inference(avatar_component_clause,[],[f16066]) ).
fof(f16074,plain,
( ~ spl0_1699
| ~ spl0_1365
| spl0_1627 ),
inference(avatar_split_clause,[],[f15825,f15284,f11357,f16071]) ).
fof(f15284,plain,
( spl0_1627
<=> 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_1627])]) ).
fof(f15825,plain,
( ~ c_lessequals(v_S,v_S,tc_set(t_a))
| ~ spl0_1365
| spl0_1627 ),
inference(superposition,[],[f15286,f11359]) ).
fof(f15286,plain,
( ~ c_lessequals(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| spl0_1627 ),
inference(avatar_component_clause,[],[f15284]) ).
fof(f16068,plain,
spl0_1698,
inference(avatar_split_clause,[],[f2828,f16066]) ).
fof(f2828,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(f16038,plain,
( spl0_1697
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1696 ),
inference(avatar_split_clause,[],[f16034,f16031,f10450,f10135,f6752,f3744,f16036]) ).
fof(f16031,plain,
( spl0_1696
<=> ! [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_1696])]) ).
fof(f16034,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1696 ),
inference(forward_demodulation,[],[f16032,f11244]) ).
fof(f16032,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_1696 ),
inference(avatar_component_clause,[],[f16031]) ).
fof(f16033,plain,
spl0_1696,
inference(avatar_split_clause,[],[f2827,f16031]) ).
fof(f2827,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(f15934,plain,
( spl0_1695
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1694 ),
inference(avatar_split_clause,[],[f15930,f15927,f10450,f10135,f6752,f3744,f15932]) ).
fof(f15932,plain,
( spl0_1695
<=> ! [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_1695])]) ).
fof(f15927,plain,
( spl0_1694
<=> ! [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_1694])]) ).
fof(f15930,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1694 ),
inference(forward_demodulation,[],[f15928,f11244]) ).
fof(f15928,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_1694 ),
inference(avatar_component_clause,[],[f15927]) ).
fof(f15929,plain,
spl0_1694,
inference(avatar_split_clause,[],[f2826,f15927]) ).
fof(f2826,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(f15834,plain,
( spl0_1693
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1692 ),
inference(avatar_split_clause,[],[f15830,f15827,f10450,f10135,f6752,f3744,f15832]) ).
fof(f15832,plain,
( spl0_1693
<=> ! [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_1693])]) ).
fof(f15827,plain,
( spl0_1692
<=> ! [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_1692])]) ).
fof(f15830,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1692 ),
inference(forward_demodulation,[],[f15828,f11244]) ).
fof(f15828,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_1692 ),
inference(avatar_component_clause,[],[f15827]) ).
fof(f15829,plain,
spl0_1692,
inference(avatar_split_clause,[],[f2825,f15827]) ).
fof(f2825,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(f15762,plain,
( spl0_1691
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1690 ),
inference(avatar_split_clause,[],[f15758,f15755,f10450,f10135,f6752,f3744,f15760]) ).
fof(f15760,plain,
( spl0_1691
<=> ! [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_1691])]) ).
fof(f15755,plain,
( spl0_1690
<=> ! [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_1690])]) ).
fof(f15758,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1690 ),
inference(forward_demodulation,[],[f15756,f11244]) ).
fof(f15756,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_1690 ),
inference(avatar_component_clause,[],[f15755]) ).
fof(f15757,plain,
spl0_1690,
inference(avatar_split_clause,[],[f2824,f15755]) ).
fof(f2824,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(f15732,plain,
( spl0_1689
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1688 ),
inference(avatar_split_clause,[],[f15728,f15725,f10450,f10135,f6752,f3744,f15730]) ).
fof(f15730,plain,
( spl0_1689
<=> ! [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_1689])]) ).
fof(f15725,plain,
( spl0_1688
<=> ! [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_1688])]) ).
fof(f15728,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1688 ),
inference(forward_demodulation,[],[f15726,f11244]) ).
fof(f15726,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_1688 ),
inference(avatar_component_clause,[],[f15725]) ).
fof(f15727,plain,
spl0_1688,
inference(avatar_split_clause,[],[f2823,f15725]) ).
fof(f2823,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(f15723,plain,
spl0_1687,
inference(avatar_split_clause,[],[f2822,f15721]) ).
fof(f15721,plain,
( spl0_1687
<=> ! [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_1687])]) ).
fof(f2822,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(f15719,plain,
spl0_1686,
inference(avatar_split_clause,[],[f1673,f15717]) ).
fof(f15717,plain,
( spl0_1686
<=> ! [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_1686])]) ).
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(f15715,plain,
spl0_1685,
inference(avatar_split_clause,[],[f1639,f15713]) ).
fof(f15713,plain,
( spl0_1685
<=> ! [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_1685])]) ).
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(f15711,plain,
spl0_1684,
inference(avatar_split_clause,[],[f1540,f15709]) ).
fof(f15709,plain,
( spl0_1684
<=> ! [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_1684])]) ).
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(f15707,plain,
( spl0_1683
| ~ spl0_1355
| ~ spl0_1303
| ~ spl0_1464 ),
inference(avatar_split_clause,[],[f15109,f12408,f10285,f10968,f15704]) ).
fof(f15704,plain,
( spl0_1683
<=> 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_1683])]) ).
fof(f12408,plain,
( spl0_1464
<=> 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_1464])]) ).
fof(f15109,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_1303
| ~ spl0_1464 ),
inference(resolution,[],[f12410,f10286]) ).
fof(f12410,plain,
( c_less(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| ~ spl0_1464 ),
inference(avatar_component_clause,[],[f12408]) ).
fof(f15702,plain,
spl0_1682,
inference(avatar_split_clause,[],[f1515,f15700]) ).
fof(f15700,plain,
( spl0_1682
<=> ! [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_1682])]) ).
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(f15698,plain,
spl0_1681,
inference(avatar_split_clause,[],[f1461,f15696]) ).
fof(f15696,plain,
( spl0_1681
<=> ! [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_1681])]) ).
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(f15694,plain,
spl0_1680,
inference(avatar_split_clause,[],[f1450,f15692]) ).
fof(f15692,plain,
( spl0_1680
<=> ! [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_1680])]) ).
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(f15690,plain,
spl0_1679,
inference(avatar_split_clause,[],[f1449,f15688]) ).
fof(f15688,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(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(f15686,plain,
spl0_1678,
inference(avatar_split_clause,[],[f1439,f15684]) ).
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(f15682,plain,
spl0_1677,
inference(avatar_split_clause,[],[f1225,f15680]) ).
fof(f15680,plain,
( spl0_1677
<=> ! [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_1677])]) ).
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(f15678,plain,
spl0_1676,
inference(avatar_split_clause,[],[f1224,f15676]) ).
fof(f15676,plain,
( spl0_1676
<=> ! [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_1676])]) ).
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(f15674,plain,
spl0_1675,
inference(avatar_split_clause,[],[f1059,f15672]) ).
fof(f15672,plain,
( spl0_1675
<=> ! [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_1675])]) ).
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(f15670,plain,
spl0_1674,
inference(avatar_split_clause,[],[f1058,f15668]) ).
fof(f15668,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(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(f15666,plain,
spl0_1673,
inference(avatar_split_clause,[],[f1057,f15664]) ).
fof(f15664,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(X31,X2,X5),c_plus(X31,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
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(f15660,plain,
spl0_1672,
inference(avatar_split_clause,[],[f1056,f15658]) ).
fof(f15658,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(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(f15656,plain,
spl0_1671,
inference(avatar_split_clause,[],[f1054,f15654]) ).
fof(f15654,plain,
( spl0_1671
<=> ! [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_1671])]) ).
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(f15652,plain,
spl0_1670,
inference(avatar_split_clause,[],[f1053,f15650]) ).
fof(f15650,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(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(f15648,plain,
spl0_1669,
inference(avatar_split_clause,[],[f1052,f15646]) ).
fof(f15646,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(X31,X2,X5),c_plus(X31,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
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(f15644,plain,
spl0_1668,
inference(avatar_split_clause,[],[f1051,f15642]) ).
fof(f15642,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(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(f15640,plain,
spl0_1667,
inference(avatar_split_clause,[],[f1011,f15638]) ).
fof(f15638,plain,
( spl0_1667
<=> ! [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_1667])]) ).
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(f15636,plain,
spl0_1666,
inference(avatar_split_clause,[],[f1010,f15634]) ).
fof(f15634,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(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(f15632,plain,
spl0_1665,
inference(avatar_split_clause,[],[f1003,f15630]) ).
fof(f15630,plain,
( spl0_1665
<=> ! [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_1665])]) ).
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(f15628,plain,
spl0_1664,
inference(avatar_split_clause,[],[f1002,f15626]) ).
fof(f15626,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(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(f15624,plain,
spl0_1663,
inference(avatar_split_clause,[],[f984,f15622]) ).
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(f15619,plain,
spl0_1662,
inference(avatar_split_clause,[],[f981,f15617]) ).
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(f15615,plain,
spl0_1661,
inference(avatar_split_clause,[],[f836,f15613]) ).
fof(f15613,plain,
( spl0_1661
<=> ! [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_1661])]) ).
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(f15611,plain,
spl0_1660,
inference(avatar_split_clause,[],[f835,f15609]) ).
fof(f15609,plain,
( spl0_1660
<=> ! [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_1660])]) ).
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(f15607,plain,
spl0_1659,
inference(avatar_split_clause,[],[f832,f15605]) ).
fof(f15605,plain,
( spl0_1659
<=> ! [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_1659])]) ).
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(f15603,plain,
spl0_1658,
inference(avatar_split_clause,[],[f831,f15601]) ).
fof(f15601,plain,
( spl0_1658
<=> ! [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_1658])]) ).
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(f15599,plain,
spl0_1657,
inference(avatar_split_clause,[],[f825,f15597]) ).
fof(f15597,plain,
( spl0_1657
<=> ! [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_1657])]) ).
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(f15595,plain,
spl0_1656,
inference(avatar_split_clause,[],[f824,f15593]) ).
fof(f15593,plain,
( spl0_1656
<=> ! [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_1656])]) ).
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(f15591,plain,
spl0_1655,
inference(avatar_split_clause,[],[f809,f15589]) ).
fof(f15589,plain,
( spl0_1655
<=> ! [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_1655])]) ).
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(f15587,plain,
spl0_1654,
inference(avatar_split_clause,[],[f808,f15585]) ).
fof(f15585,plain,
( spl0_1654
<=> ! [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_1654])]) ).
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(f15583,plain,
spl0_1653,
inference(avatar_split_clause,[],[f734,f15581]) ).
fof(f15581,plain,
( spl0_1653
<=> ! [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_1653])]) ).
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(f15577,plain,
spl0_1652,
inference(avatar_split_clause,[],[f645,f15575]) ).
fof(f15575,plain,
( spl0_1652
<=> ! [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_1652])]) ).
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(f15573,plain,
spl0_1651,
inference(avatar_split_clause,[],[f629,f15571]) ).
fof(f15571,plain,
( spl0_1651
<=> ! [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_1651])]) ).
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(f15568,plain,
spl0_1650,
inference(avatar_split_clause,[],[f592,f15566]) ).
fof(f15566,plain,
( spl0_1650
<=> ! [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_1650])]) ).
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(f15564,plain,
spl0_1649,
inference(avatar_split_clause,[],[f589,f15562]) ).
fof(f15562,plain,
( spl0_1649
<=> ! [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_1649])]) ).
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(f15560,plain,
spl0_1648,
inference(avatar_split_clause,[],[f578,f15558]) ).
fof(f15558,plain,
( spl0_1648
<=> ! [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_1648])]) ).
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(f15556,plain,
spl0_1647,
inference(avatar_split_clause,[],[f566,f15554]) ).
fof(f15554,plain,
( spl0_1647
<=> ! [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_1647])]) ).
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(f15552,plain,
spl0_1646,
inference(avatar_split_clause,[],[f565,f15550]) ).
fof(f15550,plain,
( spl0_1646
<=> ! [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_1646])]) ).
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(f15548,plain,
spl0_1645,
inference(avatar_split_clause,[],[f483,f15546]) ).
fof(f15546,plain,
( spl0_1645
<=> ! [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_1645])]) ).
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(f15544,plain,
spl0_1644,
inference(avatar_split_clause,[],[f470,f15542]) ).
fof(f15542,plain,
( spl0_1644
<=> ! [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_1644])]) ).
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(f15540,plain,
spl0_1643,
inference(avatar_split_clause,[],[f410,f15538]) ).
fof(f15538,plain,
( spl0_1643
<=> ! [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_1643])]) ).
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(f15535,plain,
spl0_1642,
inference(avatar_split_clause,[],[f403,f15533]) ).
fof(f15533,plain,
( spl0_1642
<=> ! [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_1642])]) ).
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(f15531,plain,
spl0_1641,
inference(avatar_split_clause,[],[f384,f15529]) ).
fof(f15529,plain,
( spl0_1641
<=> ! [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_1641])]) ).
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(f15527,plain,
spl0_1640,
inference(avatar_split_clause,[],[f380,f15525]) ).
fof(f15525,plain,
( spl0_1640
<=> ! [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_1640])]) ).
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(f15523,plain,
spl0_1639,
inference(avatar_split_clause,[],[f372,f15521]) ).
fof(f15521,plain,
( spl0_1639
<=> ! [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_1639])]) ).
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(f15519,plain,
spl0_1638,
inference(avatar_split_clause,[],[f371,f15517]) ).
fof(f15517,plain,
( spl0_1638
<=> ! [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_1638])]) ).
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(f15515,plain,
spl0_1637,
inference(avatar_split_clause,[],[f176,f15513]) ).
fof(f15513,plain,
( spl0_1637
<=> ! [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_1637])]) ).
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(f15511,plain,
spl0_1636,
inference(avatar_split_clause,[],[f168,f15509]) ).
fof(f15509,plain,
( spl0_1636
<=> ! [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_1636])]) ).
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(f15507,plain,
spl0_1635,
inference(avatar_split_clause,[],[f167,f15505]) ).
fof(f15505,plain,
( spl0_1635
<=> ! [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_1635])]) ).
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(f15503,plain,
spl0_1634,
inference(avatar_split_clause,[],[f166,f15501]) ).
fof(f15501,plain,
( spl0_1634
<=> ! [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_1634])]) ).
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(f15499,plain,
spl0_1633,
inference(avatar_split_clause,[],[f137,f15497]) ).
fof(f15497,plain,
( spl0_1633
<=> ! [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_1633])]) ).
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(f15495,plain,
( spl0_1632
| ~ spl0_1547
| ~ spl0_1602 ),
inference(avatar_split_clause,[],[f15254,f14375,f13342,f15493]) ).
fof(f14375,plain,
( spl0_1602
<=> ! [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_1602])]) ).
fof(f15254,plain,
( ! [X0] :
( ~ c_in(X0,v_S,t_a)
| c_in(X0,c_Union(c_Finite__Set_OFinites,t_a),t_a) )
| ~ spl0_1547
| ~ spl0_1602 ),
inference(resolution,[],[f14376,f13344]) ).
fof(f13344,plain,
( c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| ~ spl0_1547 ),
inference(avatar_component_clause,[],[f13342]) ).
fof(f14376,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_1602 ),
inference(avatar_component_clause,[],[f14375]) ).
fof(f15491,plain,
spl0_1631,
inference(avatar_split_clause,[],[f122,f15489]) ).
fof(f15489,plain,
( spl0_1631
<=> ! [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_1631])]) ).
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(f15487,plain,
spl0_1630,
inference(avatar_split_clause,[],[f18,f15485]) ).
fof(f15485,plain,
( spl0_1630
<=> ! [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_1630])]) ).
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(f15483,plain,
spl0_1629,
inference(avatar_split_clause,[],[f17,f15481]) ).
fof(f15481,plain,
( spl0_1629
<=> ! [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_1629])]) ).
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(f15479,plain,
spl0_1628,
inference(avatar_split_clause,[],[f16,f15477]) ).
fof(f15477,plain,
( spl0_1628
<=> ! [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_1628])]) ).
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(f15287,plain,
( ~ spl0_1627
| ~ spl0_1118
| ~ spl0_1464 ),
inference(avatar_split_clause,[],[f15108,f12408,f8970,f15284]) ).
fof(f8970,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(f15108,plain,
( ~ c_lessequals(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_1118
| ~ spl0_1464 ),
inference(resolution,[],[f12410,f8971]) ).
fof(f8971,plain,
( ! [X1,X35,X5] :
( ~ c_less(X1,X35,tc_set(X5))
| ~ c_lessequals(X35,X1,tc_set(X5)) )
| ~ spl0_1118 ),
inference(avatar_component_clause,[],[f8970]) ).
fof(f14758,plain,
( spl0_1626
| ~ spl0_1354
| ~ spl0_1365 ),
inference(avatar_split_clause,[],[f14405,f11357,f10964,f14755]) ).
fof(f14755,plain,
( spl0_1626
<=> c_emptyset = c_SetInterval_OatLeastLessThan(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f10964,plain,
( spl0_1354
<=> 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_1354])]) ).
fof(f14405,plain,
( c_emptyset = c_SetInterval_OatLeastLessThan(v_S,v_S,tc_set(t_a))
| ~ spl0_1354
| ~ spl0_1365 ),
inference(superposition,[],[f10966,f11359]) ).
fof(f10966,plain,
( c_emptyset = c_SetInterval_OatLeastLessThan(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),v_S,tc_set(t_a))
| ~ spl0_1354 ),
inference(avatar_component_clause,[],[f10964]) ).
fof(f14535,plain,
spl0_1625,
inference(avatar_split_clause,[],[f3171,f14533]) ).
fof(f14533,plain,
( spl0_1625
<=> ! [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_1625])]) ).
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,[],[f2968,f2763]) ).
fof(f2763,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(f2968,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(f14531,plain,
spl0_1624,
inference(avatar_split_clause,[],[f3164,f14529]) ).
fof(f14529,plain,
( spl0_1624
<=> ! [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_1624])]) ).
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,[],[f2962,f2763]) ).
fof(f2962,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(f14527,plain,
spl0_1623,
inference(avatar_split_clause,[],[f3161,f14525]) ).
fof(f14525,plain,
( spl0_1623
<=> ! [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_1623])]) ).
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,[],[f2960,f2763]) ).
fof(f2960,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(f14523,plain,
spl0_1622,
inference(avatar_split_clause,[],[f3154,f14521]) ).
fof(f14521,plain,
( spl0_1622
<=> ! [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_1622])]) ).
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,[],[f2954,f2763]) ).
fof(f2954,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(f14519,plain,
spl0_1621,
inference(avatar_split_clause,[],[f3135,f14517]) ).
fof(f14517,plain,
( spl0_1621
<=> ! [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_1621])]) ).
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,[],[f2940,f2764]) ).
fof(f2940,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(f14515,plain,
spl0_1620,
inference(avatar_split_clause,[],[f3051,f14513]) ).
fof(f14513,plain,
( spl0_1620
<=> ! [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_1620])]) ).
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(f14511,plain,
spl0_1619,
inference(avatar_split_clause,[],[f3050,f14509]) ).
fof(f14509,plain,
( spl0_1619
<=> ! [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_1619])]) ).
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(f14507,plain,
spl0_1618,
inference(avatar_split_clause,[],[f3023,f14505]) ).
fof(f14505,plain,
( spl0_1618
<=> ! [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_1618])]) ).
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(f14503,plain,
spl0_1617,
inference(avatar_split_clause,[],[f3020,f14501]) ).
fof(f14501,plain,
( spl0_1617
<=> ! [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_1617])]) ).
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,[],[f2845,f2764]) ).
fof(f2845,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(f14499,plain,
( ~ spl0_1616
| ~ spl0_1365
| spl0_1464 ),
inference(avatar_split_clause,[],[f14408,f12408,f11357,f14496]) ).
fof(f14496,plain,
( spl0_1616
<=> c_less(v_S,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f14408,plain,
( ~ c_less(v_S,v_S,tc_set(t_a))
| ~ spl0_1365
| spl0_1464 ),
inference(superposition,[],[f12409,f11359]) ).
fof(f12409,plain,
( ~ c_less(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| spl0_1464 ),
inference(avatar_component_clause,[],[f12408]) ).
fof(f14494,plain,
spl0_1615,
inference(avatar_split_clause,[],[f3016,f14492]) ).
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(f14490,plain,
spl0_1614,
inference(avatar_split_clause,[],[f2922,f14488]) ).
fof(f14488,plain,
( spl0_1614
<=> ! [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_1614])]) ).
fof(f2922,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(f14470,plain,
( spl0_1613
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1612 ),
inference(avatar_split_clause,[],[f14466,f14463,f10450,f10135,f6752,f3744,f14468]) ).
fof(f14468,plain,
( spl0_1613
<=> ! [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_1613])]) ).
fof(f14463,plain,
( spl0_1612
<=> ! [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_1612])]) ).
fof(f14466,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1612 ),
inference(forward_demodulation,[],[f14464,f11244]) ).
fof(f14464,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_1612 ),
inference(avatar_component_clause,[],[f14463]) ).
fof(f14465,plain,
spl0_1612,
inference(avatar_split_clause,[],[f2816,f14463]) ).
fof(f14447,plain,
( spl0_1611
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1610 ),
inference(avatar_split_clause,[],[f14443,f14440,f10450,f10135,f6752,f3744,f14445]) ).
fof(f14440,plain,
( spl0_1610
<=> ! [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_1610])]) ).
fof(f14443,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1610 ),
inference(forward_demodulation,[],[f14441,f11244]) ).
fof(f14441,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_1610 ),
inference(avatar_component_clause,[],[f14440]) ).
fof(f14442,plain,
spl0_1610,
inference(avatar_split_clause,[],[f2815,f14440]) ).
fof(f14418,plain,
( spl0_1609
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1608 ),
inference(avatar_split_clause,[],[f14402,f14399,f10450,f10135,f6752,f3744,f14416]) ).
fof(f14416,plain,
( spl0_1609
<=> ! [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_1609])]) ).
fof(f14399,plain,
( spl0_1608
<=> ! [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_1608])]) ).
fof(f14402,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1608 ),
inference(forward_demodulation,[],[f14400,f11244]) ).
fof(f14400,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_1608 ),
inference(avatar_component_clause,[],[f14399]) ).
fof(f14401,plain,
spl0_1608,
inference(avatar_split_clause,[],[f2814,f14399]) ).
fof(f2814,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(f14397,plain,
spl0_1607,
inference(avatar_split_clause,[],[f1719,f14395]) ).
fof(f14395,plain,
( spl0_1607
<=> ! [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_1607])]) ).
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(f14393,plain,
spl0_1606,
inference(avatar_split_clause,[],[f1717,f14391]) ).
fof(f14391,plain,
( spl0_1606
<=> ! [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_1606])]) ).
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(f14389,plain,
spl0_1605,
inference(avatar_split_clause,[],[f1672,f14387]) ).
fof(f14387,plain,
( spl0_1605
<=> ! [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_1605])]) ).
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(f14385,plain,
spl0_1604,
inference(avatar_split_clause,[],[f1587,f14383]) ).
fof(f14383,plain,
( spl0_1604
<=> ! [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_1604])]) ).
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(f14381,plain,
spl0_1603,
inference(avatar_split_clause,[],[f1584,f14379]) ).
fof(f14379,plain,
( spl0_1603
<=> ! [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_1603])]) ).
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(f14377,plain,
spl0_1602,
inference(avatar_split_clause,[],[f1522,f14375]) ).
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(f14373,plain,
spl0_1601,
inference(avatar_split_clause,[],[f1509,f14371]) ).
fof(f14369,plain,
spl0_1600,
inference(avatar_split_clause,[],[f1505,f14367]) ).
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(f14365,plain,
spl0_1599,
inference(avatar_split_clause,[],[f1485,f14363]) ).
fof(f14363,plain,
( spl0_1599
<=> ! [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_1599])]) ).
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(f14361,plain,
( spl0_1464
| spl0_1365
| ~ spl0_99
| ~ spl0_1443 ),
inference(avatar_split_clause,[],[f12748,f11678,f3665,f11357,f12408]) ).
fof(f12748,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_1443 ),
inference(resolution,[],[f11679,f3667]) ).
fof(f14360,plain,
spl0_1598,
inference(avatar_split_clause,[],[f1458,f14358]) ).
fof(f14358,plain,
( spl0_1598
<=> ! [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_1598])]) ).
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(f14356,plain,
spl0_1597,
inference(avatar_split_clause,[],[f1437,f14354]) ).
fof(f14354,plain,
( spl0_1597
<=> ! [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_1597])]) ).
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(f14352,plain,
spl0_1596,
inference(avatar_split_clause,[],[f1436,f14350]) ).
fof(f14350,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(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(f14348,plain,
spl0_1595,
inference(avatar_split_clause,[],[f1426,f14346]) ).
fof(f14346,plain,
( spl0_1595
<=> ! [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_1595])]) ).
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(f14344,plain,
spl0_1594,
inference(avatar_split_clause,[],[f1425,f14342]) ).
fof(f14342,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(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(f14340,plain,
spl0_1593,
inference(avatar_split_clause,[],[f1413,f14338]) ).
fof(f14338,plain,
( spl0_1593
<=> ! [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_1593])]) ).
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(f14336,plain,
spl0_1592,
inference(avatar_split_clause,[],[f1406,f14334]) ).
fof(f14334,plain,
( spl0_1592
<=> ! [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_1592])]) ).
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(f14332,plain,
spl0_1591,
inference(avatar_split_clause,[],[f1404,f14330]) ).
fof(f14330,plain,
( spl0_1591
<=> ! [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_1591])]) ).
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(f14328,plain,
spl0_1590,
inference(avatar_split_clause,[],[f1403,f14326]) ).
fof(f14326,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(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(f14324,plain,
spl0_1589,
inference(avatar_split_clause,[],[f1398,f14322]) ).
fof(f14322,plain,
( spl0_1589
<=> ! [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_1589])]) ).
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(f14317,plain,
spl0_1588,
inference(avatar_split_clause,[],[f1397,f14315]) ).
fof(f14315,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(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(f14313,plain,
spl0_1587,
inference(avatar_split_clause,[],[f1355,f14311]) ).
fof(f14311,plain,
( spl0_1587
<=> ! [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_1587])]) ).
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(f14309,plain,
spl0_1586,
inference(avatar_split_clause,[],[f1354,f14307]) ).
fof(f14307,plain,
( spl0_1586
<=> ! [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_1586])]) ).
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(f14305,plain,
spl0_1585,
inference(avatar_split_clause,[],[f1332,f14303]) ).
fof(f14303,plain,
( spl0_1585
<=> ! [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_1585])]) ).
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(f14301,plain,
spl0_1584,
inference(avatar_split_clause,[],[f1177,f14299]) ).
fof(f14299,plain,
( spl0_1584
<=> ! [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_1584])]) ).
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(f14297,plain,
spl0_1583,
inference(avatar_split_clause,[],[f1171,f14295]) ).
fof(f14295,plain,
( spl0_1583
<=> ! [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_1583])]) ).
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(f14293,plain,
spl0_1582,
inference(avatar_split_clause,[],[f1169,f14291]) ).
fof(f14291,plain,
( spl0_1582
<=> ! [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_1582])]) ).
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(f14289,plain,
spl0_1581,
inference(avatar_split_clause,[],[f1074,f14287]) ).
fof(f14287,plain,
( spl0_1581
<=> ! [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_1581])]) ).
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(f14285,plain,
spl0_1580,
inference(avatar_split_clause,[],[f1073,f14283]) ).
fof(f14283,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(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(f14281,plain,
spl0_1579,
inference(avatar_split_clause,[],[f945,f14279]) ).
fof(f14279,plain,
( spl0_1579
<=> ! [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_1579])]) ).
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(f14277,plain,
( spl0_1578
| ~ spl0_1434
| ~ spl0_1517 ),
inference(avatar_split_clause,[],[f13180,f13085,f11635,f14275]) ).
fof(f14275,plain,
( spl0_1578
<=> ! [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_1578])]) ).
fof(f13180,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_1434
| ~ spl0_1517 ),
inference(superposition,[],[f11636,f13087]) ).
fof(f14273,plain,
spl0_1577,
inference(avatar_split_clause,[],[f925,f14271]) ).
fof(f14271,plain,
( spl0_1577
<=> ! [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_1577])]) ).
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(f14269,plain,
spl0_1576,
inference(avatar_split_clause,[],[f923,f14267]) ).
fof(f14267,plain,
( spl0_1576
<=> ! [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_1576])]) ).
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(f14265,plain,
spl0_1575,
inference(avatar_split_clause,[],[f902,f14263]) ).
fof(f14263,plain,
( spl0_1575
<=> ! [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_1575])]) ).
fof(f14261,plain,
spl0_1574,
inference(avatar_split_clause,[],[f893,f14259]) ).
fof(f14259,plain,
( spl0_1574
<=> ! [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_1574])]) ).
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(f14257,plain,
spl0_1573,
inference(avatar_split_clause,[],[f728,f14255]) ).
fof(f14255,plain,
( spl0_1573
<=> ! [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_1573])]) ).
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(f14253,plain,
spl0_1572,
inference(avatar_split_clause,[],[f725,f14251]) ).
fof(f14251,plain,
( spl0_1572
<=> ! [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_1572])]) ).
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(f14249,plain,
spl0_1571,
inference(avatar_split_clause,[],[f712,f14247]) ).
fof(f14247,plain,
( spl0_1571
<=> ! [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_1571])]) ).
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(f14245,plain,
spl0_1570,
inference(avatar_split_clause,[],[f692,f14243]) ).
fof(f14243,plain,
( spl0_1570
<=> ! [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_1570])]) ).
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(f14241,plain,
spl0_1569,
inference(avatar_split_clause,[],[f666,f14239]) ).
fof(f14239,plain,
( spl0_1569
<=> ! [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_1569])]) ).
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(f14237,plain,
spl0_1568,
inference(avatar_split_clause,[],[f614,f14235]) ).
fof(f14235,plain,
( spl0_1568
<=> ! [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_1568])]) ).
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(f14233,plain,
spl0_1567,
inference(avatar_split_clause,[],[f604,f14231]) ).
fof(f14231,plain,
( spl0_1567
<=> ! [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_1567])]) ).
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(f14229,plain,
spl0_1566,
inference(avatar_split_clause,[],[f590,f14227]) ).
fof(f14227,plain,
( spl0_1566
<=> ! [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_1566])]) ).
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(f14225,plain,
spl0_1565,
inference(avatar_split_clause,[],[f573,f14223]) ).
fof(f14223,plain,
( spl0_1565
<=> ! [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_1565])]) ).
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(f14221,plain,
spl0_1564,
inference(avatar_split_clause,[],[f561,f14219]) ).
fof(f14219,plain,
( spl0_1564
<=> ! [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_1564])]) ).
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(f14217,plain,
spl0_1563,
inference(avatar_split_clause,[],[f556,f14215]) ).
fof(f14215,plain,
( spl0_1563
<=> ! [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_1563])]) ).
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(f14213,plain,
spl0_1562,
inference(avatar_split_clause,[],[f555,f14211]) ).
fof(f14211,plain,
( spl0_1562
<=> ! [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_1562])]) ).
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(f14209,plain,
spl0_1561,
inference(avatar_split_clause,[],[f466,f14207]) ).
fof(f14207,plain,
( spl0_1561
<=> ! [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_1561])]) ).
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(f14205,plain,
spl0_1560,
inference(avatar_split_clause,[],[f442,f14203]) ).
fof(f14203,plain,
( spl0_1560
<=> ! [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_1560])]) ).
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(f14201,plain,
spl0_1559,
inference(avatar_split_clause,[],[f439,f14199]) ).
fof(f14199,plain,
( spl0_1559
<=> ! [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_1559])]) ).
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(f14197,plain,
spl0_1558,
inference(avatar_split_clause,[],[f419,f14195]) ).
fof(f14195,plain,
( spl0_1558
<=> ! [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_1558])]) ).
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(f14193,plain,
spl0_1557,
inference(avatar_split_clause,[],[f412,f14191]) ).
fof(f14191,plain,
( spl0_1557
<=> ! [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_1557])]) ).
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(f14189,plain,
spl0_1556,
inference(avatar_split_clause,[],[f383,f14187]) ).
fof(f14187,plain,
( spl0_1556
<=> ! [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_1556])]) ).
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(f14185,plain,
spl0_1555,
inference(avatar_split_clause,[],[f373,f14183]) ).
fof(f14183,plain,
( spl0_1555
<=> ! [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_1555])]) ).
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(f14181,plain,
spl0_1554,
inference(avatar_split_clause,[],[f360,f14179]) ).
fof(f14179,plain,
( spl0_1554
<=> ! [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_1554])]) ).
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(f14177,plain,
spl0_1553,
inference(avatar_split_clause,[],[f104,f14175]) ).
fof(f14175,plain,
( spl0_1553
<=> ! [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_1553])]) ).
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(f14173,plain,
spl0_1552,
inference(avatar_split_clause,[],[f102,f14171]) ).
fof(f14171,plain,
( spl0_1552
<=> ! [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_1552])]) ).
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(f14169,plain,
spl0_1551,
inference(avatar_split_clause,[],[f82,f14167]) ).
fof(f14167,plain,
( spl0_1551
<=> ! [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_1551])]) ).
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(f14144,plain,
( spl0_1550
| ~ spl0_1066
| spl0_1548 ),
inference(avatar_split_clause,[],[f13988,f13346,f8760,f14141]) ).
fof(f14141,plain,
( spl0_1550
<=> 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_1550])]) ).
fof(f13346,plain,
( spl0_1548
<=> 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_1548])]) ).
fof(f13988,plain,
( c_0 = c_Finite__Set_Ocard(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| ~ spl0_1066
| spl0_1548 ),
inference(resolution,[],[f13348,f8761]) ).
fof(f13348,plain,
( ~ c_in(c_Tarski_Ointerval(v_r,v_a,v_b,t_a),c_Finite__Set_OFinites,tc_set(t_a))
| spl0_1548 ),
inference(avatar_component_clause,[],[f13346]) ).
fof(f13636,plain,
( spl0_1549
| ~ spl0_1066
| spl0_1547 ),
inference(avatar_split_clause,[],[f13498,f13342,f8760,f13633]) ).
fof(f13498,plain,
( c_0 = c_Finite__Set_Ocard(v_S,t_a)
| ~ spl0_1066
| spl0_1547 ),
inference(resolution,[],[f13343,f8761]) ).
fof(f13343,plain,
( ~ c_in(v_S,c_Finite__Set_OFinites,tc_set(t_a))
| spl0_1547 ),
inference(avatar_component_clause,[],[f13342]) ).
fof(f13349,plain,
( spl0_1547
| ~ spl0_1548
| ~ spl0_1362
| ~ spl0_1517 ),
inference(avatar_split_clause,[],[f13178,f13085,f11345,f13346,f13342]) ).
fof(f13178,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_1362
| ~ spl0_1517 ),
inference(superposition,[],[f11346,f13087]) ).
fof(f13218,plain,
spl0_1546,
inference(avatar_split_clause,[],[f3127,f13216]) ).
fof(f13216,plain,
( spl0_1546
<=> ! [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_1546])]) ).
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,[],[f2934,f979]) ).
fof(f2934,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(f13214,plain,
spl0_1545,
inference(avatar_split_clause,[],[f3122,f13212]) ).
fof(f13212,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(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,[],[f2930,f979]) ).
fof(f2930,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(f13210,plain,
spl0_1544,
inference(avatar_split_clause,[],[f3015,f13208]) ).
fof(f13208,plain,
( spl0_1544
<=> ! [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_1544])]) ).
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,[],[f2838,f2764]) ).
fof(f2838,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(f13206,plain,
spl0_1543,
inference(avatar_split_clause,[],[f2939,f13204]) ).
fof(f13204,plain,
( spl0_1543
<=> ! [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_1543])]) ).
fof(f2939,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(f13198,plain,
( spl0_1542
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1541 ),
inference(avatar_split_clause,[],[f13194,f13191,f10450,f10135,f6752,f3744,f13196]) ).
fof(f13196,plain,
( spl0_1542
<=> ! [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_1542])]) ).
fof(f13191,plain,
( spl0_1541
<=> ! [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_1541])]) ).
fof(f13194,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1541 ),
inference(forward_demodulation,[],[f13192,f11244]) ).
fof(f13192,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_1541 ),
inference(avatar_component_clause,[],[f13191]) ).
fof(f13193,plain,
spl0_1541,
inference(avatar_split_clause,[],[f2905,f13191]) ).
fof(f2905,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(f13189,plain,
spl0_1540,
inference(avatar_split_clause,[],[f2903,f13187]) ).
fof(f13187,plain,
( spl0_1540
<=> ! [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_1540])]) ).
fof(f2903,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(f13185,plain,
spl0_1539,
inference(avatar_split_clause,[],[f2902,f13183]) ).
fof(f13183,plain,
( spl0_1539
<=> ! [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_1539])]) ).
fof(f2902,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(f13173,plain,
spl0_1538,
inference(avatar_split_clause,[],[f2872,f13171]) ).
fof(f13171,plain,
( spl0_1538
<=> ! [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_1538])]) ).
fof(f2872,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(f13169,plain,
spl0_1537,
inference(avatar_split_clause,[],[f2820,f13167]) ).
fof(f13167,plain,
( spl0_1537
<=> ! [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_1537])]) ).
fof(f2820,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(f13165,plain,
spl0_1536,
inference(avatar_split_clause,[],[f1691,f13163]) ).
fof(f13163,plain,
( spl0_1536
<=> ! [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_1536])]) ).
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(f13161,plain,
spl0_1535,
inference(avatar_split_clause,[],[f1688,f13159]) ).
fof(f13159,plain,
( spl0_1535
<=> ! [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_1535])]) ).
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(f13157,plain,
spl0_1534,
inference(avatar_split_clause,[],[f1651,f13155]) ).
fof(f13155,plain,
( spl0_1534
<=> ! [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_1534])]) ).
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(f13153,plain,
spl0_1533,
inference(avatar_split_clause,[],[f1640,f13151]) ).
fof(f13151,plain,
( spl0_1533
<=> ! [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_1533])]) ).
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(f13149,plain,
spl0_1532,
inference(avatar_split_clause,[],[f1635,f13147]) ).
fof(f13147,plain,
( spl0_1532
<=> ! [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_1532])]) ).
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(f13145,plain,
spl0_1531,
inference(avatar_split_clause,[],[f1619,f13143]) ).
fof(f13143,plain,
( spl0_1531
<=> ! [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_1531])]) ).
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(f13141,plain,
spl0_1530,
inference(avatar_split_clause,[],[f1592,f13139]) ).
fof(f13139,plain,
( spl0_1530
<=> ! [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_1530])]) ).
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(f13137,plain,
spl0_1529,
inference(avatar_split_clause,[],[f1591,f13135]) ).
fof(f13135,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(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(f13133,plain,
( spl0_1528
| ~ spl0_801
| ~ spl0_1356
| ~ spl0_1433 ),
inference(avatar_split_clause,[],[f12670,f11631,f11146,f7299,f13130]) ).
fof(f12670,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_801
| ~ spl0_1356
| ~ spl0_1433 ),
inference(forward_demodulation,[],[f12657,f7300]) ).
fof(f12657,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_1356
| ~ spl0_1433 ),
inference(superposition,[],[f11632,f11148]) ).
fof(f13128,plain,
spl0_1527,
inference(avatar_split_clause,[],[f1548,f13126]) ).
fof(f13126,plain,
( spl0_1527
<=> ! [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_1527])]) ).
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(f13124,plain,
spl0_1526,
inference(avatar_split_clause,[],[f1523,f13122]) ).
fof(f13122,plain,
( spl0_1526
<=> ! [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_1526])]) ).
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(f13120,plain,
spl0_1525,
inference(avatar_split_clause,[],[f1520,f13118]) ).
fof(f13118,plain,
( spl0_1525
<=> ! [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_1525])]) ).
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(f13116,plain,
spl0_1524,
inference(avatar_split_clause,[],[f1486,f13114]) ).
fof(f13114,plain,
( spl0_1524
<=> ! [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_1524])]) ).
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(f13112,plain,
spl0_1523,
inference(avatar_split_clause,[],[f1353,f13110]) ).
fof(f13110,plain,
( spl0_1523
<=> ! [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_1523])]) ).
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(f13108,plain,
spl0_1522,
inference(avatar_split_clause,[],[f1337,f13106]) ).
fof(f13106,plain,
( spl0_1522
<=> ! [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_1522])]) ).
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(f13104,plain,
spl0_1521,
inference(avatar_split_clause,[],[f1336,f13102]) ).
fof(f13102,plain,
( spl0_1521
<=> ! [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_1521])]) ).
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(f13100,plain,
spl0_1520,
inference(avatar_split_clause,[],[f1228,f13098]) ).
fof(f13098,plain,
( spl0_1520
<=> ! [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_1520])]) ).
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(f13096,plain,
spl0_1519,
inference(avatar_split_clause,[],[f1227,f13094]) ).
fof(f13094,plain,
( spl0_1519
<=> ! [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_1519])]) ).
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(f13092,plain,
spl0_1518,
inference(avatar_split_clause,[],[f1214,f13090]) ).
fof(f13090,plain,
( spl0_1518
<=> ! [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_1518])]) ).
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(f13088,plain,
( spl0_1517
| ~ spl0_800
| ~ spl0_1356
| ~ spl0_1432 ),
inference(avatar_split_clause,[],[f12652,f11627,f11146,f7295,f13085]) ).
fof(f12652,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_800
| ~ spl0_1356
| ~ spl0_1432 ),
inference(forward_demodulation,[],[f12639,f7296]) ).
fof(f12639,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_1356
| ~ spl0_1432 ),
inference(superposition,[],[f11628,f11148]) ).
fof(f13083,plain,
spl0_1516,
inference(avatar_split_clause,[],[f1213,f13081]) ).
fof(f13081,plain,
( spl0_1516
<=> ! [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_1516])]) ).
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(f13079,plain,
spl0_1515,
inference(avatar_split_clause,[],[f1133,f13077]) ).
fof(f13077,plain,
( spl0_1515
<=> ! [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_1515])]) ).
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(f13075,plain,
spl0_1514,
inference(avatar_split_clause,[],[f1128,f13073]) ).
fof(f13073,plain,
( spl0_1514
<=> ! [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_1514])]) ).
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(f13071,plain,
spl0_1513,
inference(avatar_split_clause,[],[f1111,f13069]) ).
fof(f13069,plain,
( spl0_1513
<=> ! [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_1513])]) ).
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(f13067,plain,
spl0_1512,
inference(avatar_split_clause,[],[f1107,f13065]) ).
fof(f13065,plain,
( spl0_1512
<=> ! [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_1512])]) ).
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(f13063,plain,
spl0_1511,
inference(avatar_split_clause,[],[f1101,f13061]) ).
fof(f13061,plain,
( spl0_1511
<=> ! [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_1511])]) ).
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(f13059,plain,
spl0_1510,
inference(avatar_split_clause,[],[f1100,f13057]) ).
fof(f13057,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(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(f13055,plain,
spl0_1509,
inference(avatar_split_clause,[],[f1097,f13053]) ).
fof(f13053,plain,
( spl0_1509
<=> ! [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_1509])]) ).
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(f13051,plain,
spl0_1508,
inference(avatar_split_clause,[],[f1096,f13049]) ).
fof(f13049,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(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(f13047,plain,
spl0_1507,
inference(avatar_split_clause,[],[f1060,f13045]) ).
fof(f13045,plain,
( spl0_1507
<=> ! [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_1507])]) ).
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(f13043,plain,
spl0_1506,
inference(avatar_split_clause,[],[f1055,f13041]) ).
fof(f13041,plain,
( spl0_1506
<=> ! [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_1506])]) ).
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(f13039,plain,
spl0_1505,
inference(avatar_split_clause,[],[f976,f13037]) ).
fof(f13037,plain,
( spl0_1505
<=> ! [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_1505])]) ).
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(f13035,plain,
spl0_1504,
inference(avatar_split_clause,[],[f950,f13033]) ).
fof(f13033,plain,
( spl0_1504
<=> ! [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_1504])]) ).
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(f13031,plain,
spl0_1503,
inference(avatar_split_clause,[],[f949,f13029]) ).
fof(f13029,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(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(f13027,plain,
spl0_1502,
inference(avatar_split_clause,[],[f948,f13025]) ).
fof(f13025,plain,
( spl0_1502
<=> ! [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_1502])]) ).
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(f13023,plain,
spl0_1501,
inference(avatar_split_clause,[],[f947,f13021]) ).
fof(f13021,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(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(f13019,plain,
spl0_1500,
inference(avatar_split_clause,[],[f941,f13017]) ).
fof(f13017,plain,
( spl0_1500
<=> ! [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_1500])]) ).
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(f13015,plain,
spl0_1499,
inference(avatar_split_clause,[],[f940,f13013]) ).
fof(f13013,plain,
( spl0_1499
<=> ! [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_1499])]) ).
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(f13011,plain,
spl0_1498,
inference(avatar_split_clause,[],[f938,f13009]) ).
fof(f13009,plain,
( spl0_1498
<=> ! [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_1498])]) ).
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(f13007,plain,
spl0_1497,
inference(avatar_split_clause,[],[f937,f13005]) ).
fof(f13005,plain,
( spl0_1497
<=> ! [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_1497])]) ).
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(f13003,plain,
spl0_1496,
inference(avatar_split_clause,[],[f936,f13001]) ).
fof(f13001,plain,
( spl0_1496
<=> ! [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_1496])]) ).
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(f12999,plain,
spl0_1495,
inference(avatar_split_clause,[],[f935,f12997]) ).
fof(f12997,plain,
( spl0_1495
<=> ! [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_1495])]) ).
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(f12995,plain,
spl0_1494,
inference(avatar_split_clause,[],[f933,f12993]) ).
fof(f12993,plain,
( spl0_1494
<=> ! [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_1494])]) ).
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(f12991,plain,
spl0_1493,
inference(avatar_split_clause,[],[f932,f12989]) ).
fof(f12989,plain,
( spl0_1493
<=> ! [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_1493])]) ).
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(f12987,plain,
spl0_1492,
inference(avatar_split_clause,[],[f792,f12985]) ).
fof(f12985,plain,
( spl0_1492
<=> ! [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_1492])]) ).
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(f12983,plain,
spl0_1491,
inference(avatar_split_clause,[],[f733,f12981]) ).
fof(f12981,plain,
( spl0_1491
<=> ! [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_1491])]) ).
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(f12979,plain,
spl0_1490,
inference(avatar_split_clause,[],[f685,f12977]) ).
fof(f12977,plain,
( spl0_1490
<=> ! [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_1490])]) ).
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(f12975,plain,
spl0_1489,
inference(avatar_split_clause,[],[f684,f12973]) ).
fof(f12973,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(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(f12971,plain,
spl0_1488,
inference(avatar_split_clause,[],[f682,f12969]) ).
fof(f12969,plain,
( spl0_1488
<=> ! [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_1488])]) ).
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(f12967,plain,
spl0_1487,
inference(avatar_split_clause,[],[f681,f12965]) ).
fof(f12965,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(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(f12963,plain,
( spl0_1486
| ~ spl0_131
| ~ spl0_1439 ),
inference(avatar_split_clause,[],[f12709,f11662,f3809,f12961]) ).
fof(f12961,plain,
( spl0_1486
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f3809,plain,
( spl0_131
<=> ! [X4,X5] : c_in(X4,c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f11662,plain,
( spl0_1439
<=> ! [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_1439])]) ).
fof(f12709,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_131
| ~ spl0_1439 ),
inference(resolution,[],[f11663,f3810]) ).
fof(f3810,plain,
( ! [X4,X5] : c_in(X4,c_UNIV,X5)
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f3809]) ).
fof(f11663,plain,
( ! [X2,X6,X5] :
( ~ c_in(c_Pair(X2,X2,X5,X5),X6,tc_prod(X5,X5))
| ~ c_Wellfounded__Recursion_Owf(X6,X5) )
| ~ spl0_1439 ),
inference(avatar_component_clause,[],[f11662]) ).
fof(f12959,plain,
spl0_1485,
inference(avatar_split_clause,[],[f625,f12957]) ).
fof(f12957,plain,
( spl0_1485
<=> ! [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_1485])]) ).
fof(f625,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_Osingleton__rev__conv_0) ).
fof(f12955,plain,
spl0_1484,
inference(avatar_split_clause,[],[f621,f12953]) ).
fof(f12953,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(f12951,plain,
spl0_1483,
inference(avatar_split_clause,[],[f575,f12949]) ).
fof(f12949,plain,
( spl0_1483
<=> ! [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_1483])]) ).
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(f12947,plain,
spl0_1482,
inference(avatar_split_clause,[],[f505,f12945]) ).
fof(f12945,plain,
( spl0_1482
<=> ! [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_1482])]) ).
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(f12943,plain,
spl0_1481,
inference(avatar_split_clause,[],[f497,f12941]) ).
fof(f12941,plain,
( spl0_1481
<=> ! [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_1481])]) ).
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(f12939,plain,
spl0_1480,
inference(avatar_split_clause,[],[f477,f12937]) ).
fof(f12937,plain,
( spl0_1480
<=> ! [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_1480])]) ).
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(f12935,plain,
spl0_1479,
inference(avatar_split_clause,[],[f465,f12933]) ).
fof(f12933,plain,
( spl0_1479
<=> ! [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_1479])]) ).
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(f12931,plain,
spl0_1478,
inference(avatar_split_clause,[],[f461,f12929]) ).
fof(f12929,plain,
( spl0_1478
<=> ! [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_1478])]) ).
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(f12927,plain,
spl0_1477,
inference(avatar_split_clause,[],[f409,f12925]) ).
fof(f12925,plain,
( spl0_1477
<=> ! [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_1477])]) ).
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(f12923,plain,
spl0_1476,
inference(avatar_split_clause,[],[f321,f12921]) ).
fof(f12921,plain,
( spl0_1476
<=> ! [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_1476])]) ).
fof(f12919,plain,
( spl0_1475
| ~ spl0_1113
| ~ spl0_1439 ),
inference(avatar_split_clause,[],[f12708,f11662,f8950,f12917]) ).
fof(f12917,plain,
( spl0_1475
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f8950,plain,
( spl0_1113
<=> ! [X4,X5] : c_in(c_Pair(X4,X4,X5,X5),c_Relation_OId,tc_prod(X5,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f12708,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1113
| ~ spl0_1439 ),
inference(resolution,[],[f11663,f8951]) ).
fof(f8951,plain,
( ! [X4,X5] : c_in(c_Pair(X4,X4,X5,X5),c_Relation_OId,tc_prod(X5,X5))
| ~ spl0_1113 ),
inference(avatar_component_clause,[],[f8950]) ).
fof(f12915,plain,
spl0_1474,
inference(avatar_split_clause,[],[f296,f12913]) ).
fof(f12913,plain,
( spl0_1474
<=> ! [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_1474])]) ).
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(f12911,plain,
spl0_1473,
inference(avatar_split_clause,[],[f280,f12909]) ).
fof(f12909,plain,
( spl0_1473
<=> ! [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_1473])]) ).
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(f12907,plain,
spl0_1472,
inference(avatar_split_clause,[],[f279,f12905]) ).
fof(f12905,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(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(f12903,plain,
spl0_1471,
inference(avatar_split_clause,[],[f276,f12901]) ).
fof(f12901,plain,
( spl0_1471
<=> ! [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_1471])]) ).
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(f12899,plain,
spl0_1470,
inference(avatar_split_clause,[],[f275,f12897]) ).
fof(f12897,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(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(f12895,plain,
spl0_1469,
inference(avatar_split_clause,[],[f146,f12893]) ).
fof(f12893,plain,
( spl0_1469
<=> ! [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_1469])]) ).
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(f12891,plain,
spl0_1468,
inference(avatar_split_clause,[],[f63,f12889]) ).
fof(f12889,plain,
( spl0_1468
<=> ! [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_1468])]) ).
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(f12887,plain,
spl0_1467,
inference(avatar_split_clause,[],[f62,f12885]) ).
fof(f12885,plain,
( spl0_1467
<=> ! [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_1467])]) ).
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(f12773,plain,
( spl0_1466
| ~ spl0_99
| ~ spl0_1444 ),
inference(avatar_split_clause,[],[f12769,f11682,f3665,f12771]) ).
fof(f12769,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_1444 ),
inference(resolution,[],[f11683,f3667]) ).
fof(f12415,plain,
( ~ spl0_1463
| spl0_1464
| ~ spl0_1465
| ~ spl0_1356
| ~ spl0_1393 ),
inference(avatar_split_clause,[],[f12299,f11470,f11146,f12412,f12408,f12404]) ).
fof(f12404,plain,
( spl0_1463
<=> class_OrderedGroup_Opordered__ab__group__add(tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f12412,plain,
( spl0_1465
<=> c_less(c_emptyset,c_0,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f11470,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(f12299,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_1356
| ~ spl0_1393 ),
inference(superposition,[],[f11471,f11148]) ).
fof(f11471,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_1393 ),
inference(avatar_component_clause,[],[f11470]) ).
fof(f11810,plain,
spl0_1462,
inference(avatar_split_clause,[],[f3081,f11808]) ).
fof(f11808,plain,
( spl0_1462
<=> ! [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_1462])]) ).
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,[],[f2906,f2764]) ).
fof(f2906,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(f11806,plain,
spl0_1461,
inference(avatar_split_clause,[],[f3069,f11804]) ).
fof(f11804,plain,
( spl0_1461
<=> ! [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_1461])]) ).
fof(f3069,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,[],[f2890,f2815]) ).
fof(f2890,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(f11802,plain,
spl0_1460,
inference(avatar_split_clause,[],[f3019,f11800]) ).
fof(f11800,plain,
( spl0_1460
<=> ! [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_1460])]) ).
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(f11798,plain,
spl0_1459,
inference(avatar_split_clause,[],[f3007,f11796]) ).
fof(f11796,plain,
( spl0_1459
<=> ! [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_1459])]) ).
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(f11794,plain,
spl0_1458,
inference(avatar_split_clause,[],[f3004,f11792]) ).
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,[],[f2806,f2779]) ).
fof(f2779,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(f2806,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(f11790,plain,
spl0_1457,
inference(avatar_split_clause,[],[f2916,f11788]) ).
fof(f11788,plain,
( spl0_1457
<=> ! [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_1457])]) ).
fof(f2916,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(f11786,plain,
spl0_1456,
inference(avatar_split_clause,[],[f2914,f11784]) ).
fof(f11784,plain,
( spl0_1456
<=> ! [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_1456])]) ).
fof(f2914,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(f11745,plain,
( spl0_1455
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1454 ),
inference(avatar_split_clause,[],[f11741,f11738,f10450,f10135,f6752,f3744,f11743]) ).
fof(f11743,plain,
( spl0_1455
<=> ! [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_1455])]) ).
fof(f11738,plain,
( spl0_1454
<=> ! [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_1454])]) ).
fof(f11741,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_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1454 ),
inference(forward_demodulation,[],[f11739,f11244]) ).
fof(f11739,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_1454 ),
inference(avatar_component_clause,[],[f11738]) ).
fof(f11740,plain,
spl0_1454,
inference(avatar_split_clause,[],[f2899,f11738]) ).
fof(f2899,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(f11736,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2862,f11734]) ).
fof(f2862,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(f11728,plain,
( spl0_1452
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1451 ),
inference(avatar_split_clause,[],[f11724,f11721,f10450,f10135,f6752,f3744,f11726]) ).
fof(f11726,plain,
( spl0_1452
<=> ! [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_1452])]) ).
fof(f11721,plain,
( spl0_1451
<=> ! [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_1451])]) ).
fof(f11724,plain,
( ! [X30] : c_insert(X30,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X30,c_plus(c_1,X30,tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1451 ),
inference(forward_demodulation,[],[f11722,f11244]) ).
fof(f11722,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_1451 ),
inference(avatar_component_clause,[],[f11721]) ).
fof(f11723,plain,
spl0_1451,
inference(avatar_split_clause,[],[f2807,f11721]) ).
fof(f2807,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(f11719,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2805,f11717]) ).
fof(f11717,plain,
( spl0_1450
<=> ! [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_1450])]) ).
fof(f2805,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(f11715,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2794,f11713]) ).
fof(f11713,plain,
( spl0_1449
<=> ! [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_1449])]) ).
fof(f2794,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(f11711,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2793,f11709]) ).
fof(f11709,plain,
( spl0_1448
<=> ! [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_1448])]) ).
fof(f2793,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(f11697,plain,
( spl0_1447
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1446 ),
inference(avatar_split_clause,[],[f11693,f11690,f10450,f10135,f6752,f3744,f11695]) ).
fof(f11695,plain,
( spl0_1447
<=> ! [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_1447])]) ).
fof(f11690,plain,
( spl0_1446
<=> ! [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_1446])]) ).
fof(f11693,plain,
( ! [X19] : c_plus(c_1,X19,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X19,tc_nat),X19)
| ~ spl0_116
| ~ spl0_674
| ~ spl0_1267
| ~ spl0_1344
| ~ spl0_1446 ),
inference(forward_demodulation,[],[f11691,f11244]) ).
fof(f11691,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_1446 ),
inference(avatar_component_clause,[],[f11690]) ).
fof(f11692,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2789,f11690]) ).
fof(f2789,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(f11688,plain,
spl0_1445,
inference(avatar_split_clause,[],[f1703,f11686]) ).
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(f11684,plain,
spl0_1444,
inference(avatar_split_clause,[],[f1700,f11682]) ).
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(f11680,plain,
spl0_1443,
inference(avatar_split_clause,[],[f1696,f11678]) ).
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(f11676,plain,
spl0_1442,
inference(avatar_split_clause,[],[f1692,f11674]) ).
fof(f11674,plain,
( spl0_1442
<=> ! [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_1442])]) ).
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(f11672,plain,
spl0_1441,
inference(avatar_split_clause,[],[f1689,f11670]) ).
fof(f11670,plain,
( spl0_1441
<=> ! [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_1441])]) ).
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(f11668,plain,
spl0_1440,
inference(avatar_split_clause,[],[f1621,f11666]) ).
fof(f11666,plain,
( spl0_1440
<=> ! [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_1440])]) ).
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(f11664,plain,
spl0_1439,
inference(avatar_split_clause,[],[f1590,f11662]) ).
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(f11653,plain,
spl0_1438,
inference(avatar_split_clause,[],[f1554,f11651]) ).
fof(f11651,plain,
( spl0_1438
<=> ! [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_1438])]) ).
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(f11649,plain,
spl0_1437,
inference(avatar_split_clause,[],[f1521,f11647]) ).
fof(f11647,plain,
( spl0_1437
<=> ! [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_1437])]) ).
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(f11645,plain,
spl0_1436,
inference(avatar_split_clause,[],[f1517,f11643]) ).
fof(f11643,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(f1517,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_OUnion__empty__conv_0) ).
fof(f11641,plain,
spl0_1435,
inference(avatar_split_clause,[],[f1511,f11639]) ).
fof(f11639,plain,
( spl0_1435
<=> ! [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_1435])]) ).
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(f11637,plain,
spl0_1434,
inference(avatar_split_clause,[],[f1510,f11635]) ).
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(f11633,plain,
spl0_1433,
inference(avatar_split_clause,[],[f1496,f11631]) ).
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(f11629,plain,
spl0_1432,
inference(avatar_split_clause,[],[f1495,f11627]) ).
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(f11625,plain,
spl0_1431,
inference(avatar_split_clause,[],[f1487,f11623]) ).
fof(f11623,plain,
( spl0_1431
<=> ! [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_1431])]) ).
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(f11621,plain,
spl0_1430,
inference(avatar_split_clause,[],[f1478,f11619]) ).
fof(f11619,plain,
( spl0_1430
<=> ! [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_1430])]) ).
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(f11617,plain,
spl0_1429,
inference(avatar_split_clause,[],[f1420,f11615]) ).
fof(f11615,plain,
( spl0_1429
<=> ! [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_1429])]) ).
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(f11613,plain,
( spl0_1428
| ~ spl0_1048
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f11189,f10438,f8542,f11611]) ).
fof(f11611,plain,
( spl0_1428
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f8542,plain,
( spl0_1048
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f11189,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1048
| ~ spl0_1341 ),
inference(resolution,[],[f10439,f8543]) ).
fof(f8543,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1048 ),
inference(avatar_component_clause,[],[f8542]) ).
fof(f11609,plain,
spl0_1427,
inference(avatar_split_clause,[],[f1419,f11607]) ).
fof(f11607,plain,
( spl0_1427
<=> ! [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_1427])]) ).
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(f11605,plain,
spl0_1426,
inference(avatar_split_clause,[],[f1417,f11603]) ).
fof(f11603,plain,
( spl0_1426
<=> ! [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_1426])]) ).
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(f11601,plain,
spl0_1425,
inference(avatar_split_clause,[],[f1416,f11599]) ).
fof(f11599,plain,
( spl0_1425
<=> ! [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_1425])]) ).
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(f11597,plain,
spl0_1424,
inference(avatar_split_clause,[],[f1390,f11595]) ).
fof(f11595,plain,
( spl0_1424
<=> ! [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_1424])]) ).
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(f11593,plain,
spl0_1423,
inference(avatar_split_clause,[],[f1389,f11591]) ).
fof(f11591,plain,
( spl0_1423
<=> ! [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_1423])]) ).
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(f11589,plain,
spl0_1422,
inference(avatar_split_clause,[],[f1385,f11587]) ).
fof(f11587,plain,
( spl0_1422
<=> ! [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_1422])]) ).
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(f11585,plain,
spl0_1421,
inference(avatar_split_clause,[],[f1384,f11583]) ).
fof(f11583,plain,
( spl0_1421
<=> ! [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_1421])]) ).
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(f11581,plain,
spl0_1420,
inference(avatar_split_clause,[],[f1252,f11579]) ).
fof(f11579,plain,
( spl0_1420
<=> ! [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_1420])]) ).
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(f11577,plain,
spl0_1419,
inference(avatar_split_clause,[],[f1232,f11575]) ).
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(f11573,plain,
spl0_1418,
inference(avatar_split_clause,[],[f1230,f11571]) ).
fof(f11571,plain,
( spl0_1418
<=> ! [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_1418])]) ).
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(f11569,plain,
spl0_1417,
inference(avatar_split_clause,[],[f1226,f11567]) ).
fof(f11567,plain,
( spl0_1417
<=> ! [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_1417])]) ).
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(f11565,plain,
spl0_1416,
inference(avatar_split_clause,[],[f1223,f11563]) ).
fof(f11563,plain,
( spl0_1416
<=> ! [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_1416])]) ).
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(f11561,plain,
spl0_1415,
inference(avatar_split_clause,[],[f1212,f11559]) ).
fof(f11559,plain,
( spl0_1415
<=> ! [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_1415])]) ).
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(f11557,plain,
spl0_1414,
inference(avatar_split_clause,[],[f1204,f11555]) ).
fof(f11555,plain,
( spl0_1414
<=> ! [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_1414])]) ).
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(f11553,plain,
spl0_1413,
inference(avatar_split_clause,[],[f1160,f11551]) ).
fof(f11551,plain,
( spl0_1413
<=> ! [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_1413])]) ).
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(f11549,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1147,f11547]) ).
fof(f11547,plain,
( spl0_1412
<=> ! [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_1412])]) ).
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(f11545,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1130,f11543]) ).
fof(f11543,plain,
( spl0_1411
<=> ! [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_1411])]) ).
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(f11541,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1129,f11539]) ).
fof(f11539,plain,
( spl0_1410
<=> ! [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_1410])]) ).
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(f11537,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1125,f11535]) ).
fof(f11535,plain,
( spl0_1409
<=> ! [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_1409])]) ).
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(f11533,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1124,f11531]) ).
fof(f11531,plain,
( spl0_1408
<=> ! [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_1408])]) ).
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(f11529,plain,
( spl0_1407
| ~ spl0_1355
| ~ spl0_99
| ~ spl0_1313 ),
inference(avatar_split_clause,[],[f11010,f10325,f3665,f10968,f11526]) ).
fof(f11010,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(f11524,plain,
spl0_1406,
inference(avatar_split_clause,[],[f1122,f11522]) ).
fof(f11522,plain,
( spl0_1406
<=> ! [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_1406])]) ).
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(f11520,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1121,f11518]) ).
fof(f11518,plain,
( spl0_1405
<=> ! [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_1405])]) ).
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(f11516,plain,
spl0_1404,
inference(avatar_split_clause,[],[f1119,f11514]) ).
fof(f11514,plain,
( spl0_1404
<=> ! [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_1404])]) ).
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(f11512,plain,
spl0_1403,
inference(avatar_split_clause,[],[f1118,f11510]) ).
fof(f11510,plain,
( spl0_1403
<=> ! [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_1403])]) ).
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(f11508,plain,
spl0_1402,
inference(avatar_split_clause,[],[f1114,f11506]) ).
fof(f11506,plain,
( spl0_1402
<=> ! [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_1402])]) ).
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(f11504,plain,
spl0_1401,
inference(avatar_split_clause,[],[f1113,f11502]) ).
fof(f11502,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(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(f11500,plain,
spl0_1400,
inference(avatar_split_clause,[],[f1080,f11498]) ).
fof(f11498,plain,
( spl0_1400
<=> ! [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_1400])]) ).
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(f11496,plain,
spl0_1399,
inference(avatar_split_clause,[],[f1077,f11494]) ).
fof(f11494,plain,
( spl0_1399
<=> ! [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_1399])]) ).
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(f11492,plain,
spl0_1398,
inference(avatar_split_clause,[],[f1075,f11490]) ).
fof(f11490,plain,
( spl0_1398
<=> ! [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_1398])]) ).
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(f11488,plain,
spl0_1397,
inference(avatar_split_clause,[],[f1072,f11486]) ).
fof(f11486,plain,
( spl0_1397
<=> ! [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_1397])]) ).
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(f11484,plain,
spl0_1396,
inference(avatar_split_clause,[],[f1071,f11482]) ).
fof(f11482,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(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(f11480,plain,
spl0_1395,
inference(avatar_split_clause,[],[f1069,f11478]) ).
fof(f11478,plain,
( spl0_1395
<=> ! [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_1395])]) ).
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(f11476,plain,
spl0_1394,
inference(avatar_split_clause,[],[f1068,f11474]) ).
fof(f11474,plain,
( spl0_1394
<=> ! [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_1394])]) ).
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(f11472,plain,
spl0_1393,
inference(avatar_split_clause,[],[f1067,f11470]) ).
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(f11468,plain,
spl0_1392,
inference(avatar_split_clause,[],[f1066,f11466]) ).
fof(f11466,plain,
( spl0_1392
<=> ! [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_1392])]) ).
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(f11464,plain,
spl0_1391,
inference(avatar_split_clause,[],[f1065,f11462]) ).
fof(f11462,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(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(f11460,plain,
spl0_1390,
inference(avatar_split_clause,[],[f1049,f11458]) ).
fof(f11458,plain,
( spl0_1390
<=> ! [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_1390])]) ).
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(f11456,plain,
spl0_1389,
inference(avatar_split_clause,[],[f975,f11454]) ).
fof(f11454,plain,
( spl0_1389
<=> ! [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_1389])]) ).
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(f11452,plain,
spl0_1388,
inference(avatar_split_clause,[],[f974,f11450]) ).
fof(f11450,plain,
( spl0_1388
<=> ! [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_1388])]) ).
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(f11448,plain,
spl0_1387,
inference(avatar_split_clause,[],[f910,f11446]) ).
fof(f11446,plain,
( spl0_1387
<=> ! [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_1387])]) ).
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(f11444,plain,
spl0_1386,
inference(avatar_split_clause,[],[f909,f11442]) ).
fof(f11442,plain,
( spl0_1386
<=> ! [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_1386])]) ).
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(f11440,plain,
spl0_1385,
inference(avatar_split_clause,[],[f717,f11438]) ).
fof(f11438,plain,
( spl0_1385
<=> ! [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_1385])]) ).
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(f11436,plain,
spl0_1384,
inference(avatar_split_clause,[],[f664,f11434]) ).
fof(f11434,plain,
( spl0_1384
<=> ! [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_1384])]) ).
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(f11432,plain,
spl0_1383,
inference(avatar_split_clause,[],[f630,f11430]) ).
fof(f11430,plain,
( spl0_1383
<=> ! [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_1383])]) ).
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(f11428,plain,
spl0_1382,
inference(avatar_split_clause,[],[f613,f11426]) ).
fof(f11426,plain,
( spl0_1382
<=> ! [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_1382])]) ).
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(f11424,plain,
spl0_1381,
inference(avatar_split_clause,[],[f607,f11422]) ).
fof(f11422,plain,
( spl0_1381
<=> ! [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_1381])]) ).
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(f11420,plain,
spl0_1380,
inference(avatar_split_clause,[],[f567,f11418]) ).
fof(f11418,plain,
( spl0_1380
<=> ! [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_1380])]) ).
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(f11416,plain,
spl0_1379,
inference(avatar_split_clause,[],[f469,f11414]) ).
fof(f11414,plain,
( spl0_1379
<=> ! [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_1379])]) ).
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(f11412,plain,
spl0_1378,
inference(avatar_split_clause,[],[f456,f11410]) ).
fof(f11410,plain,
( spl0_1378
<=> ! [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_1378])]) ).
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(f11408,plain,
spl0_1377,
inference(avatar_split_clause,[],[f454,f11406]) ).
fof(f11406,plain,
( spl0_1377
<=> ! [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_1377])]) ).
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(f11404,plain,
spl0_1376,
inference(avatar_split_clause,[],[f446,f11402]) ).
fof(f11402,plain,
( spl0_1376
<=> ! [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_1376])]) ).
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(f11400,plain,
spl0_1375,
inference(avatar_split_clause,[],[f445,f11398]) ).
fof(f11398,plain,
( spl0_1375
<=> ! [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_1375])]) ).
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(f11396,plain,
spl0_1374,
inference(avatar_split_clause,[],[f443,f11394]) ).
fof(f11394,plain,
( spl0_1374
<=> ! [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_1374])]) ).
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(f11392,plain,
spl0_1373,
inference(avatar_split_clause,[],[f441,f11390]) ).
fof(f11390,plain,
( spl0_1373
<=> ! [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_1373])]) ).
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(f11388,plain,
spl0_1372,
inference(avatar_split_clause,[],[f440,f11386]) ).
fof(f11386,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(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(f11384,plain,
spl0_1371,
inference(avatar_split_clause,[],[f340,f11382]) ).
fof(f11382,plain,
( spl0_1371
<=> ! [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_1371])]) ).
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(f11380,plain,
spl0_1370,
inference(avatar_split_clause,[],[f281,f11378]) ).
fof(f11378,plain,
( spl0_1370
<=> ! [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_1370])]) ).
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(f11376,plain,
spl0_1369,
inference(avatar_split_clause,[],[f170,f11374]) ).
fof(f11374,plain,
( spl0_1369
<=> ! [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_1369])]) ).
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(f11372,plain,
spl0_1368,
inference(avatar_split_clause,[],[f169,f11370]) ).
fof(f11370,plain,
( spl0_1368
<=> ! [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_1368])]) ).
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(f11368,plain,
spl0_1367,
inference(avatar_split_clause,[],[f156,f11366]) ).
fof(f11366,plain,
( spl0_1367
<=> ! [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_1367])]) ).
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(f11364,plain,
( ~ spl0_1364
| spl0_1365
| ~ spl0_1366
| ~ spl0_1188
| ~ spl0_1356 ),
inference(avatar_split_clause,[],[f11314,f11146,f9451,f11361,f11357,f11353]) ).
fof(f11353,plain,
( spl0_1364
<=> class_OrderedGroup_Oab__group__add(tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f11361,plain,
( spl0_1366
<=> c_emptyset = c_0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f9451,plain,
( spl0_1188
<=> ! [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_1188])]) ).
fof(f11314,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_1188
| ~ spl0_1356 ),
inference(superposition,[],[f9452,f11148]) ).
fof(f9452,plain,
( ! [X2,X7,X5] :
( c_0 != c_minus(X2,X7,X5)
| X2 = X7
| ~ class_OrderedGroup_Oab__group__add(X5) )
| ~ spl0_1188 ),
inference(avatar_component_clause,[],[f9451]) ).
fof(f11351,plain,
spl0_1363,
inference(avatar_split_clause,[],[f152,f11349]) ).
fof(f11349,plain,
( spl0_1363
<=> ! [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_1363])]) ).
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(f11347,plain,
spl0_1362,
inference(avatar_split_clause,[],[f151,f11345]) ).
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(f11343,plain,
spl0_1361,
inference(avatar_split_clause,[],[f150,f11341]) ).
fof(f11341,plain,
( spl0_1361
<=> ! [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_1361])]) ).
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(f11339,plain,
spl0_1360,
inference(avatar_split_clause,[],[f149,f11337]) ).
fof(f11337,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(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(f11335,plain,
spl0_1359,
inference(avatar_split_clause,[],[f141,f11333]) ).
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(f11331,plain,
spl0_1358,
inference(avatar_split_clause,[],[f88,f11329]) ).
fof(f11329,plain,
( spl0_1358
<=> ! [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_1358])]) ).
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(f11327,plain,
spl0_1357,
inference(avatar_split_clause,[],[f86,f11325]) ).
fof(f11325,plain,
( spl0_1357
<=> ! [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_1357])]) ).
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(f11149,plain,
( spl0_1356
| ~ spl0_99
| ~ spl0_1323 ),
inference(avatar_split_clause,[],[f11055,f10366,f3665,f11146]) ).
fof(f11055,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_1323 ),
inference(resolution,[],[f10367,f3667]) ).
fof(f11017,plain,
( ~ spl0_114
| spl0_1355 ),
inference(avatar_contradiction_clause,[],[f11016]) ).
fof(f11016,plain,
( $false
| ~ spl0_114
| spl0_1355 ),
inference(resolution,[],[f10970,f3737]) ).
fof(f3737,plain,
( ! [X92] : class_Orderings_Oorder(tc_set(X92))
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f3736]) ).
fof(f3736,plain,
( spl0_114
<=> ! [X92] : class_Orderings_Oorder(tc_set(X92)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f10970,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| spl0_1355 ),
inference(avatar_component_clause,[],[f10968]) ).
fof(f10971,plain,
( spl0_1354
| ~ spl0_1355
| ~ spl0_99
| ~ spl0_1304 ),
inference(avatar_split_clause,[],[f10956,f10289,f3665,f10968,f10964]) ).
fof(f10956,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_1304 ),
inference(resolution,[],[f10290,f3667]) ).
fof(f10868,plain,
( spl0_1353
| ~ spl0_713
| ~ spl0_1111 ),
inference(avatar_split_clause,[],[f9212,f8941,f6929,f10866]) ).
fof(f10866,plain,
( spl0_1353
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f6929,plain,
( spl0_713
<=> ! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
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(f9212,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_713
| ~ spl0_1111 ),
inference(superposition,[],[f8942,f6930]) ).
fof(f6930,plain,
( ! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5)
| ~ spl0_713 ),
inference(avatar_component_clause,[],[f6929]) ).
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(f10680,plain,
( spl0_1352
| ~ spl0_120
| ~ spl0_1082 ),
inference(avatar_split_clause,[],[f9129,f8825,f3763,f10678]) ).
fof(f10678,plain,
( spl0_1352
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f3763,plain,
( spl0_120
<=> ! [X30] : c_Divides_Oop_Advd(X30,X30,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f8825,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(f9129,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_120
| ~ spl0_1082 ),
inference(resolution,[],[f8826,f3764]) ).
fof(f3764,plain,
( ! [X30] : c_Divides_Oop_Advd(X30,X30,tc_IntDef_Oint)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f3763]) ).
fof(f8826,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,[],[f8825]) ).
fof(f10623,plain,
( spl0_1351
| ~ spl0_120
| ~ spl0_1078 ),
inference(avatar_split_clause,[],[f9119,f8808,f3763,f10621]) ).
fof(f10621,plain,
( spl0_1351
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f8808,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(f9119,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_120
| ~ spl0_1078 ),
inference(resolution,[],[f8809,f3764]) ).
fof(f8809,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,[],[f8808]) ).
fof(f10476,plain,
spl0_1350,
inference(avatar_split_clause,[],[f3126,f10474]) ).
fof(f10474,plain,
( spl0_1350
<=> ! [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_1350])]) ).
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,[],[f2933,f2763]) ).
fof(f2933,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(f10472,plain,
spl0_1349,
inference(avatar_split_clause,[],[f3056,f10470]) ).
fof(f10470,plain,
( spl0_1349
<=> ! [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_1349])]) ).
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(f10468,plain,
spl0_1348,
inference(avatar_split_clause,[],[f3049,f10466]) ).
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(f10464,plain,
spl0_1347,
inference(avatar_split_clause,[],[f2874,f10462]) ).
fof(f10462,plain,
( spl0_1347
<=> ! [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_1347])]) ).
fof(f2874,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(f10460,plain,
spl0_1346,
inference(avatar_split_clause,[],[f2873,f10458]) ).
fof(f10458,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(f10456,plain,
spl0_1345,
inference(avatar_split_clause,[],[f2868,f10454]) ).
fof(f10454,plain,
( spl0_1345
<=> ! [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_1345])]) ).
fof(f2868,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(f10452,plain,
spl0_1344,
inference(avatar_split_clause,[],[f2800,f10450]) ).
fof(f2800,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(f10448,plain,
spl0_1343,
inference(avatar_split_clause,[],[f2797,f10446]) ).
fof(f10446,plain,
( spl0_1343
<=> ! [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_1343])]) ).
fof(f2797,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(f10444,plain,
spl0_1342,
inference(avatar_split_clause,[],[f2796,f10442]) ).
fof(f10442,plain,
( spl0_1342
<=> ! [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_1342])]) ).
fof(f2796,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(f10440,plain,
spl0_1341,
inference(avatar_split_clause,[],[f1702,f10438]) ).
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(f10436,plain,
spl0_1340,
inference(avatar_split_clause,[],[f1701,f10434]) ).
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(f10432,plain,
spl0_1339,
inference(avatar_split_clause,[],[f1641,f10430]) ).
fof(f10430,plain,
( spl0_1339
<=> ! [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_1339])]) ).
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(f10428,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1594,f10426]) ).
fof(f10426,plain,
( spl0_1338
<=> ! [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_1338])]) ).
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(f10424,plain,
spl0_1337,
inference(avatar_split_clause,[],[f1593,f10422]) ).
fof(f10422,plain,
( spl0_1337
<=> ! [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_1337])]) ).
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(f10420,plain,
spl0_1336,
inference(avatar_split_clause,[],[f1568,f10418]) ).
fof(f10418,plain,
( spl0_1336
<=> ! [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_1336])]) ).
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(f10416,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1566,f10414]) ).
fof(f10414,plain,
( spl0_1335
<=> ! [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_1335])]) ).
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(f10412,plain,
spl0_1334,
inference(avatar_split_clause,[],[f1557,f10410]) ).
fof(f1557,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_0) ).
fof(f10408,plain,
spl0_1333,
inference(avatar_split_clause,[],[f1553,f10406]) ).
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(f10404,plain,
spl0_1332,
inference(avatar_split_clause,[],[f1541,f10402]) ).
fof(f10402,plain,
( spl0_1332
<=> ! [X4,X5,X1] : c_insert(X4,X1,X5) = c_insert(X4,c_insert(X4,X1,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
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(f10400,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1535,f10398]) ).
fof(f10398,plain,
( spl0_1331
<=> ! [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_1331])]) ).
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(f10396,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1518,f10394]) ).
fof(f10394,plain,
( spl0_1330
<=> ! [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_1330])]) ).
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(f10392,plain,
spl0_1329,
inference(avatar_split_clause,[],[f1493,f10390]) ).
fof(f10390,plain,
( spl0_1329
<=> ! [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_1329])]) ).
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(f10388,plain,
spl0_1328,
inference(avatar_split_clause,[],[f1492,f10386]) ).
fof(f10386,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(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(f10384,plain,
spl0_1327,
inference(avatar_split_clause,[],[f1482,f10382]) ).
fof(f10382,plain,
( spl0_1327
<=> ! [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_1327])]) ).
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(f10380,plain,
spl0_1326,
inference(avatar_split_clause,[],[f1479,f10378]) ).
fof(f10378,plain,
( spl0_1326
<=> ! [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_1326])]) ).
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(f10376,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1460,f10374]) ).
fof(f10374,plain,
( spl0_1325
<=> ! [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_1325])]) ).
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(f10372,plain,
spl0_1324,
inference(avatar_split_clause,[],[f1459,f10370]) ).
fof(f10370,plain,
( spl0_1324
<=> ! [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_1324])]) ).
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(f10368,plain,
spl0_1323,
inference(avatar_split_clause,[],[f1457,f10366]) ).
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(f10364,plain,
spl0_1322,
inference(avatar_split_clause,[],[f1456,f10362]) ).
fof(f10362,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(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(f10360,plain,
spl0_1321,
inference(avatar_split_clause,[],[f1446,f10358]) ).
fof(f10358,plain,
( spl0_1321
<=> ! [X5,X1,X35] :
( X1 = X35
| c_uminus(X1,tc_set(X5)) != c_uminus(X35,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
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(f10356,plain,
spl0_1320,
inference(avatar_split_clause,[],[f1435,f10354]) ).
fof(f10354,plain,
( spl0_1320
<=> ! [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_1320])]) ).
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(f10352,plain,
spl0_1319,
inference(avatar_split_clause,[],[f1434,f10350]) ).
fof(f10350,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(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(f10348,plain,
spl0_1318,
inference(avatar_split_clause,[],[f1433,f10346]) ).
fof(f10346,plain,
( spl0_1318
<=> ! [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_1318])]) ).
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(f10344,plain,
spl0_1317,
inference(avatar_split_clause,[],[f1424,f10342]) ).
fof(f10342,plain,
( spl0_1317
<=> ! [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_1317])]) ).
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(f10340,plain,
spl0_1316,
inference(avatar_split_clause,[],[f1423,f10338]) ).
fof(f10338,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(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(f10336,plain,
( spl0_1315
| ~ spl0_704
| ~ spl0_783
| ~ spl0_1042 ),
inference(avatar_split_clause,[],[f8686,f8465,f7226,f6890,f10333]) ).
fof(f10333,plain,
( spl0_1315
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f6890,plain,
( spl0_704
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f8465,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(f8686,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_704
| ~ spl0_783
| ~ spl0_1042 ),
inference(forward_demodulation,[],[f8683,f6892]) ).
fof(f6892,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_704 ),
inference(avatar_component_clause,[],[f6890]) ).
fof(f8683,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_783
| ~ spl0_1042 ),
inference(superposition,[],[f8466,f7228]) ).
fof(f8466,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,[],[f8465]) ).
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,
inference(avatar_split_clause,[],[f1388,f10289]) ).
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(f10287,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1383,f10285]) ).
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(f10283,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1382,f10281]) ).
fof(f10281,plain,
( spl0_1302
<=> ! [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_1302])]) ).
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(f10279,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1381,f10277]) ).
fof(f10277,plain,
( spl0_1301
<=> ! [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_1301])]) ).
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(f10275,plain,
spl0_1300,
inference(avatar_split_clause,[],[f1380,f10273]) ).
fof(f10273,plain,
( spl0_1300
<=> ! [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_1300])]) ).
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(f10271,plain,
spl0_1299,
inference(avatar_split_clause,[],[f1379,f10269]) ).
fof(f10269,plain,
( spl0_1299
<=> ! [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_1299])]) ).
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(f10267,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1167,f10265]) ).
fof(f10265,plain,
( spl0_1298
<=> ! [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_1298])]) ).
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(f10263,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1166,f10261]) ).
fof(f10261,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(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(f10259,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1165,f10257]) ).
fof(f10257,plain,
( spl0_1296
<=> ! [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_1296])]) ).
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(f10255,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1164,f10253]) ).
fof(f10253,plain,
( spl0_1295
<=> ! [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_1295])]) ).
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(f10251,plain,
( spl0_1293
| ~ spl0_1294
| ~ spl0_785
| ~ spl0_1015 ),
inference(avatar_split_clause,[],[f8631,f8356,f7235,f10248,f10245]) ).
fof(f10245,plain,
( spl0_1293
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f10248,plain,
( spl0_1294
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f7235,plain,
( spl0_785
<=> ! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f8356,plain,
( spl0_1015
<=> ! [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_1015])]) ).
fof(f8631,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_785
| ~ spl0_1015 ),
inference(superposition,[],[f8357,f7236]) ).
fof(f7236,plain,
( ! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_nat)
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f7235]) ).
fof(f8357,plain,
( ! [X8,X4] :
( ~ c_Parity_Oeven(c_Nat_Opower(X4,X8,tc_nat),tc_nat)
| c_Parity_Oeven(X4,tc_nat) )
| ~ spl0_1015 ),
inference(avatar_component_clause,[],[f8356]) ).
fof(f10243,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1161,f10241]) ).
fof(f10241,plain,
( spl0_1292
<=> ! [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_1292])]) ).
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(f10239,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1154,f10237]) ).
fof(f10237,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(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(f10235,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1153,f10233]) ).
fof(f10233,plain,
( spl0_1290
<=> ! [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_1290])]) ).
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(f10231,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1152,f10229]) ).
fof(f10229,plain,
( spl0_1289
<=> ! [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_1289])]) ).
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(f10227,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1151,f10225]) ).
fof(f10225,plain,
( spl0_1288
<=> ! [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_1288])]) ).
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(f10223,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1148,f10221]) ).
fof(f10221,plain,
( spl0_1287
<=> ! [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_1287])]) ).
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(f10219,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1142,f10217]) ).
fof(f10217,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(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(f10215,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1141,f10213]) ).
fof(f10213,plain,
( spl0_1285
<=> ! [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_1285])]) ).
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(f10211,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1140,f10209]) ).
fof(f10209,plain,
( spl0_1284
<=> ! [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_1284])]) ).
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(f10207,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1139,f10205]) ).
fof(f10205,plain,
( spl0_1283
<=> ! [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_1283])]) ).
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(f10203,plain,
( spl0_1282
| ~ spl0_751
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f8546,f8210,f7098,f10201]) ).
fof(f10201,plain,
( spl0_1282
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f7098,plain,
( spl0_751
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
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(f8546,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_751
| ~ spl0_979 ),
inference(superposition,[],[f8211,f7099]) ).
fof(f7099,plain,
( ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8
| ~ spl0_751 ),
inference(avatar_component_clause,[],[f7098]) ).
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(f10199,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1099,f10197]) ).
fof(f10197,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(f10195,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1098,f10193]) ).
fof(f10193,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(f10191,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1095,f10189]) ).
fof(f10189,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(f10187,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1094,f10185]) ).
fof(f10185,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(f10183,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1092,f10181]) ).
fof(f10181,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(f10179,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1089,f10177]) ).
fof(f10177,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(f10175,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1088,f10173]) ).
fof(f10173,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(f10171,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1087,f10169]) ).
fof(f10169,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(f10167,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1086,f10165]) ).
fof(f10165,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(f10163,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1032,f10161]) ).
fof(f10161,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(f10153,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1031,f10151]) ).
fof(f10151,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(f10149,plain,
spl0_1270,
inference(avatar_split_clause,[],[f951,f10147]) ).
fof(f10147,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(f10145,plain,
spl0_1269,
inference(avatar_split_clause,[],[f946,f10143]) ).
fof(f10143,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(f10141,plain,
spl0_1268,
inference(avatar_split_clause,[],[f930,f10139]) ).
fof(f10139,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(f10137,plain,
spl0_1267,
inference(avatar_split_clause,[],[f715,f10135]) ).
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(f10133,plain,
spl0_1266,
inference(avatar_split_clause,[],[f678,f10131]) ).
fof(f10131,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(f10129,plain,
spl0_1265,
inference(avatar_split_clause,[],[f672,f10127]) ).
fof(f10127,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(f10125,plain,
spl0_1264,
inference(avatar_split_clause,[],[f671,f10123]) ).
fof(f10123,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(f10121,plain,
spl0_1263,
inference(avatar_split_clause,[],[f649,f10119]) ).
fof(f10119,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(f10117,plain,
spl0_1262,
inference(avatar_split_clause,[],[f608,f10115]) ).
fof(f10115,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(f10107,plain,
spl0_1261,
inference(avatar_split_clause,[],[f602,f10105]) ).
fof(f10105,plain,
( spl0_1261
<=> ! [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_1261])]) ).
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(f10103,plain,
spl0_1260,
inference(avatar_split_clause,[],[f491,f10101]) ).
fof(f10101,plain,
( spl0_1260
<=> ! [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_1260])]) ).
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(f10099,plain,
spl0_1259,
inference(avatar_split_clause,[],[f490,f10097]) ).
fof(f10097,plain,
( spl0_1259
<=> ! [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_1259])]) ).
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(f10095,plain,
spl0_1258,
inference(avatar_split_clause,[],[f475,f10093]) ).
fof(f10093,plain,
( spl0_1258
<=> ! [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_1258])]) ).
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(f10091,plain,
spl0_1257,
inference(avatar_split_clause,[],[f417,f10089]) ).
fof(f10089,plain,
( spl0_1257
<=> ! [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_1257])]) ).
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(f10087,plain,
spl0_1256,
inference(avatar_split_clause,[],[f395,f10085]) ).
fof(f10085,plain,
( spl0_1256
<=> ! [X44,X47,X5,X45] :
( X45 = X47
| c_append(X45,X44,X5) != c_append(X47,X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
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(f10083,plain,
spl0_1255,
inference(avatar_split_clause,[],[f358,f10081]) ).
fof(f10081,plain,
( spl0_1255
<=> ! [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_1255])]) ).
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(f10079,plain,
spl0_1254,
inference(avatar_split_clause,[],[f357,f10077]) ).
fof(f10077,plain,
( spl0_1254
<=> ! [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_1254])]) ).
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(f10075,plain,
spl0_1253,
inference(avatar_split_clause,[],[f350,f10073]) ).
fof(f10073,plain,
( spl0_1253
<=> ! [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_1253])]) ).
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(f10065,plain,
( spl0_1252
| ~ spl0_876
| ~ spl0_1251 ),
inference(avatar_split_clause,[],[f10061,f10058,f7652,f10063]) ).
fof(f10063,plain,
( spl0_1252
<=> ! [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_1252])]) ).
fof(f7652,plain,
( spl0_876
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f10058,plain,
( spl0_1251
<=> ! [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_1251])]) ).
fof(f10061,plain,
( ! [X19] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X19,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X19 )
| ~ spl0_876
| ~ spl0_1251 ),
inference(forward_demodulation,[],[f10059,f7654]) ).
fof(f7654,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_876 ),
inference(avatar_component_clause,[],[f7652]) ).
fof(f10059,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_1251 ),
inference(avatar_component_clause,[],[f10058]) ).
fof(f10060,plain,
spl0_1251,
inference(avatar_split_clause,[],[f349,f10058]) ).
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(f10056,plain,
spl0_1250,
inference(avatar_split_clause,[],[f342,f10054]) ).
fof(f10054,plain,
( spl0_1250
<=> ! [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_1250])]) ).
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(f10052,plain,
spl0_1249,
inference(avatar_split_clause,[],[f341,f10050]) ).
fof(f10050,plain,
( spl0_1249
<=> ! [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_1249])]) ).
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(f10048,plain,
spl0_1248,
inference(avatar_split_clause,[],[f322,f10046]) ).
fof(f10046,plain,
( spl0_1248
<=> ! [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_1248])]) ).
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(f10044,plain,
spl0_1247,
inference(avatar_split_clause,[],[f307,f10042]) ).
fof(f10042,plain,
( spl0_1247
<=> ! [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_1247])]) ).
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(f10040,plain,
spl0_1246,
inference(avatar_split_clause,[],[f278,f10038]) ).
fof(f10038,plain,
( spl0_1246
<=> ! [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_1246])]) ).
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(f10036,plain,
spl0_1245,
inference(avatar_split_clause,[],[f277,f10034]) ).
fof(f10034,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(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(f10032,plain,
spl0_1244,
inference(avatar_split_clause,[],[f274,f10030]) ).
fof(f10030,plain,
( spl0_1244
<=> ! [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_1244])]) ).
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(f10028,plain,
spl0_1243,
inference(avatar_split_clause,[],[f273,f10026]) ).
fof(f10026,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(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_1242
| ~ spl0_58
| ~ spl0_964 ),
inference(avatar_split_clause,[],[f8154,f8033,f3460,f10021]) ).
fof(f10021,plain,
( spl0_1242
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f8033,plain,
( spl0_964
<=> ! [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_964])]) ).
fof(f8154,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_964 ),
inference(resolution,[],[f8034,f3462]) ).
fof(f8034,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X5) )
| ~ spl0_964 ),
inference(avatar_component_clause,[],[f8033]) ).
fof(f10019,plain,
spl0_1241,
inference(avatar_split_clause,[],[f271,f10017]) ).
fof(f10017,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(f10015,plain,
spl0_1240,
inference(avatar_split_clause,[],[f265,f10013]) ).
fof(f10013,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(f10011,plain,
spl0_1239,
inference(avatar_split_clause,[],[f264,f10009]) ).
fof(f10009,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(f10007,plain,
spl0_1238,
inference(avatar_split_clause,[],[f263,f10005]) ).
fof(f10005,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(f10003,plain,
spl0_1237,
inference(avatar_split_clause,[],[f262,f10001]) ).
fof(f10001,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(f9999,plain,
spl0_1236,
inference(avatar_split_clause,[],[f226,f9997]) ).
fof(f9997,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(f9995,plain,
spl0_1235,
inference(avatar_split_clause,[],[f221,f9993]) ).
fof(f9993,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(f9991,plain,
spl0_1234,
inference(avatar_split_clause,[],[f207,f9989]) ).
fof(f9989,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(f9987,plain,
spl0_1233,
inference(avatar_split_clause,[],[f206,f9985]) ).
fof(f9985,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(f9983,plain,
spl0_1232,
inference(avatar_split_clause,[],[f108,f9981]) ).
fof(f9981,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
| ~ spl0_858
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8138,f7946,f7530,f9976]) ).
fof(f9976,plain,
( spl0_1231
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f7530,plain,
( spl0_858
<=> ! [X4,X5,X1] : c_in(X4,c_insert(X4,X1,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f7946,plain,
( spl0_943
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f8138,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_858
| ~ spl0_943 ),
inference(superposition,[],[f7531,f7948]) ).
fof(f7948,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_943 ),
inference(avatar_component_clause,[],[f7946]) ).
fof(f7531,plain,
( ! [X1,X4,X5] : c_in(X4,c_insert(X4,X1,X5),X5)
| ~ spl0_858 ),
inference(avatar_component_clause,[],[f7530]) ).
fof(f9974,plain,
spl0_1230,
inference(avatar_split_clause,[],[f98,f9972]) ).
fof(f9972,plain,
( spl0_1230
<=> ! [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_1230])]) ).
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(f9970,plain,
spl0_1229,
inference(avatar_split_clause,[],[f97,f9968]) ).
fof(f9968,plain,
( spl0_1229
<=> ! [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_1229])]) ).
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(f9966,plain,
spl0_1228,
inference(avatar_split_clause,[],[f56,f9964]) ).
fof(f9964,plain,
( spl0_1228
<=> ! [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_1228])]) ).
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(f9962,plain,
spl0_1227,
inference(avatar_split_clause,[],[f54,f9960]) ).
fof(f9960,plain,
( spl0_1227
<=> ! [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_1227])]) ).
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(f9958,plain,
spl0_1226,
inference(avatar_split_clause,[],[f50,f9956]) ).
fof(f9956,plain,
( spl0_1226
<=> ! [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_1226])]) ).
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(f9954,plain,
spl0_1225,
inference(avatar_split_clause,[],[f14,f9952]) ).
fof(f9952,plain,
( spl0_1225
<=> ! [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_1225])]) ).
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(f9941,plain,
( spl0_1224
| ~ spl0_93
| ~ spl0_931 ),
inference(avatar_split_clause,[],[f8118,f7898,f3635,f9939]) ).
fof(f9939,plain,
( spl0_1224
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f3635,plain,
( spl0_93
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f7898,plain,
( spl0_931
<=> ! [X5,X8] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X8,c_1,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f8118,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_93
| ~ spl0_931 ),
inference(resolution,[],[f7899,f3637]) ).
fof(f3637,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f3635]) ).
fof(f7899,plain,
( ! [X8,X5] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X8,c_1,X5) = X8 )
| ~ spl0_931 ),
inference(avatar_component_clause,[],[f7898]) ).
fof(f9802,plain,
( ~ spl0_1222
| spl0_1223
| ~ spl0_773
| ~ spl0_1188 ),
inference(avatar_split_clause,[],[f9794,f9451,f7186,f9800,f9796]) ).
fof(f9796,plain,
( spl0_1222
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f9800,plain,
( spl0_1223
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f7186,plain,
( spl0_773
<=> ! [X19] : c_0 = c_minus(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f9794,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_773
| ~ spl0_1188 ),
inference(trivial_inequality_removal,[],[f9787]) ).
fof(f9787,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_773
| ~ spl0_1188 ),
inference(superposition,[],[f9452,f7187]) ).
fof(f7187,plain,
( ! [X19] : c_0 = c_minus(c_0,X19,tc_nat)
| ~ spl0_773 ),
inference(avatar_component_clause,[],[f7186]) ).
fof(f9735,plain,
( spl0_1221
| ~ spl0_59
| ~ spl0_931 ),
inference(avatar_split_clause,[],[f8117,f7898,f3465,f9733]) ).
fof(f9733,plain,
( spl0_1221
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f3465,plain,
( spl0_59
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f8117,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_59
| ~ spl0_931 ),
inference(resolution,[],[f7899,f3467]) ).
fof(f3467,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f9688,plain,
( spl0_1220
| ~ spl0_93
| ~ spl0_930 ),
inference(avatar_split_clause,[],[f8116,f7894,f3635,f9686]) ).
fof(f9686,plain,
( spl0_1220
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f7894,plain,
( spl0_930
<=> ! [X5,X19] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f8116,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_93
| ~ spl0_930 ),
inference(resolution,[],[f7895,f3637]) ).
fof(f7895,plain,
( ! [X19,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X19,X5) )
| ~ spl0_930 ),
inference(avatar_component_clause,[],[f7894]) ).
fof(f9636,plain,
( spl0_1219
| ~ spl0_59
| ~ spl0_930 ),
inference(avatar_split_clause,[],[f8115,f7894,f3465,f9634]) ).
fof(f9634,plain,
( spl0_1219
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f8115,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_930 ),
inference(resolution,[],[f7895,f3467]) ).
fof(f9608,plain,
( spl0_1218
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_1146 ),
inference(avatar_split_clause,[],[f9285,f9282,f8336,f3460,f9606]) ).
fof(f9606,plain,
( spl0_1218
<=> ! [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_1218])]) ).
fof(f9282,plain,
( spl0_1146
<=> ! [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_1146])]) ).
fof(f9285,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_1010
| ~ spl0_1146 ),
inference(forward_demodulation,[],[f9283,f8622]) ).
fof(f9283,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_1146 ),
inference(avatar_component_clause,[],[f9282]) ).
fof(f9602,plain,
( spl0_1217
| ~ spl0_97
| ~ spl0_927 ),
inference(avatar_split_clause,[],[f8111,f7882,f3655,f9600]) ).
fof(f9600,plain,
( spl0_1217
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f3655,plain,
( spl0_97
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f7882,plain,
( spl0_927
<=> ! [X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omax(X8,X8,X23) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f8111,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_97
| ~ spl0_927 ),
inference(resolution,[],[f7883,f3657]) ).
fof(f3657,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f3655]) ).
fof(f7883,plain,
( ! [X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omax(X8,X8,X23) = X8 )
| ~ spl0_927 ),
inference(avatar_component_clause,[],[f7882]) ).
fof(f9570,plain,
spl0_1216,
inference(avatar_split_clause,[],[f3073,f9568]) ).
fof(f9568,plain,
( spl0_1216
<=> ! [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_1216])]) ).
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,[],[f2897,f2764]) ).
fof(f2897,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(f9566,plain,
spl0_1215,
inference(avatar_split_clause,[],[f3072,f9564]) ).
fof(f9564,plain,
( spl0_1215
<=> ! [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_1215])]) ).
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,[],[f2896,f2764]) ).
fof(f2896,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(f9562,plain,
( spl0_1214
| ~ spl0_33
| ~ spl0_927 ),
inference(avatar_split_clause,[],[f8110,f7882,f3335,f9560]) ).
fof(f9560,plain,
( spl0_1214
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f3335,plain,
( spl0_33
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f8110,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_33
| ~ spl0_927 ),
inference(resolution,[],[f7883,f3337]) ).
fof(f3337,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f3335]) ).
fof(f9558,plain,
spl0_1213,
inference(avatar_split_clause,[],[f3066,f9556]) ).
fof(f9556,plain,
( spl0_1213
<=> ! [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_1213])]) ).
fof(f3066,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,[],[f2885,f2764]) ).
fof(f2885,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(f9554,plain,
spl0_1212,
inference(avatar_split_clause,[],[f3003,f9552]) ).
fof(f9552,plain,
( spl0_1212
<=> ! [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_1212])]) ).
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,[],[f2804,f2800]) ).
fof(f2804,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(f9550,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2999,f9548]) ).
fof(f9548,plain,
( spl0_1211
<=> ! [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_1211])]) ).
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,[],[f2802,f2779]) ).
fof(f2802,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(f9546,plain,
spl0_1210,
inference(avatar_split_clause,[],[f2803,f9544]) ).
fof(f9544,plain,
( spl0_1210
<=> ! [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_1210])]) ).
fof(f2803,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(f9538,plain,
( spl0_1209
| ~ spl0_1208 ),
inference(avatar_split_clause,[],[f9534,f9531,f9536]) ).
fof(f9536,plain,
( spl0_1209
<=> ! [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_1209])]) ).
fof(f9531,plain,
( spl0_1208
<=> ! [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_1208])]) ).
fof(f9534,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_1208 ),
inference(forward_demodulation,[],[f9532,f2800]) ).
fof(f9532,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_1208 ),
inference(avatar_component_clause,[],[f9531]) ).
fof(f9533,plain,
spl0_1208,
inference(avatar_split_clause,[],[f2792,f9531]) ).
fof(f2792,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(f9529,plain,
spl0_1207,
inference(avatar_split_clause,[],[f1580,f9527]) ).
fof(f9527,plain,
( spl0_1207
<=> ! [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_1207])]) ).
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(f9525,plain,
spl0_1206,
inference(avatar_split_clause,[],[f1578,f9523]) ).
fof(f9523,plain,
( spl0_1206
<=> ! [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_1206])]) ).
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(f9521,plain,
spl0_1205,
inference(avatar_split_clause,[],[f1550,f9519]) ).
fof(f9519,plain,
( spl0_1205
<=> ! [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_1205])]) ).
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(f9517,plain,
( spl0_1204
| ~ spl0_97
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8109,f7878,f3655,f9515]) ).
fof(f9515,plain,
( spl0_1204
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f7878,plain,
( spl0_926
<=> ! [X23,X8] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omin(X8,X8,X23) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f8109,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_97
| ~ spl0_926 ),
inference(resolution,[],[f7879,f3657]) ).
fof(f7879,plain,
( ! [X8,X23] :
( ~ class_Orderings_Olinorder(X23)
| c_Orderings_Omin(X8,X8,X23) = X8 )
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f7878]) ).
fof(f9513,plain,
spl0_1203,
inference(avatar_split_clause,[],[f1507,f9511]) ).
fof(f9511,plain,
( spl0_1203
<=> ! [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_1203])]) ).
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(f9509,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1506,f9507]) ).
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(f9505,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1448,f9503]) ).
fof(f9503,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(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(f9501,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1447,f9499]) ).
fof(f9499,plain,
( spl0_1200
<=> ! [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_1200])]) ).
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(f9497,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1410,f9495]) ).
fof(f9495,plain,
( spl0_1199
<=> ! [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_1199])]) ).
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(f9493,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1407,f9491]) ).
fof(f9491,plain,
( spl0_1198
<=> ! [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_1198])]) ).
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(f9489,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1387,f9487]) ).
fof(f9487,plain,
( spl0_1197
<=> ! [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_1197])]) ).
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(f9485,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1136,f9483]) ).
fof(f9483,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(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(f9481,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1135,f9479]) ).
fof(f9479,plain,
( spl0_1195
<=> ! [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_1195])]) ).
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(f9477,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1117,f9475]) ).
fof(f9475,plain,
( spl0_1194
<=> ! [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_1194])]) ).
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(f9473,plain,
( spl0_1193
| ~ spl0_33
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8108,f7878,f3335,f9471]) ).
fof(f9471,plain,
( spl0_1193
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f8108,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_33
| ~ spl0_926 ),
inference(resolution,[],[f7879,f3337]) ).
fof(f9469,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1110,f9467]) ).
fof(f9467,plain,
( spl0_1192
<=> ! [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_1192])]) ).
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(f9465,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1109,f9463]) ).
fof(f9463,plain,
( spl0_1191
<=> ! [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_1191])]) ).
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(f9461,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1105,f9459]) ).
fof(f9459,plain,
( spl0_1190
<=> ! [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_1190])]) ).
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(f9457,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1104,f9455]) ).
fof(f9455,plain,
( spl0_1189
<=> ! [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_1189])]) ).
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(f9453,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1064,f9451]) ).
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(f9449,plain,
spl0_1187,
inference(avatar_split_clause,[],[f1048,f9447]) ).
fof(f9447,plain,
( spl0_1187
<=> ! [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_1187])]) ).
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(f9445,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1046,f9443]) ).
fof(f9443,plain,
( spl0_1186
<=> ! [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_1186])]) ).
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(f9441,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1044,f9439]) ).
fof(f9439,plain,
( spl0_1185
<=> ! [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_1185])]) ).
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(f9437,plain,
spl0_1184,
inference(avatar_split_clause,[],[f1043,f9435]) ).
fof(f9435,plain,
( spl0_1184
<=> ! [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_1184])]) ).
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(f9433,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1012,f9431]) ).
fof(f9431,plain,
( spl0_1183
<=> ! [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_1183])]) ).
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(f9429,plain,
( spl0_1182
| ~ spl0_70
| ~ spl0_922 ),
inference(avatar_split_clause,[],[f8103,f7862,f3520,f9427]) ).
fof(f9427,plain,
( spl0_1182
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f3520,plain,
( spl0_70
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f7862,plain,
( spl0_922
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X8,c_1,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f8103,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_70
| ~ spl0_922 ),
inference(resolution,[],[f7863,f3522]) ).
fof(f3522,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f3520]) ).
fof(f7863,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X8,c_1,X5) = X8 )
| ~ spl0_922 ),
inference(avatar_component_clause,[],[f7862]) ).
fof(f9425,plain,
spl0_1181,
inference(avatar_split_clause,[],[f992,f9423]) ).
fof(f9423,plain,
( spl0_1181
<=> ! [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_1181])]) ).
fof(f9421,plain,
spl0_1180,
inference(avatar_split_clause,[],[f969,f9419]) ).
fof(f9419,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(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(f9417,plain,
spl0_1179,
inference(avatar_split_clause,[],[f968,f9415]) ).
fof(f9415,plain,
( spl0_1179
<=> ! [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_1179])]) ).
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(f9413,plain,
spl0_1178,
inference(avatar_split_clause,[],[f944,f9411]) ).
fof(f9411,plain,
( spl0_1178
<=> ! [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_1178])]) ).
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(f9409,plain,
spl0_1177,
inference(avatar_split_clause,[],[f943,f9407]) ).
fof(f9407,plain,
( spl0_1177
<=> ! [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_1177])]) ).
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(f9405,plain,
spl0_1176,
inference(avatar_split_clause,[],[f895,f9403]) ).
fof(f9403,plain,
( spl0_1176
<=> ! [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_1176])]) ).
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(f9401,plain,
spl0_1175,
inference(avatar_split_clause,[],[f894,f9399]) ).
fof(f9399,plain,
( spl0_1175
<=> ! [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_1175])]) ).
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(f9397,plain,
spl0_1174,
inference(avatar_split_clause,[],[f716,f9395]) ).
fof(f9395,plain,
( spl0_1174
<=> ! [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_1174])]) ).
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(f9393,plain,
spl0_1173,
inference(avatar_split_clause,[],[f679,f9391]) ).
fof(f9391,plain,
( spl0_1173
<=> ! [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_1173])]) ).
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(f9389,plain,
spl0_1172,
inference(avatar_split_clause,[],[f626,f9387]) ).
fof(f9387,plain,
( spl0_1172
<=> ! [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_1172])]) ).
fof(f626,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_Osingleton__rev__conv_1) ).
fof(f9385,plain,
( spl0_1171
| ~ spl0_21
| ~ spl0_922 ),
inference(avatar_split_clause,[],[f8102,f7862,f3275,f9383]) ).
fof(f9383,plain,
( spl0_1171
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f3275,plain,
( spl0_21
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f8102,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_21
| ~ spl0_922 ),
inference(resolution,[],[f7863,f3277]) ).
fof(f3277,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f3275]) ).
fof(f9381,plain,
spl0_1170,
inference(avatar_split_clause,[],[f596,f9379]) ).
fof(f9379,plain,
( spl0_1170
<=> ! [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_1170])]) ).
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(f9377,plain,
spl0_1169,
inference(avatar_split_clause,[],[f577,f9375]) ).
fof(f9375,plain,
( spl0_1169
<=> ! [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_1169])]) ).
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(f9373,plain,
spl0_1168,
inference(avatar_split_clause,[],[f478,f9371]) ).
fof(f9371,plain,
( spl0_1168
<=> ! [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_1168])]) ).
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(f9369,plain,
spl0_1167,
inference(avatar_split_clause,[],[f474,f9367]) ).
fof(f9367,plain,
( spl0_1167
<=> ! [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_1167])]) ).
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(f9365,plain,
spl0_1166,
inference(avatar_split_clause,[],[f473,f9363]) ).
fof(f9363,plain,
( spl0_1166
<=> ! [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_1166])]) ).
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(f9361,plain,
spl0_1165,
inference(avatar_split_clause,[],[f460,f9359]) ).
fof(f9359,plain,
( spl0_1165
<=> ! [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_1165])]) ).
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(f9357,plain,
spl0_1164,
inference(avatar_split_clause,[],[f459,f9355]) ).
fof(f9355,plain,
( spl0_1164
<=> ! [X5,X8,X19] :
( c_0 = X19
| c_List_Olast(c_List_Oreplicate(X19,X8,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
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(f9353,plain,
spl0_1163,
inference(avatar_split_clause,[],[f458,f9351]) ).
fof(f9351,plain,
( spl0_1163
<=> ! [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_1163])]) ).
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(f9349,plain,
spl0_1162,
inference(avatar_split_clause,[],[f449,f9347]) ).
fof(f9347,plain,
( spl0_1162
<=> ! [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_1162])]) ).
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(f9345,plain,
spl0_1161,
inference(avatar_split_clause,[],[f448,f9343]) ).
fof(f9343,plain,
( spl0_1161
<=> ! [X5,X8,X19] :
( c_0 = X19
| c_List_Ohd(c_List_Oreplicate(X19,X8,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
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(f9341,plain,
( spl0_1160
| ~ spl0_70
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8101,f7858,f3520,f9339]) ).
fof(f9339,plain,
( spl0_1160
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f7858,plain,
( spl0_921
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f8101,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_70
| ~ spl0_921 ),
inference(resolution,[],[f7859,f3522]) ).
fof(f7859,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X8,X5) = X8 )
| ~ spl0_921 ),
inference(avatar_component_clause,[],[f7858]) ).
fof(f9337,plain,
spl0_1159,
inference(avatar_split_clause,[],[f447,f9335]) ).
fof(f9335,plain,
( spl0_1159
<=> ! [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_1159])]) ).
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(f9333,plain,
spl0_1158,
inference(avatar_split_clause,[],[f404,f9331]) ).
fof(f9331,plain,
( spl0_1158
<=> ! [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_1158])]) ).
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(f9329,plain,
spl0_1157,
inference(avatar_split_clause,[],[f328,f9327]) ).
fof(f9327,plain,
( spl0_1157
<=> ! [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_1157])]) ).
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(f9325,plain,
spl0_1156,
inference(avatar_split_clause,[],[f327,f9323]) ).
fof(f9323,plain,
( spl0_1156
<=> ! [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_1156])]) ).
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(f9321,plain,
spl0_1155,
inference(avatar_split_clause,[],[f320,f9319]) ).
fof(f9319,plain,
( spl0_1155
<=> ! [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_1155])]) ).
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(f9317,plain,
spl0_1154,
inference(avatar_split_clause,[],[f319,f9315]) ).
fof(f9315,plain,
( spl0_1154
<=> ! [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_1154])]) ).
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(f9313,plain,
spl0_1153,
inference(avatar_split_clause,[],[f283,f9311]) ).
fof(f9311,plain,
( spl0_1153
<=> ! [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_1153])]) ).
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(f9309,plain,
spl0_1152,
inference(avatar_split_clause,[],[f219,f9307]) ).
fof(f9307,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(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(f9305,plain,
spl0_1151,
inference(avatar_split_clause,[],[f218,f9303]) ).
fof(f9303,plain,
( spl0_1151
<=> ! [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_1151])]) ).
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(f9301,plain,
spl0_1150,
inference(avatar_split_clause,[],[f217,f9299]) ).
fof(f9299,plain,
( spl0_1150
<=> ! [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_1150])]) ).
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(f9297,plain,
( spl0_1149
| ~ spl0_21
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8100,f7858,f3275,f9295]) ).
fof(f9295,plain,
( spl0_1149
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f8100,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_21
| ~ spl0_921 ),
inference(resolution,[],[f7859,f3277]) ).
fof(f9293,plain,
spl0_1148,
inference(avatar_split_clause,[],[f216,f9291]) ).
fof(f9291,plain,
( spl0_1148
<=> ! [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_1148])]) ).
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(f9289,plain,
spl0_1147,
inference(avatar_split_clause,[],[f213,f9287]) ).
fof(f9287,plain,
( spl0_1147
<=> ! [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_1147])]) ).
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(f9284,plain,
spl0_1146,
inference(avatar_split_clause,[],[f210,f9282]) ).
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(f9280,plain,
spl0_1145,
inference(avatar_split_clause,[],[f175,f9278]) ).
fof(f9278,plain,
( spl0_1145
<=> ! [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_1145])]) ).
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(f9276,plain,
spl0_1144,
inference(avatar_split_clause,[],[f172,f9274]) ).
fof(f9274,plain,
( spl0_1144
<=> ! [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_1144])]) ).
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(f9272,plain,
spl0_1143,
inference(avatar_split_clause,[],[f101,f9270]) ).
fof(f9270,plain,
( spl0_1143
<=> ! [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_1143])]) ).
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(f9268,plain,
spl0_1142,
inference(avatar_split_clause,[],[f99,f9266]) ).
fof(f9266,plain,
( spl0_1142
<=> ! [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_1142])]) ).
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(f9264,plain,
spl0_1141,
inference(avatar_split_clause,[],[f43,f9262]) ).
fof(f9262,plain,
( spl0_1141
<=> ! [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_1141])]) ).
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(f9260,plain,
spl0_1140,
inference(avatar_split_clause,[],[f31,f9258]) ).
fof(f9258,plain,
( spl0_1140
<=> ! [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_1140])]) ).
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(f9256,plain,
spl0_1139,
inference(avatar_split_clause,[],[f21,f9254]) ).
fof(f9254,plain,
( spl0_1139
<=> ! [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_1139])]) ).
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(f9252,plain,
( spl0_1138
| ~ spl0_15
| ~ spl0_920 ),
inference(avatar_split_clause,[],[f8099,f7854,f3245,f9250]) ).
fof(f9250,plain,
( spl0_1138
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f3245,plain,
( spl0_15
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f7854,plain,
( spl0_920
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X2,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f8099,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_15
| ~ spl0_920 ),
inference(resolution,[],[f7855,f3247]) ).
fof(f3247,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f3245]) ).
fof(f7855,plain,
( ! [X2,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X2,X2,X5) )
| ~ spl0_920 ),
inference(avatar_component_clause,[],[f7854]) ).
fof(f9248,plain,
spl0_1137,
inference(avatar_split_clause,[],[f20,f9246]) ).
fof(f9246,plain,
( spl0_1137
<=> ! [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_1137])]) ).
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(f9244,plain,
spl0_1136,
inference(avatar_split_clause,[],[f19,f9242]) ).
fof(f9242,plain,
( spl0_1136
<=> ! [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_1136])]) ).
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(f9220,plain,
( spl0_1135
| ~ spl0_15
| ~ spl0_919 ),
inference(avatar_split_clause,[],[f8098,f7850,f3245,f9218]) ).
fof(f9218,plain,
( spl0_1135
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f7850,plain,
( spl0_919
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X8,c_0,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f8098,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_15
| ~ spl0_919 ),
inference(resolution,[],[f7851,f3247]) ).
fof(f7851,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X8,c_0,X5) = X8 )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f7850]) ).
fof(f9206,plain,
( spl0_1134
| ~ spl0_10
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8096,f7846,f3220,f9204]) ).
fof(f9204,plain,
( spl0_1134
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f3220,plain,
( spl0_10
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f7846,plain,
( spl0_918
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X8,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f8096,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_10
| ~ spl0_918 ),
inference(resolution,[],[f7847,f3222]) ).
fof(f3222,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f3220]) ).
fof(f7847,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X8,X5) = X8 )
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f7846]) ).
fof(f9182,plain,
( spl0_1133
| ~ spl0_10
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8094,f7842,f3220,f9180]) ).
fof(f9180,plain,
( spl0_1133
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f7842,plain,
( spl0_917
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X8,c_0,X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f8094,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_10
| ~ spl0_917 ),
inference(resolution,[],[f7843,f3222]) ).
fof(f7843,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X8,c_0,X5) = X8 )
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f7842]) ).
fof(f9128,plain,
( spl0_1132
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_1081 ),
inference(avatar_split_clause,[],[f8823,f8820,f8336,f3460,f9126]) ).
fof(f9126,plain,
( spl0_1132
<=> ! [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_1132])]) ).
fof(f8820,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(f8823,plain,
( ! [X2] : c_uminus(X2,tc_IntDef_Oint) = c_div(X2,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1010
| ~ spl0_1081 ),
inference(forward_demodulation,[],[f8821,f8622]) ).
fof(f8821,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,[],[f8820]) ).
fof(f9092,plain,
( spl0_1131
| spl0_672
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f9065,f8760,f6743,f9089]) ).
fof(f9089,plain,
( spl0_1131
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f6743,plain,
( spl0_672
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f9065,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_672
| ~ spl0_1066 ),
inference(resolution,[],[f8761,f6745]) ).
fof(f6745,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_672 ),
inference(avatar_component_clause,[],[f6743]) ).
fof(f9032,plain,
( spl0_1130
| ~ spl0_10
| ~ spl0_117
| ~ spl0_917
| ~ spl0_1124 ),
inference(avatar_split_clause,[],[f9001,f8996,f7842,f3749,f3220,f9029]) ).
fof(f9029,plain,
( spl0_1130
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f3749,plain,
( spl0_117
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f8996,plain,
( spl0_1124
<=> ! [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_1124])]) ).
fof(f9001,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_117
| ~ spl0_917
| ~ spl0_1124 ),
inference(forward_demodulation,[],[f9000,f8094]) ).
fof(f9000,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_117
| ~ spl0_1124 ),
inference(superposition,[],[f8997,f3751]) ).
fof(f3751,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f3749]) ).
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(avatar_component_clause,[],[f8996]) ).
fof(f9021,plain,
spl0_1129,
inference(avatar_split_clause,[],[f3121,f9019]) ).
fof(f9019,plain,
( spl0_1129
<=> ! [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_1129])]) ).
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,[],[f2929,f2763]) ).
fof(f2929,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(f9017,plain,
spl0_1128,
inference(avatar_split_clause,[],[f3006,f9015]) ).
fof(f9015,plain,
( spl0_1128
<=> ! [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_1128])]) ).
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,[],[f2809,f2764]) ).
fof(f2809,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(f9013,plain,
spl0_1127,
inference(avatar_split_clause,[],[f3005,f9011]) ).
fof(f9011,plain,
( spl0_1127
<=> ! [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_1127])]) ).
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,[],[f2808,f2764]) ).
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_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(f9009,plain,
spl0_1126,
inference(avatar_split_clause,[],[f2880,f9007]) ).
fof(f9007,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(f2880,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(f9005,plain,
spl0_1125,
inference(avatar_split_clause,[],[f2870,f9003]) ).
fof(f9003,plain,
( spl0_1125
<=> ! [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_1125])]) ).
fof(f2870,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(f8998,plain,
( spl0_1124
| ~ spl0_1123 ),
inference(avatar_split_clause,[],[f8994,f8991,f8996]) ).
fof(f8991,plain,
( spl0_1123
<=> ! [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_1123])]) ).
fof(f8994,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_1123 ),
inference(forward_demodulation,[],[f8992,f2800]) ).
fof(f8992,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_1123 ),
inference(avatar_component_clause,[],[f8991]) ).
fof(f8993,plain,
spl0_1123,
inference(avatar_split_clause,[],[f2791,f8991]) ).
fof(f2791,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(f8989,plain,
( spl0_1122
| ~ spl0_800
| ~ spl0_1121 ),
inference(avatar_split_clause,[],[f8985,f8982,f7295,f8987]) ).
fof(f8987,plain,
( spl0_1122
<=> ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f8982,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(f8985,plain,
( ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X5)
| ~ spl0_800
| ~ spl0_1121 ),
inference(forward_demodulation,[],[f8983,f7296]) ).
fof(f8983,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,[],[f8982]) ).
fof(f8984,plain,
spl0_1121,
inference(avatar_split_clause,[],[f2765,f8982]) ).
fof(f2765,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(f8980,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1697,f8978]) ).
fof(f8978,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(f8976,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1695,f8974]) ).
fof(f8974,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(f8972,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1694,f8970]) ).
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(f8968,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1536,f8966]) ).
fof(f8966,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(f8964,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1519,f8962]) ).
fof(f8962,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(f8960,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1483,f8958]) ).
fof(f8958,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(f8956,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1480,f8954]) ).
fof(f8954,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(f8952,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1253,f8950]) ).
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(f8948,plain,
( spl0_1112
| ~ spl0_703
| ~ spl0_870
| ~ spl0_913 ),
inference(avatar_split_clause,[],[f8083,f7826,f7579,f6885,f8945]) ).
fof(f8945,plain,
( spl0_1112
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f7579,plain,
( spl0_870
<=> 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_870])]) ).
fof(f7826,plain,
( spl0_913
<=> ! [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_913])]) ).
fof(f8083,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_703
| ~ spl0_870
| ~ spl0_913 ),
inference(forward_demodulation,[],[f8081,f6887]) ).
fof(f8081,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_870
| ~ spl0_913 ),
inference(superposition,[],[f7827,f7581]) ).
fof(f7581,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f7579]) ).
fof(f7827,plain,
( ! [X39] : c_Numeral_OBit(X39,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X39,c_Numeral_Obit_OB0))
| ~ spl0_913 ),
inference(avatar_component_clause,[],[f7826]) ).
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(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(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,[],[f1084,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(f1084,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__0__equal__iff__equal_0) ).
fof(f8907,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1078,f8905]) ).
fof(f8905,plain,
( spl0_1102
<=> ! [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_1102])]) ).
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(f8903,plain,
( spl0_1101
| ~ spl0_88
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f8060,f7744,f3610,f8901]) ).
fof(f8901,plain,
( spl0_1101
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
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(f8060,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(f8899,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1076,f8897]) ).
fof(f8897,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(f8895,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1062,f8893]) ).
fof(f8893,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(f8891,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1040,f8889]) ).
fof(f8889,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(f1040,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__eq__0_0) ).
fof(f8887,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1036,f8885]) ).
fof(f8885,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(f8883,plain,
spl0_1096,
inference(avatar_split_clause,[],[f904,f8881]) ).
fof(f8881,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(f8879,plain,
spl0_1095,
inference(avatar_split_clause,[],[f903,f8877]) ).
fof(f8877,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(f8875,plain,
spl0_1094,
inference(avatar_split_clause,[],[f714,f8873]) ).
fof(f8873,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(f714,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__number__of__0_2) ).
fof(f8871,plain,
spl0_1093,
inference(avatar_split_clause,[],[f697,f8869]) ).
fof(f8869,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(f8867,plain,
spl0_1092,
inference(avatar_split_clause,[],[f676,f8865]) ).
fof(f8865,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(f8863,plain,
spl0_1091,
inference(avatar_split_clause,[],[f624,f8861]) ).
fof(f8861,plain,
( spl0_1091
<=> ! [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_1091])]) ).
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(f8859,plain,
( spl0_1090
| ~ spl0_30
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f8059,f7744,f3320,f8857]) ).
fof(f8857,plain,
( spl0_1090
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f3320,plain,
( spl0_30
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f8059,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(f8855,plain,
spl0_1089,
inference(avatar_split_clause,[],[f595,f8853]) ).
fof(f8853,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(f8851,plain,
spl0_1088,
inference(avatar_split_clause,[],[f468,f8849]) ).
fof(f8849,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(f8847,plain,
spl0_1087,
inference(avatar_split_clause,[],[f413,f8845]) ).
fof(f8845,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(f8843,plain,
spl0_1086,
inference(avatar_split_clause,[],[f406,f8841]) ).
fof(f8841,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(f8839,plain,
spl0_1085,
inference(avatar_split_clause,[],[f405,f8837]) ).
fof(f8837,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(f8835,plain,
spl0_1084,
inference(avatar_split_clause,[],[f374,f8833]) ).
fof(f8833,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(f8831,plain,
spl0_1083,
inference(avatar_split_clause,[],[f353,f8829]) ).
fof(f8829,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(f8827,plain,
spl0_1082,
inference(avatar_split_clause,[],[f352,f8825]) ).
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(f8822,plain,
spl0_1081,
inference(avatar_split_clause,[],[f332,f8820]) ).
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(f8818,plain,
spl0_1080,
inference(avatar_split_clause,[],[f305,f8816]) ).
fof(f8816,plain,
( spl0_1080
<=> ! [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_1080])]) ).
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(f8814,plain,
( spl0_1079
| ~ spl0_95
| ~ spl0_892 ),
inference(avatar_split_clause,[],[f8058,f7740,f3645,f8812]) ).
fof(f8812,plain,
( spl0_1079
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
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(f8058,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(f8810,plain,
spl0_1078,
inference(avatar_split_clause,[],[f304,f8808]) ).
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(f8806,plain,
spl0_1077,
inference(avatar_split_clause,[],[f295,f8804]) ).
fof(f8804,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(f8802,plain,
spl0_1076,
inference(avatar_split_clause,[],[f294,f8800]) ).
fof(f8800,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(f8798,plain,
spl0_1075,
inference(avatar_split_clause,[],[f293,f8796]) ).
fof(f8796,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(f8794,plain,
spl0_1074,
inference(avatar_split_clause,[],[f292,f8792]) ).
fof(f8792,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(f8790,plain,
spl0_1073,
inference(avatar_split_clause,[],[f291,f8788]) ).
fof(f8788,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(f8786,plain,
spl0_1072,
inference(avatar_split_clause,[],[f290,f8784]) ).
fof(f8784,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(f8782,plain,
spl0_1071,
inference(avatar_split_clause,[],[f272,f8780]) ).
fof(f8780,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(f8778,plain,
spl0_1070,
inference(avatar_split_clause,[],[f269,f8776]) ).
fof(f8776,plain,
( spl0_1070
<=> ! [X5,X39] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X39
| c_0 != c_IntDef_Oof__int(X39,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f269,axiom,
! [X39,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X39
| c_0 != c_IntDef_Oof__int(X39,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
fof(f8774,plain,
spl0_1069,
inference(avatar_split_clause,[],[f255,f8772]) ).
fof(f8772,plain,
( spl0_1069
<=> ! [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_1069])]) ).
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(f8770,plain,
( spl0_1068
| ~ spl0_31
| ~ spl0_892 ),
inference(avatar_split_clause,[],[f8057,f7740,f3325,f8768]) ).
fof(f8768,plain,
( spl0_1068
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f3325,plain,
( spl0_31
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f8057,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(f8766,plain,
spl0_1067,
inference(avatar_split_clause,[],[f254,f8764]) ).
fof(f8764,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(f8762,plain,
spl0_1066,
inference(avatar_split_clause,[],[f144,f8760]) ).
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(f8758,plain,
spl0_1065,
inference(avatar_split_clause,[],[f140,f8756]) ).
fof(f8756,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(f8754,plain,
spl0_1064,
inference(avatar_split_clause,[],[f130,f8752]) ).
fof(f8752,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(f8750,plain,
spl0_1063,
inference(avatar_split_clause,[],[f100,f8748]) ).
fof(f8748,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(f8746,plain,
spl0_1062,
inference(avatar_split_clause,[],[f89,f8744]) ).
fof(f8744,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(f8742,plain,
spl0_1061,
inference(avatar_split_clause,[],[f81,f8740]) ).
fof(f8740,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(f8738,plain,
spl0_1060,
inference(avatar_split_clause,[],[f66,f8736]) ).
fof(f8736,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(f8734,plain,
spl0_1059,
inference(avatar_split_clause,[],[f64,f8732]) ).
fof(f8732,plain,
( spl0_1059
<=> ! [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_1059])]) ).
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(f8730,plain,
spl0_1058,
inference(avatar_split_clause,[],[f59,f8728]) ).
fof(f8728,plain,
( spl0_1058
<=> ! [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_1058])]) ).
fof(f59,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_OLeaf__not__Scons_0) ).
fof(f8725,plain,
spl0_1057,
inference(avatar_split_clause,[],[f45,f8723]) ).
fof(f8723,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(f8721,plain,
spl0_1056,
inference(avatar_split_clause,[],[f44,f8719]) ).
fof(f8719,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(f8717,plain,
spl0_1055,
inference(avatar_split_clause,[],[f40,f8715]) ).
fof(f8715,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(f8713,plain,
spl0_1054,
inference(avatar_split_clause,[],[f35,f8711]) ).
fof(f8711,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(f8709,plain,
spl0_1053,
inference(avatar_split_clause,[],[f34,f8707]) ).
fof(f8707,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(f8705,plain,
spl0_1052,
inference(avatar_split_clause,[],[f33,f8703]) ).
fof(f8703,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(f8663,plain,
( spl0_1051
| ~ spl0_802
| ~ spl0_1024 ),
inference(avatar_split_clause,[],[f8644,f8392,f7303,f8661]) ).
fof(f8661,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(f8644,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_802
| ~ spl0_1024 ),
inference(superposition,[],[f7304,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_874
| ~ spl0_1006 ),
inference(avatar_split_clause,[],[f8605,f8319,f7610,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(f7610,plain,
( spl0_874
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
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(f8605,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_874
| ~ spl0_1006 ),
inference(resolution,[],[f8320,f7611]) ).
fof(f7611,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_874 ),
inference(avatar_component_clause,[],[f7610]) ).
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(f8595,plain,
( spl0_1049
| ~ spl0_802
| ~ spl0_999 ),
inference(avatar_split_clause,[],[f8591,f8291,f7303,f8593]) ).
fof(f8593,plain,
( spl0_1049
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f8291,plain,
( spl0_999
<=> ! [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_999])]) ).
fof(f8591,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_802
| ~ spl0_999 ),
inference(superposition,[],[f7304,f8292]) ).
fof(f8292,plain,
( ! [X21] : c_List_Olistset(c_List_Olist_ONil,X21) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X21))
| ~ spl0_999 ),
inference(avatar_component_clause,[],[f8291]) ).
fof(f8544,plain,
( ~ spl0_80
| spl0_1048
| ~ spl0_670
| ~ spl0_890 ),
inference(avatar_split_clause,[],[f8056,f7732,f6735,f8542,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(f6735,plain,
( spl0_670
<=> ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
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(f8056,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_670
| ~ spl0_890 ),
inference(superposition,[],[f7733,f6736]) ).
fof(f6736,plain,
( ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8
| ~ spl0_670 ),
inference(avatar_component_clause,[],[f6735]) ).
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(f8491,plain,
( spl0_1047
| ~ spl0_823
| ~ spl0_863 ),
inference(avatar_split_clause,[],[f7671,f7550,f7390,f8489]) ).
fof(f8489,plain,
( spl0_1047
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f7390,plain,
( spl0_823
<=> ! [X30] :
( c_0 = X30
| ~ c_Divides_Oop_Advd(c_0,X30,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f7550,plain,
( spl0_863
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f7671,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_823
| ~ spl0_863 ),
inference(resolution,[],[f7551,f7391]) ).
fof(f7391,plain,
( ! [X30] :
( ~ c_Divides_Oop_Advd(c_0,X30,tc_IntDef_Oint)
| c_0 = X30 )
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f7390]) ).
fof(f7551,plain,
( ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_863 ),
inference(avatar_component_clause,[],[f7550]) ).
fof(f8483,plain,
spl0_1046,
inference(avatar_split_clause,[],[f3074,f8481]) ).
fof(f8481,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,[],[f2901,f2764]) ).
fof(f2901,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(f8479,plain,
spl0_1045,
inference(avatar_split_clause,[],[f3067,f8477]) ).
fof(f8477,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(f3067,plain,
! [X9] :
( c_less(c_1,c_IntDef_Onat(X9),tc_nat)
| ~ c_less(c_1,X9,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2888,f2764]) ).
fof(f2888,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(f8475,plain,
spl0_1044,
inference(avatar_split_clause,[],[f3059,f8473]) ).
fof(f8473,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(f3059,plain,
! [X19,X30] :
( c_1 != c_times(X30,X19,tc_nat)
| c_1 = X30 ),
inference(forward_demodulation,[],[f2877,f2764]) ).
fof(f2877,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(f8471,plain,
spl0_1043,
inference(avatar_split_clause,[],[f3057,f8469]) ).
fof(f8469,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,[],[f2875,f2764]) ).
fof(f2875,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,[],[f958,f1409]) ).
fof(f958,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_Oone__eq__mult__iff_1) ).
fof(f8467,plain,
spl0_1042,
inference(avatar_split_clause,[],[f2795,f8465]) ).
fof(f2795,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(f8463,plain,
spl0_1041,
inference(avatar_split_clause,[],[f2784,f8461]) ).
fof(f8461,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(f2784,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(f8459,plain,
spl0_1040,
inference(avatar_split_clause,[],[f2783,f8457]) ).
fof(f8457,plain,
( spl0_1040
<=> ! [X5,X8] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X5),X8,X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f2783,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(f8455,plain,
( spl0_1039
| ~ spl0_823
| ~ spl0_862 ),
inference(avatar_split_clause,[],[f7665,f7546,f7390,f8453]) ).
fof(f8453,plain,
( spl0_1039
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f7546,plain,
( spl0_862
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f7665,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_823
| ~ spl0_862 ),
inference(resolution,[],[f7547,f7391]) ).
fof(f7547,plain,
( ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_862 ),
inference(avatar_component_clause,[],[f7546]) ).
fof(f8451,plain,
spl0_1038,
inference(avatar_split_clause,[],[f2782,f8449]) ).
fof(f8449,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(f2782,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(f8447,plain,
spl0_1037,
inference(avatar_split_clause,[],[f2776,f8445]) ).
fof(f8445,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(f2776,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(f8443,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1655,f8441]) ).
fof(f8441,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(f8439,plain,
spl0_1035,
inference(avatar_split_clause,[],[f1654,f8437]) ).
fof(f8437,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(f8435,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1627,f8433]) ).
fof(f8433,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(f8431,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1626,f8429]) ).
fof(f8429,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(f8427,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1583,f8425]) ).
fof(f8425,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(f8423,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1582,f8421]) ).
fof(f8421,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(f8419,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1567,f8417]) ).
fof(f8417,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(f8415,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1532,f8413]) ).
fof(f8413,plain,
( spl0_1029
<=> ! [X5,X8] : c_uminus(c_uminus(X8,tc_set(X5)),tc_set(X5)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
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(f8411,plain,
( spl0_1028
| ~ spl0_116
| ~ spl0_820 ),
inference(avatar_split_clause,[],[f7604,f7378,f3744,f8408]) ).
fof(f8408,plain,
( spl0_1028
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f7378,plain,
( spl0_820
<=> ! [X19] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f7604,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_116
| ~ spl0_820 ),
inference(superposition,[],[f7379,f3746]) ).
fof(f7379,plain,
( ! [X19] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint))
| ~ spl0_820 ),
inference(avatar_component_clause,[],[f7378]) ).
fof(f8406,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1524,f8404]) ).
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,
inference(avatar_split_clause,[],[f1158,f8368]) ).
fof(f8368,plain,
( spl0_1018
<=> ! [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_1018])]) ).
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(f8366,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1150,f8364]) ).
fof(f8364,plain,
( spl0_1017
<=> ! [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_1017])]) ).
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(f8362,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1149,f8360]) ).
fof(f8360,plain,
( spl0_1016
<=> ! [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_1016])]) ).
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(f8358,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1145,f8356]) ).
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(f8354,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1081,f8352]) ).
fof(f8352,plain,
( spl0_1014
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_uminus(X8,X5),X5) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
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(f8350,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1019,f8348]) ).
fof(f8348,plain,
( spl0_1013
<=> ! [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_1013])]) ).
fof(f8346,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1015,f8344]) ).
fof(f8344,plain,
( spl0_1012
<=> ! [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_1012])]) ).
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(f8342,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1001,f8340]) ).
fof(f8340,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_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
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(f8338,plain,
spl0_1010,
inference(avatar_split_clause,[],[f983,f8336]) ).
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(f8334,plain,
spl0_1009,
inference(avatar_split_clause,[],[f897,f8332]) ).
fof(f8332,plain,
( spl0_1009
<=> ! [X30,X19] :
( c_0 = X19
| c_0 != c_plus(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
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(f8330,plain,
spl0_1008,
inference(avatar_split_clause,[],[f896,f8328]) ).
fof(f8328,plain,
( spl0_1008
<=> ! [X19,X30] :
( c_0 = X30
| c_0 != c_plus(X30,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
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(f8326,plain,
( ~ spl0_58
| spl0_1007
| ~ spl0_838
| ~ spl0_952 ),
inference(avatar_split_clause,[],[f8150,f7983,f7450,f8323,f3460]) ).
fof(f8323,plain,
( spl0_1007
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f7450,plain,
( spl0_838
<=> ! [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_838])]) ).
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(f8150,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_838
| ~ spl0_952 ),
inference(superposition,[],[f7451,f7985]) ).
fof(f7985,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_952 ),
inference(avatar_component_clause,[],[f7983]) ).
fof(f7451,plain,
( ! [X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_838 ),
inference(avatar_component_clause,[],[f7450]) ).
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,[],[f605,f8303]) ).
fof(f8303,plain,
( spl0_1002
<=> ! [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_1002])]) ).
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(f8301,plain,
spl0_1001,
inference(avatar_split_clause,[],[f585,f8299]) ).
fof(f8299,plain,
( spl0_1001
<=> ! [X4,X5,X44] : c_List_Oremove1(X4,c_List_Olist_OCons(X4,X44,X5),X5) = X44 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
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(f8297,plain,
spl0_1000,
inference(avatar_split_clause,[],[f557,f8295]) ).
fof(f8295,plain,
( spl0_1000
<=> ! [X5,X44,X8] : c_List_Onth(c_List_Olist_OCons(X8,X44,X5),c_0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
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(f8293,plain,
spl0_999,
inference(avatar_split_clause,[],[f504,f8291]) ).
fof(f8289,plain,
spl0_998,
inference(avatar_split_clause,[],[f472,f8287]) ).
fof(f8287,plain,
( spl0_998
<=> ! [X4,X5,X8] : c_Nat_Osize(c_List_Oreplicate(X8,X4,X5),tc_List_Olist(X5)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
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(f8285,plain,
spl0_997,
inference(avatar_split_clause,[],[f462,f8283]) ).
fof(f8283,plain,
( spl0_997
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_0 != c_Nat_Osize(X44,tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
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(f8281,plain,
spl0_996,
inference(avatar_split_clause,[],[f430,f8279]) ).
fof(f8279,plain,
( spl0_996
<=> ! [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_996])]) ).
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(f8277,plain,
spl0_995,
inference(avatar_split_clause,[],[f429,f8275]) ).
fof(f8275,plain,
( spl0_995
<=> ! [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_995])]) ).
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(f8273,plain,
spl0_994,
inference(avatar_split_clause,[],[f428,f8271]) ).
fof(f8271,plain,
( spl0_994
<=> ! [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_994])]) ).
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(f8269,plain,
spl0_993,
inference(avatar_split_clause,[],[f425,f8267]) ).
fof(f8267,plain,
( spl0_993
<=> ! [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_993])]) ).
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(f8265,plain,
spl0_992,
inference(avatar_split_clause,[],[f424,f8263]) ).
fof(f8263,plain,
( spl0_992
<=> ! [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_992])]) ).
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(f8261,plain,
spl0_991,
inference(avatar_split_clause,[],[f421,f8259]) ).
fof(f8259,plain,
( spl0_991
<=> ! [X45,X5,X44] :
( c_List_Odistinct(X45,X5)
| ~ c_List_Odistinct(c_append(X44,X45,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
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(f8257,plain,
spl0_990,
inference(avatar_split_clause,[],[f420,f8255]) ).
fof(f8255,plain,
( spl0_990
<=> ! [X45,X5,X44] :
( c_List_Odistinct(X44,X5)
| ~ c_List_Odistinct(c_append(X44,X45,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
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(f8253,plain,
spl0_989,
inference(avatar_split_clause,[],[f418,f8251]) ).
fof(f8251,plain,
( spl0_989
<=> ! [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_989])]) ).
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(f8249,plain,
spl0_988,
inference(avatar_split_clause,[],[f398,f8247]) ).
fof(f8247,plain,
( spl0_988
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X45
| c_append(X44,X45,X5) != X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
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(f8245,plain,
spl0_987,
inference(avatar_split_clause,[],[f396,f8243]) ).
fof(f8243,plain,
( spl0_987
<=> ! [X45,X5,X44] :
( c_List_Olist_ONil = X44
| c_append(X44,X45,X5) != X45 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f396,axiom,
! [X44,X45,X5] :
( c_List_Olist_ONil = X44
| c_append(X44,X45,X5) != X45 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_0) ).
fof(f8241,plain,
( ~ spl0_986
| ~ spl0_802
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8139,f7946,f7303,f8238]) ).
fof(f8238,plain,
( spl0_986
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f8139,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_802
| ~ spl0_943 ),
inference(superposition,[],[f7304,f7948]) ).
fof(f8236,plain,
spl0_985,
inference(avatar_split_clause,[],[f393,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(f393,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_Oappend__is__Nil__conv_1) ).
fof(f8232,plain,
spl0_984,
inference(avatar_split_clause,[],[f392,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(f392,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_Oappend__is__Nil__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,
inference(avatar_split_clause,[],[f286,f8198]) ).
fof(f8198,plain,
( spl0_976
<=> ! [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_976])]) ).
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(f8195,plain,
spl0_975,
inference(avatar_split_clause,[],[f285,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(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(f8191,plain,
spl0_974,
inference(avatar_split_clause,[],[f245,f8189]) ).
fof(f8189,plain,
( spl0_974
<=> ! [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_974])]) ).
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(f8187,plain,
spl0_973,
inference(avatar_split_clause,[],[f244,f8185]) ).
fof(f8185,plain,
( spl0_973
<=> ! [X9] :
( ~ c_lessequals(c_0,X9,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X9)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
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(f8183,plain,
spl0_972,
inference(avatar_split_clause,[],[f214,f8181]) ).
fof(f8181,plain,
( spl0_972
<=> ! [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_972])]) ).
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(f8179,plain,
spl0_971,
inference(avatar_split_clause,[],[f109,f8177]) ).
fof(f8177,plain,
( spl0_971
<=> ! [X6,X5,X1] :
( c_emptyset = X1
| c_emptyset != c_Equiv__Relations_Oquotient(X1,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f109,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__empty2_0) ).
fof(f8175,plain,
spl0_970,
inference(avatar_split_clause,[],[f107,f8173]) ).
fof(f8173,plain,
( spl0_970
<=> ! [X30,X19] : c_0 = c_div(c_Divides_Oop_Amod(X30,X19,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
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(f8171,plain,
spl0_969,
inference(avatar_split_clause,[],[f105,f8169]) ).
fof(f8169,plain,
( spl0_969
<=> ! [X30,X19] : c_0 = c_Divides_Oop_Amod(c_times(X30,X19,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
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(f8167,plain,
spl0_968,
inference(avatar_split_clause,[],[f103,f8165]) ).
fof(f8165,plain,
( spl0_968
<=> ! [X30,X19] : c_0 = c_Divides_Oop_Amod(c_times(X19,X30,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
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(f8163,plain,
spl0_967,
inference(avatar_split_clause,[],[f58,f8161]) ).
fof(f8161,plain,
( spl0_967
<=> ! [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_967])]) ).
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(f8159,plain,
spl0_966,
inference(avatar_split_clause,[],[f57,f8157]) ).
fof(f8157,plain,
( spl0_966
<=> ! [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_966])]) ).
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(f8055,plain,
( spl0_965
| ~ spl0_46
| ~ spl0_848 ),
inference(avatar_split_clause,[],[f7648,f7490,f3400,f8052]) ).
fof(f8052,plain,
( spl0_965
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f3400,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f7490,plain,
( spl0_848
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f7648,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_46
| ~ spl0_848 ),
inference(resolution,[],[f7491,f3402]) ).
fof(f3402,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f3400]) ).
fof(f7491,plain,
( ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) )
| ~ spl0_848 ),
inference(avatar_component_clause,[],[f7490]) ).
fof(f8035,plain,
spl0_964,
inference(avatar_split_clause,[],[f3046,f8033]) ).
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(f8031,plain,
( spl0_963
| ~ spl0_46
| ~ spl0_847 ),
inference(avatar_split_clause,[],[f7647,f7486,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(f7486,plain,
( spl0_847
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f7647,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_46
| ~ spl0_847 ),
inference(resolution,[],[f7487,f3402]) ).
fof(f7487,plain,
( ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) )
| ~ spl0_847 ),
inference(avatar_component_clause,[],[f7486]) ).
fof(f8026,plain,
spl0_962,
inference(avatar_split_clause,[],[f2998,f8024]) ).
fof(f8024,plain,
( spl0_962
<=> ! [X30] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X30,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2998,plain,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X30,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2799,f2764]) ).
fof(f2799,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(f8022,plain,
spl0_961,
inference(avatar_split_clause,[],[f2997,f8020]) ).
fof(f8020,plain,
( spl0_961
<=> ! [X30] : c_1 = c_GCD_Ogcd(c_Pair(X30,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2997,plain,
! [X30] : c_1 = c_GCD_Ogcd(c_Pair(X30,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2798,f2764]) ).
fof(f2798,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(f8018,plain,
spl0_960,
inference(avatar_split_clause,[],[f2770,f8016]) ).
fof(f8016,plain,
( spl0_960
<=> ! [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_960])]) ).
fof(f2770,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(f8014,plain,
spl0_959,
inference(avatar_split_clause,[],[f2767,f8012]) ).
fof(f8012,plain,
( spl0_959
<=> ! [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_959])]) ).
fof(f2767,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(f8010,plain,
spl0_958,
inference(avatar_split_clause,[],[f1844,f8008]) ).
fof(f8008,plain,
( spl0_958
<=> ! [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_958])]) ).
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(f8006,plain,
spl0_957,
inference(avatar_split_clause,[],[f1838,f8004]) ).
fof(f8004,plain,
( spl0_957
<=> ! [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_957])]) ).
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(f8002,plain,
spl0_956,
inference(avatar_split_clause,[],[f1788,f8000]) ).
fof(f8000,plain,
( spl0_956
<=> ! [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_956])]) ).
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(f7998,plain,
spl0_955,
inference(avatar_split_clause,[],[f1686,f7996]) ).
fof(f7996,plain,
( spl0_955
<=> ! [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_955])]) ).
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(f7994,plain,
spl0_954,
inference(avatar_split_clause,[],[f1685,f7992]) ).
fof(f7992,plain,
( spl0_954
<=> ! [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_954])]) ).
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(f7990,plain,
spl0_953,
inference(avatar_split_clause,[],[f1684,f7988]) ).
fof(f7988,plain,
( spl0_953
<=> ! [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_953])]) ).
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(f7986,plain,
( spl0_952
| ~ spl0_58
| ~ spl0_844 ),
inference(avatar_split_clause,[],[f7644,f7474,f3460,f7983]) ).
fof(f7474,plain,
( spl0_844
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f7644,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_844 ),
inference(resolution,[],[f7475,f3462]) ).
fof(f7475,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) )
| ~ spl0_844 ),
inference(avatar_component_clause,[],[f7474]) ).
fof(f7981,plain,
spl0_951,
inference(avatar_split_clause,[],[f1683,f7979]) ).
fof(f7979,plain,
( spl0_951
<=> ! [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_951])]) ).
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(f7977,plain,
spl0_950,
inference(avatar_split_clause,[],[f1681,f7975]) ).
fof(f7975,plain,
( spl0_950
<=> ! [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_950])]) ).
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(f7973,plain,
spl0_949,
inference(avatar_split_clause,[],[f1680,f7971]) ).
fof(f7971,plain,
( spl0_949
<=> ! [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_949])]) ).
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(f7969,plain,
spl0_948,
inference(avatar_split_clause,[],[f1679,f7967]) ).
fof(f7967,plain,
( spl0_948
<=> ! [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_948])]) ).
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(f7965,plain,
spl0_947,
inference(avatar_split_clause,[],[f1678,f7963]) ).
fof(f7963,plain,
( spl0_947
<=> ! [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_947])]) ).
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(f7961,plain,
spl0_946,
inference(avatar_split_clause,[],[f1629,f7959]) ).
fof(f7959,plain,
( spl0_946
<=> ! [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_946])]) ).
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(f7957,plain,
spl0_945,
inference(avatar_split_clause,[],[f1564,f7955]) ).
fof(f7955,plain,
( spl0_945
<=> ! [X5,X1] :
( c_emptyset = X1
| ~ c_lessequals(X1,c_emptyset,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
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(f7953,plain,
spl0_944,
inference(avatar_split_clause,[],[f1525,f7951]) ).
fof(f7951,plain,
( spl0_944
<=> ! [X5,X8] : c_Set_Ocontents(c_insert(X8,c_emptyset,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
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(f7949,plain,
spl0_943,
inference(avatar_split_clause,[],[f1399,f7946]) ).
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(f7944,plain,
spl0_942,
inference(avatar_split_clause,[],[f1357,f7942]) ).
fof(f7942,plain,
( spl0_942
<=> ! [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_942])]) ).
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(f7940,plain,
spl0_941,
inference(avatar_split_clause,[],[f1356,f7938]) ).
fof(f7938,plain,
( spl0_941
<=> ! [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_941])]) ).
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(f7936,plain,
spl0_940,
inference(avatar_split_clause,[],[f1339,f7934]) ).
fof(f7934,plain,
( spl0_940
<=> ! [X5,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(c_1,X31,X5) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
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(f7932,plain,
spl0_939,
inference(avatar_split_clause,[],[f1338,f7930]) ).
fof(f7930,plain,
( spl0_939
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(X7,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
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(f7928,plain,
spl0_938,
inference(avatar_split_clause,[],[f1335,f7926]) ).
fof(f7926,plain,
( spl0_938
<=> ! [X5,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(X31,c_1,X5) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
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(f7924,plain,
spl0_937,
inference(avatar_split_clause,[],[f1334,f7922]) ).
fof(f7922,plain,
( spl0_937
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(c_0,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
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(f7920,plain,
spl0_936,
inference(avatar_split_clause,[],[f1244,f7918]) ).
fof(f7918,plain,
( spl0_936
<=> ! [X5,X8] : c_Relation_ORange(c_Relation_Odiag(X8,X5),X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
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(f7916,plain,
spl0_935,
inference(avatar_split_clause,[],[f1242,f7914]) ).
fof(f7914,plain,
( spl0_935
<=> ! [X5,X8,X23] : c_Relation_Orel__comp(X8,c_Relation_OId,X5,X23,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
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(f7912,plain,
spl0_934,
inference(avatar_split_clause,[],[f1236,f7910]) ).
fof(f7910,plain,
( spl0_934
<=> ! [X5,X8,X23] : c_Relation_Orel__comp(c_Relation_OId,X8,X23,X23,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
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(f7908,plain,
spl0_933,
inference(avatar_split_clause,[],[f1234,f7906]) ).
fof(f7906,plain,
( spl0_933
<=> ! [X5,X8] : c_Relation_ODomain(c_Relation_Odiag(X8,X5),X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
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(f7904,plain,
spl0_932,
inference(avatar_split_clause,[],[f1222,f7902]) ).
fof(f7902,plain,
( spl0_932
<=> ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(X2,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
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(f7900,plain,
spl0_931,
inference(avatar_split_clause,[],[f1219,f7898]) ).
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(f7896,plain,
spl0_930,
inference(avatar_split_clause,[],[f1218,f7894]) ).
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(f7892,plain,
spl0_929,
inference(avatar_split_clause,[],[f1157,f7890]) ).
fof(f7890,plain,
( spl0_929
<=> ! [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_929])]) ).
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(f7888,plain,
spl0_928,
inference(avatar_split_clause,[],[f1156,f7886]) ).
fof(f7886,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(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(f7884,plain,
spl0_927,
inference(avatar_split_clause,[],[f1132,f7882]) ).
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(f7880,plain,
spl0_926,
inference(avatar_split_clause,[],[f1127,f7878]) ).
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(f7876,plain,
spl0_925,
inference(avatar_split_clause,[],[f1116,f7874]) ).
fof(f7874,plain,
( spl0_925
<=> ! [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_925])]) ).
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(f7872,plain,
spl0_924,
inference(avatar_split_clause,[],[f1115,f7870]) ).
fof(f7870,plain,
( spl0_924
<=> ! [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_924])]) ).
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(f7868,plain,
spl0_923,
inference(avatar_split_clause,[],[f1106,f7866]) ).
fof(f7866,plain,
( spl0_923
<=> ! [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_923])]) ).
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(f7864,plain,
spl0_922,
inference(avatar_split_clause,[],[f1083,f7862]) ).
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(f7860,plain,
spl0_921,
inference(avatar_split_clause,[],[f1082,f7858]) ).
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(f7856,plain,
spl0_920,
inference(avatar_split_clause,[],[f1070,f7854]) ).
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(f7852,plain,
spl0_919,
inference(avatar_split_clause,[],[f1063,f7850]) ).
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(f7848,plain,
spl0_918,
inference(avatar_split_clause,[],[f1061,f7846]) ).
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(f7844,plain,
spl0_917,
inference(avatar_split_clause,[],[f1050,f7842]) ).
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(f7840,plain,
spl0_916,
inference(avatar_split_clause,[],[f1047,f7838]) ).
fof(f7838,plain,
( spl0_916
<=> ! [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_916])]) ).
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(f7836,plain,
spl0_915,
inference(avatar_split_clause,[],[f1045,f7834]) ).
fof(f7834,plain,
( spl0_915
<=> ! [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_915])]) ).
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(f7832,plain,
spl0_914,
inference(avatar_split_clause,[],[f1042,f7830]) ).
fof(f7830,plain,
( spl0_914
<=> ! [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_914])]) ).
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(f7828,plain,
spl0_913,
inference(avatar_split_clause,[],[f1018,f7826]) ).
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(f7824,plain,
spl0_912,
inference(avatar_split_clause,[],[f730,f7822]) ).
fof(f7822,plain,
( spl0_912
<=> ! [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_912])]) ).
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(f7820,plain,
( ~ spl0_910
| spl0_911
| ~ spl0_702
| ~ spl0_838 ),
inference(avatar_split_clause,[],[f7638,f7450,f6880,f7817,f7813]) ).
fof(f7813,plain,
( spl0_910
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f7817,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_702
| ~ spl0_838 ),
inference(superposition,[],[f7451,f6882]) ).
fof(f7811,plain,
spl0_909,
inference(avatar_split_clause,[],[f683,f7809]) ).
fof(f7809,plain,
( spl0_909
<=> ! [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_909])]) ).
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(f7807,plain,
spl0_908,
inference(avatar_split_clause,[],[f680,f7805]) ).
fof(f7805,plain,
( spl0_908
<=> ! [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_908])]) ).
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(f7803,plain,
spl0_907,
inference(avatar_split_clause,[],[f670,f7801]) ).
fof(f7801,plain,
( spl0_907
<=> ! [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_907])]) ).
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(f7799,plain,
spl0_906,
inference(avatar_split_clause,[],[f644,f7797]) ).
fof(f7797,plain,
( spl0_906
<=> ! [X4,X21,X8] : c_List_Otl(c_List_Olist_OCons(X4,X8,X21),X21) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
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(f7795,plain,
spl0_905,
inference(avatar_split_clause,[],[f617,f7793]) ).
fof(f7793,plain,
( spl0_905
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_emptyset != c_List_Oset(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f617,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__empty_0) ).
fof(f7791,plain,
spl0_904,
inference(avatar_split_clause,[],[f600,f7789]) ).
fof(f7789,plain,
( spl0_904
<=> ! [X5,X44] :
( c_List_Olist_ONil = X44
| c_List_Olist_ONil != c_List_Orotate1(X44,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
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(f7787,plain,
spl0_903,
inference(avatar_split_clause,[],[f582,f7785]) ).
fof(f7785,plain,
( spl0_903
<=> ! [X4,X5] :
( c_List_Olist_ONil = X4
| c_List_Olist_ONil != c_List_Oremdups(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
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(f7783,plain,
spl0_902,
inference(avatar_split_clause,[],[f453,f7781]) ).
fof(f7781,plain,
( spl0_902
<=> ! [X4,X5] : c_List_Olast(c_List_Olist_OCons(X4,c_List_Olist_ONil,X5),X5) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
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(f7779,plain,
spl0_901,
inference(avatar_split_clause,[],[f444,f7777]) ).
fof(f7777,plain,
( spl0_901
<=> ! [X5,X44,X8] : c_List_Ohd(c_List_Olist_OCons(X8,X44,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
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(f7775,plain,
spl0_900,
inference(avatar_split_clause,[],[f427,f7773]) ).
fof(f7773,plain,
( spl0_900
<=> ! [X5,X44] :
( ~ c_List_Odistinct(X44,X5)
| c_List_Odistinct(c_List_Orev(X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
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(f7771,plain,
( spl0_899
| ~ spl0_54
| ~ spl0_831 ),
inference(avatar_split_clause,[],[f7618,f7422,f3440,f7768]) ).
fof(f7768,plain,
( spl0_899
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f3440,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f7422,plain,
( spl0_831
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f7618,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_831 ),
inference(resolution,[],[f7423,f3442]) ).
fof(f3442,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f7423,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) )
| ~ spl0_831 ),
inference(avatar_component_clause,[],[f7422]) ).
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,
inference(avatar_split_clause,[],[f257,f7728]) ).
fof(f7728,plain,
( spl0_889
<=> ! [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_889])]) ).
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(f7726,plain,
( spl0_888
| ~ spl0_27
| ~ spl0_830 ),
inference(avatar_split_clause,[],[f7616,f7418,f3305,f7723]) ).
fof(f7723,plain,
( spl0_888
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
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(f7418,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(f7616,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_27
| ~ spl0_830 ),
inference(resolution,[],[f7419,f3307]) ).
fof(f3307,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f3305]) ).
fof(f7419,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,[],[f7418]) ).
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(f7682,plain,
( spl0_878
| ~ spl0_56
| ~ spl0_822 ),
inference(avatar_split_clause,[],[f7608,f7386,f3450,f7679]) ).
fof(f7679,plain,
( spl0_878
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f3450,plain,
( spl0_56
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f7386,plain,
( spl0_822
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f7608,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_822 ),
inference(resolution,[],[f7387,f3452]) ).
fof(f3452,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f3450]) ).
fof(f7387,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) )
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f7386]) ).
fof(f7670,plain,
( spl0_877
| ~ spl0_28
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f7607,f7382,f3310,f7667]) ).
fof(f7667,plain,
( spl0_877
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f3310,plain,
( spl0_28
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f7382,plain,
( spl0_821
<=> ! [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_821])]) ).
fof(f7607,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_28
| ~ spl0_821 ),
inference(resolution,[],[f7383,f3312]) ).
fof(f3312,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3310]) ).
fof(f7383,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_1 = c_IntDef_Oof__int(c_1,X5) )
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f7382]) ).
fof(f7655,plain,
( spl0_876
| ~ spl0_117
| ~ spl0_818 ),
inference(avatar_split_clause,[],[f7601,f7370,f3749,f7652]) ).
fof(f7370,plain,
( spl0_818
<=> ! [X30] : c_IntDef_Oint(X30) = c_HOL_Oabs(c_IntDef_Oint(X30),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f7601,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_117
| ~ spl0_818 ),
inference(superposition,[],[f7371,f3751]) ).
fof(f7371,plain,
( ! [X30] : c_IntDef_Oint(X30) = c_HOL_Oabs(c_IntDef_Oint(X30),tc_IntDef_Oint)
| ~ spl0_818 ),
inference(avatar_component_clause,[],[f7370]) ).
fof(f7643,plain,
( spl0_875
| ~ spl0_116
| ~ spl0_818 ),
inference(avatar_split_clause,[],[f7600,f7370,f3744,f7640]) ).
fof(f7640,plain,
( spl0_875
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f7600,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_818 ),
inference(superposition,[],[f7371,f3746]) ).
fof(f7612,plain,
( spl0_874
| ~ spl0_809
| ~ spl0_812 ),
inference(avatar_split_clause,[],[f7596,f7346,f7334,f7610]) ).
fof(f7334,plain,
( spl0_809
<=> ! [X8] : c_div(X8,c_1,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f7346,plain,
( spl0_812
<=> ! [X19,X30] : c_lessequals(c_div(X30,X19,tc_nat),X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f7596,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_809
| ~ spl0_812 ),
inference(superposition,[],[f7347,f7335]) ).
fof(f7335,plain,
( ! [X8] : c_div(X8,c_1,tc_nat) = X8
| ~ spl0_809 ),
inference(avatar_component_clause,[],[f7334]) ).
fof(f7347,plain,
( ! [X19,X30] : c_lessequals(c_div(X30,X19,tc_nat),X30,tc_nat)
| ~ spl0_812 ),
inference(avatar_component_clause,[],[f7346]) ).
fof(f7594,plain,
spl0_873,
inference(avatar_split_clause,[],[f3071,f7592]) ).
fof(f7592,plain,
( spl0_873
<=> ! [X30] :
( ~ c_Divides_Oop_Advd(X30,c_1,tc_nat)
| c_1 = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f3071,plain,
! [X30] :
( ~ c_Divides_Oop_Advd(X30,c_1,tc_nat)
| c_1 = X30 ),
inference(forward_demodulation,[],[f3070,f2764]) ).
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,[],[f2895,f2764]) ).
fof(f2895,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(f7590,plain,
spl0_872,
inference(avatar_split_clause,[],[f2985,f7588]) ).
fof(f7588,plain,
( spl0_872
<=> ! [X5,X35] : c_emptyset = c_Relation_OImage(c_emptyset,X35,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2985,plain,
! [X35,X5] : c_emptyset = c_Relation_OImage(c_emptyset,X35,X5,X5),
inference(forward_demodulation,[],[f2775,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(f2775,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(f7586,plain,
spl0_871,
inference(avatar_split_clause,[],[f2779,f7584]) ).
fof(f7582,plain,
spl0_870,
inference(avatar_split_clause,[],[f2777,f7579]) ).
fof(f2777,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(f7577,plain,
spl0_869,
inference(avatar_split_clause,[],[f2764,f7574]) ).
fof(f7574,plain,
( spl0_869
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f7572,plain,
spl0_868,
inference(avatar_split_clause,[],[f2760,f7570]) ).
fof(f7570,plain,
( spl0_868
<=> ! [X30] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X30,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2760,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(f7568,plain,
spl0_867,
inference(avatar_split_clause,[],[f1687,f7566]) ).
fof(f7566,plain,
( spl0_867
<=> ! [X18] : c_in(c_SetInterval_OlessThan(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
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(f7564,plain,
spl0_866,
inference(avatar_split_clause,[],[f1682,f7562]) ).
fof(f7562,plain,
( spl0_866
<=> ! [X18] : c_in(c_SetInterval_OatMost(X18,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
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(f7560,plain,
spl0_865,
inference(avatar_split_clause,[],[f1653,f7558]) ).
fof(f7558,plain,
( spl0_865
<=> ! [X5,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X1,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
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(f7556,plain,
spl0_864,
inference(avatar_split_clause,[],[f1637,f7554]) ).
fof(f7554,plain,
( spl0_864
<=> ! [X5,X44] : c_in(c_List_Oset(X44,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
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(f7552,plain,
spl0_863,
inference(avatar_split_clause,[],[f1634,f7550]) ).
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(f7548,plain,
spl0_862,
inference(avatar_split_clause,[],[f1633,f7546]) ).
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(f7544,plain,
spl0_861,
inference(avatar_split_clause,[],[f1618,f7542]) ).
fof(f7542,plain,
( spl0_861
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X30,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
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(f7540,plain,
spl0_860,
inference(avatar_split_clause,[],[f1617,f7538]) ).
fof(f7538,plain,
( spl0_860
<=> ! [X18,X30] : c_Divides_Oop_Advd(X18,c_times(X18,X30,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
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(f7536,plain,
spl0_859,
inference(avatar_split_clause,[],[f1570,f7534]) ).
fof(f7534,plain,
( spl0_859
<=> ! [X5,X23] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
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(f7532,plain,
spl0_858,
inference(avatar_split_clause,[],[f1549,f7530]) ).
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(f7528,plain,
spl0_857,
inference(avatar_split_clause,[],[f1533,f7526]) ).
fof(f7526,plain,
( spl0_857
<=> ! [X5,X1] : c_emptyset = c_minus(c_emptyset,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
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(f7524,plain,
spl0_856,
inference(avatar_split_clause,[],[f1513,f7522]) ).
fof(f7522,plain,
( spl0_856
<=> ! [X5,X8] : c_Union(c_Pow(X8,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
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(f7520,plain,
spl0_855,
inference(avatar_split_clause,[],[f1455,f7518]) ).
fof(f7518,plain,
( spl0_855
<=> ! [X5,X8] : c_minus(X8,c_emptyset,tc_set(X5)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
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(f7516,plain,
spl0_854,
inference(avatar_split_clause,[],[f1453,f7514]) ).
fof(f7514,plain,
( spl0_854
<=> ! [X5,X1] : c_emptyset = c_minus(X1,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
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(f7512,plain,
spl0_853,
inference(avatar_split_clause,[],[f1452,f7510]) ).
fof(f7510,plain,
( spl0_853
<=> ! [X5,X1] : c_emptyset = c_minus(X1,c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
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(f7508,plain,
spl0_852,
inference(avatar_split_clause,[],[f1414,f7506]) ).
fof(f7506,plain,
( spl0_852
<=> ! [X8] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X8,tc_nat),tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
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(f7504,plain,
spl0_851,
inference(avatar_split_clause,[],[f1259,f7502]) ).
fof(f7502,plain,
( spl0_851
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
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(f7500,plain,
spl0_850,
inference(avatar_split_clause,[],[f1239,f7498]) ).
fof(f7498,plain,
( spl0_850
<=> ! [X82,X5,X23] : c_emptyset = c_Relation_OImage(X82,c_emptyset,X23,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
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(f7496,plain,
spl0_849,
inference(avatar_split_clause,[],[f1237,f7494]) ).
fof(f7494,plain,
( spl0_849
<=> ! [X5,X8] : c_Relation_OImage(c_Relation_OId,X8,X5,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
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(f7492,plain,
spl0_848,
inference(avatar_split_clause,[],[f1108,f7490]) ).
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(f7488,plain,
spl0_847,
inference(avatar_split_clause,[],[f1103,f7486]) ).
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(f7484,plain,
spl0_846,
inference(avatar_split_clause,[],[f1085,f7482]) ).
fof(f7482,plain,
( spl0_846
<=> ! [X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_uminus(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
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(f7480,plain,
spl0_845,
inference(avatar_split_clause,[],[f1038,f7478]) ).
fof(f7478,plain,
( spl0_845
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = c_HOL_Oabs(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
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(f7476,plain,
spl0_844,
inference(avatar_split_clause,[],[f1034,f7474]) ).
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(f7472,plain,
spl0_843,
inference(avatar_split_clause,[],[f1027,f7470]) ).
fof(f7470,plain,
( spl0_843
<=> ! [X5,X8,X33] : c_Numeral_Obit_Obit__rec(X33,X8,c_Numeral_Obit_OB1,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
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(f7468,plain,
spl0_842,
inference(avatar_split_clause,[],[f1026,f7466]) ).
fof(f7466,plain,
( spl0_842
<=> ! [X5,X8,X32] : c_Numeral_Obit_Obit__rec(X8,X32,c_Numeral_Obit_OB0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
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(f7464,plain,
spl0_841,
inference(avatar_split_clause,[],[f1023,f7462]) ).
fof(f7462,plain,
( spl0_841
<=> ! [X5,X8,X33] : c_Numeral_Obit_Obit__case(X33,X8,c_Numeral_Obit_OB1,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
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(f7460,plain,
spl0_840,
inference(avatar_split_clause,[],[f1022,f7458]) ).
fof(f7458,plain,
( spl0_840
<=> ! [X5,X8,X32] : c_Numeral_Obit_Obit__case(X8,X32,c_Numeral_Obit_OB0,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
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(f7456,plain,
spl0_839,
inference(avatar_split_clause,[],[f1009,f7454]) ).
fof(f7454,plain,
( spl0_839
<=> ! [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_839])]) ).
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(f7452,plain,
spl0_838,
inference(avatar_split_clause,[],[f1008,f7450]) ).
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(f7448,plain,
spl0_837,
inference(avatar_split_clause,[],[f954,f7446]) ).
fof(f7446,plain,
( spl0_837
<=> ! [X19] :
( c_0 = X19
| c_less(c_0,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
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(f7444,plain,
spl0_836,
inference(avatar_split_clause,[],[f953,f7442]) ).
fof(f7442,plain,
( spl0_836
<=> ! [X29,X55] : ~ c_less(c_plus(X55,X29,tc_nat),X29,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
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(f7440,plain,
spl0_835,
inference(avatar_split_clause,[],[f952,f7438]) ).
fof(f7438,plain,
( spl0_835
<=> ! [X29,X55] : ~ c_less(c_plus(X29,X55,tc_nat),X29,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
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(f7436,plain,
spl0_834,
inference(avatar_split_clause,[],[f913,f7434]) ).
fof(f7434,plain,
( spl0_834
<=> ! [X19] :
( c_0 = X19
| ~ c_less(X19,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
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(f7432,plain,
spl0_833,
inference(avatar_split_clause,[],[f907,f7430]) ).
fof(f7430,plain,
( spl0_833
<=> ! [X29] :
( c_0 = X29
| ~ c_lessequals(X29,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
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(f7428,plain,
spl0_832,
inference(avatar_split_clause,[],[f905,f7426]) ).
fof(f7426,plain,
( spl0_832
<=> ! [X19,X30] : c_lessequals(c_minus(X30,X19,tc_nat),X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
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(f7424,plain,
spl0_831,
inference(avatar_split_clause,[],[f677,f7422]) ).
fof(f677,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__eq__0__iff_1) ).
fof(f7420,plain,
spl0_830,
inference(avatar_split_clause,[],[f673,f7418]) ).
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(f7416,plain,
spl0_829,
inference(avatar_split_clause,[],[f655,f7414]) ).
fof(f7414,plain,
( spl0_829
<=> ! [X45,X5,X23] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X45,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
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(f7412,plain,
spl0_828,
inference(avatar_split_clause,[],[f653,f7410]) ).
fof(f7410,plain,
( spl0_828
<=> ! [X21,X44,X79] : c_List_Olist_ONil = c_List_Ozip(X44,c_List_Olist_ONil,X21,X79) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
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(f7408,plain,
spl0_827,
inference(avatar_split_clause,[],[f597,f7406]) ).
fof(f7406,plain,
( spl0_827
<=> ! [X5,X8] : c_List_Orev(c_List_Orev(X8,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
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(f7404,plain,
spl0_826,
inference(avatar_split_clause,[],[f576,f7402]) ).
fof(f7402,plain,
( spl0_826
<=> ! [X45,X4,X5] : c_List_Oop_Amem(X4,c_List_Olist_OCons(X4,X45,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
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(f7400,plain,
spl0_825,
inference(avatar_split_clause,[],[f496,f7398]) ).
fof(f7398,plain,
( spl0_825
<=> ! [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_825])]) ).
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(f7396,plain,
spl0_824,
inference(avatar_split_clause,[],[f407,f7394]) ).
fof(f7394,plain,
( spl0_824
<=> ! [X50,X51] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X50,X51),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
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(f7392,plain,
spl0_823,
inference(avatar_split_clause,[],[f343,f7390]) ).
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(f7388,plain,
spl0_822,
inference(avatar_split_clause,[],[f270,f7386]) ).
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(f7384,plain,
spl0_821,
inference(avatar_split_clause,[],[f266,f7382]) ).
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(f7380,plain,
spl0_820,
inference(avatar_split_clause,[],[f252,f7378]) ).
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(f7376,plain,
spl0_819,
inference(avatar_split_clause,[],[f238,f7374]) ).
fof(f7374,plain,
( spl0_819
<=> ! [X19] :
( c_0 = X19
| c_0 != c_IntDef_Oint(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
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(f7372,plain,
spl0_818,
inference(avatar_split_clause,[],[f232,f7370]) ).
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(f7368,plain,
spl0_817,
inference(avatar_split_clause,[],[f118,f7366]) ).
fof(f7366,plain,
( spl0_817
<=> ! [X5,X8,X33] : c_Extraction_Osumbool_Osumbool__rec(X33,X8,c_Extraction_Osumbool_ORight,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
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(f7364,plain,
spl0_816,
inference(avatar_split_clause,[],[f117,f7362]) ).
fof(f7362,plain,
( spl0_816
<=> ! [X5,X8,X32] : c_Extraction_Osumbool_Osumbool__rec(X8,X32,c_Extraction_Osumbool_OLeft,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
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(f7360,plain,
spl0_815,
inference(avatar_split_clause,[],[f114,f7358]) ).
fof(f7358,plain,
( spl0_815
<=> ! [X5,X8,X33] : c_Extraction_Osumbool_Osumbool__case(X33,X8,c_Extraction_Osumbool_ORight,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
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(f7356,plain,
spl0_814,
inference(avatar_split_clause,[],[f113,f7354]) ).
fof(f7354,plain,
( spl0_814
<=> ! [X5,X8,X32] : c_Extraction_Osumbool_Osumbool__case(X8,X32,c_Extraction_Osumbool_OLeft,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
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(f7352,plain,
spl0_813,
inference(avatar_split_clause,[],[f90,f7350]) ).
fof(f7350,plain,
( spl0_813
<=> ! [X30] :
( c_0 = X30
| ~ c_Divides_Oop_Advd(c_0,X30,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
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(f7348,plain,
spl0_812,
inference(avatar_split_clause,[],[f80,f7346]) ).
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(f7344,plain,
spl0_811,
inference(avatar_split_clause,[],[f67,f7342]) ).
fof(f7342,plain,
( spl0_811
<=> ! [X24,X5,X23] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X24,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
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(f7340,plain,
spl0_810,
inference(avatar_split_clause,[],[f46,f7338]) ).
fof(f7338,plain,
( spl0_810
<=> ! [X5,X8] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X5),X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
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(f7336,plain,
spl0_809,
inference(avatar_split_clause,[],[f2995,f7334]) ).
fof(f2995,plain,
! [X8] : c_div(X8,c_1,tc_nat) = X8,
inference(forward_demodulation,[],[f2790,f2764]) ).
fof(f2790,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(f7332,plain,
spl0_808,
inference(avatar_split_clause,[],[f2993,f7329]) ).
fof(f7329,plain,
( spl0_808
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f2993,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2787,f2764]) ).
fof(f2787,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(f7327,plain,
spl0_807,
inference(avatar_split_clause,[],[f2991,f7325]) ).
fof(f7325,plain,
( spl0_807
<=> ! [X30] : c_0 = c_Divides_Oop_Amod(X30,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2991,plain,
! [X30] : c_0 = c_Divides_Oop_Amod(X30,c_1,tc_nat),
inference(forward_demodulation,[],[f2786,f2764]) ).
fof(f2786,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(f7323,plain,
spl0_806,
inference(avatar_split_clause,[],[f2990,f7320]) ).
fof(f7320,plain,
( spl0_806
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
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(f7318,plain,
spl0_805,
inference(avatar_split_clause,[],[f2988,f7316]) ).
fof(f7316,plain,
( spl0_805
<=> ! [X21,X8] : c_append(c_List_Olist_ONil,X8,X21) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2988,plain,
! [X21,X8] : c_append(c_List_Olist_ONil,X8,X21) = X8,
inference(forward_demodulation,[],[f2781,f594]) ).
fof(f594,axiom,
! [X5] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
fof(f2781,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(f7314,plain,
spl0_804,
inference(avatar_split_clause,[],[f2986,f7311]) ).
fof(f7311,plain,
( spl0_804
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2986,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2778,f1021]) ).
fof(f2778,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(f7309,plain,
spl0_803,
inference(avatar_split_clause,[],[f1660,f7307]) ).
fof(f7307,plain,
( spl0_803
<=> ! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
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(f7305,plain,
spl0_802,
inference(avatar_split_clause,[],[f1552,f7303]) ).
fof(f1552,axiom,
! [X2,X1,X5] : c_emptyset != c_insert(X2,X1,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
fof(f7301,plain,
spl0_801,
inference(avatar_split_clause,[],[f1504,f7299]) ).
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(f7297,plain,
spl0_800,
inference(avatar_split_clause,[],[f1503,f7295]) ).
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(f7293,plain,
spl0_799,
inference(avatar_split_clause,[],[f1499,f7291]) ).
fof(f1499,axiom,
! [X8,X5] : c_union(X8,X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7289,plain,
spl0_798,
inference(avatar_split_clause,[],[f1498,f7287]) ).
fof(f7287,plain,
( spl0_798
<=> ! [X5,X1] : c_UNIV = c_union(X1,c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
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(f7285,plain,
spl0_797,
inference(avatar_split_clause,[],[f1497,f7283]) ).
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(f7281,plain,
spl0_796,
inference(avatar_split_clause,[],[f1445,f7279]) ).
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(f7277,plain,
spl0_795,
inference(avatar_split_clause,[],[f1441,f7275]) ).
fof(f7275,plain,
( spl0_795
<=> ! [X5] : c_emptyset = c_uminus(c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
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(f7273,plain,
spl0_794,
inference(avatar_split_clause,[],[f1376,f7271]) ).
fof(f7271,plain,
( spl0_794
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
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(f7269,plain,
spl0_793,
inference(avatar_split_clause,[],[f1364,f7267]) ).
fof(f7267,plain,
( spl0_793
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
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(f7265,plain,
spl0_792,
inference(avatar_split_clause,[],[f1359,f7263]) ).
fof(f7263,plain,
( spl0_792
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
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(f7261,plain,
spl0_791,
inference(avatar_split_clause,[],[f1358,f7259]) ).
fof(f7259,plain,
( spl0_791
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(c_1,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
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(f7257,plain,
spl0_790,
inference(avatar_split_clause,[],[f1246,f7255]) ).
fof(f7255,plain,
( spl0_790
<=> ! [X5] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
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(f7253,plain,
spl0_789,
inference(avatar_split_clause,[],[f1245,f7251]) ).
fof(f7251,plain,
( spl0_789
<=> ! [X5,X23] : c_emptyset = c_Relation_ORange(c_emptyset,X23,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
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(f7249,plain,
spl0_788,
inference(avatar_split_clause,[],[f1243,f7247]) ).
fof(f7247,plain,
( spl0_788
<=> ! [X5] : c_UNIV = c_Relation_ORange(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
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(f7245,plain,
spl0_787,
inference(avatar_split_clause,[],[f1235,f7243]) ).
fof(f7243,plain,
( spl0_787
<=> ! [X5,X23] : c_emptyset = c_Relation_ODomain(c_emptyset,X5,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
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(f7241,plain,
spl0_786,
inference(avatar_split_clause,[],[f1233,f7239]) ).
fof(f7239,plain,
( spl0_786
<=> ! [X5] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
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(f7237,plain,
spl0_785,
inference(avatar_split_clause,[],[f1209,f7235]) ).
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(f7233,plain,
spl0_784,
inference(avatar_split_clause,[],[f1134,f7231]) ).
fof(f7231,plain,
( spl0_784
<=> ! [X4,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
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(f7229,plain,
spl0_783,
inference(avatar_split_clause,[],[f1021,f7226]) ).
fof(f7224,plain,
spl0_782,
inference(avatar_split_clause,[],[f967,f7222]) ).
fof(f7222,plain,
( spl0_782
<=> ! [X8] : c_minus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
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(f7220,plain,
spl0_781,
inference(avatar_split_clause,[],[f965,f7218]) ).
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(f7216,plain,
spl0_780,
inference(avatar_split_clause,[],[f963,f7214]) ).
fof(f7214,plain,
( spl0_780
<=> ! [X19] : c_0 = c_times(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
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(f7212,plain,
spl0_779,
inference(avatar_split_clause,[],[f921,f7210]) ).
fof(f7210,plain,
( spl0_779
<=> ! [X30] : c_0 = c_times(X30,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
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(f7208,plain,
spl0_778,
inference(avatar_split_clause,[],[f919,f7206]) ).
fof(f7206,plain,
( spl0_778
<=> ! [X19] : c_0 = c_Orderings_Omin(X19,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
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(f7204,plain,
spl0_777,
inference(avatar_split_clause,[],[f918,f7202]) ).
fof(f7202,plain,
( spl0_777
<=> ! [X19] : c_0 = c_Orderings_Omin(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
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(f7200,plain,
spl0_776,
inference(avatar_split_clause,[],[f916,f7198]) ).
fof(f7198,plain,
( spl0_776
<=> ! [X8] : c_Orderings_Omax(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
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(f7196,plain,
spl0_775,
inference(avatar_split_clause,[],[f915,f7194]) ).
fof(f7194,plain,
( spl0_775
<=> ! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
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(f7192,plain,
spl0_774,
inference(avatar_split_clause,[],[f906,f7190]) ).
fof(f7190,plain,
( spl0_774
<=> ! [X30] : c_0 = c_minus(X30,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
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(f7188,plain,
spl0_773,
inference(avatar_split_clause,[],[f899,f7186]) ).
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(f7184,plain,
spl0_772,
inference(avatar_split_clause,[],[f891,f7182]) ).
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(f7180,plain,
spl0_771,
inference(avatar_split_clause,[],[f652,f7178]) ).
fof(f7178,plain,
( spl0_771
<=> ! [X4,X5,X78] : c_List_Olist_OCons(X4,X78,X5) != X78 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
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(f7176,plain,
spl0_770,
inference(avatar_split_clause,[],[f628,f7174]) ).
fof(f7174,plain,
( spl0_770
<=> ! [X5,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X1,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
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(f7172,plain,
spl0_769,
inference(avatar_split_clause,[],[f627,f7170]) ).
fof(f7170,plain,
( spl0_769
<=> ! [X5,X44] : c_List_Olist_ONil = c_List_Osublist(X44,c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
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(f7168,plain,
spl0_768,
inference(avatar_split_clause,[],[f612,f7166]) ).
fof(f7166,plain,
( spl0_768
<=> ! [X5,X44] : c_append(X44,c_List_Olist_ONil,X5) = X44 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
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(f7164,plain,
spl0_767,
inference(avatar_split_clause,[],[f606,f7162]) ).
fof(f7162,plain,
( spl0_767
<=> ! [X5,X19] : c_List_Olist_ONil = c_List_Orotate(X19,c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
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(f7160,plain,
spl0_766,
inference(avatar_split_clause,[],[f587,f7158]) ).
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(f7156,plain,
spl0_765,
inference(avatar_split_clause,[],[f584,f7154]) ).
fof(f7154,plain,
( spl0_765
<=> ! [X4,X21] : c_List_Olist_ONil = c_List_Oremove1(X4,c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
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(f7152,plain,
spl0_764,
inference(avatar_split_clause,[],[f572,f7150]) ).
fof(f7150,plain,
( spl0_764
<=> ! [X4,X21,X44] : ~ c_List_Onull(c_List_Olist_OCons(X4,X44,X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
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(f7148,plain,
spl0_763,
inference(avatar_split_clause,[],[f493,f7146]) ).
fof(f7146,plain,
( spl0_763
<=> ! [X61,X21] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X61,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
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(f7144,plain,
spl0_762,
inference(avatar_split_clause,[],[f489,f7142]) ).
fof(f7142,plain,
( spl0_762
<=> ! [X22,X5,X59] : c_List_Olist_ONil != c_List_Olist_OCons(X22,X59,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f489,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__2_0) ).
fof(f7140,plain,
spl0_761,
inference(avatar_split_clause,[],[f480,f7138]) ).
fof(f7138,plain,
( spl0_761
<=> ! [X6,X21] : c_emptyset = c_List_Olexn(X6,c_0,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
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(f7136,plain,
spl0_760,
inference(avatar_split_clause,[],[f463,f7134]) ).
fof(f7134,plain,
( spl0_760
<=> ! [X5] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
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(f7132,plain,
spl0_759,
inference(avatar_split_clause,[],[f434,f7130]) ).
fof(f7130,plain,
( spl0_759
<=> ! [X5,X8] : c_List_Odrop(c_0,X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
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(f7128,plain,
spl0_758,
inference(avatar_split_clause,[],[f433,f7126]) ).
fof(f7126,plain,
( spl0_758
<=> ! [X21,X19] : c_List_Olist_ONil = c_List_Odrop(X19,c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
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(f7124,plain,
spl0_757,
inference(avatar_split_clause,[],[f359,f7122]) ).
fof(f7122,plain,
( spl0_757
<=> ! [X7] : c_0 = c_Divides_Oop_Amod(c_0,X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
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(f7120,plain,
spl0_756,
inference(avatar_split_clause,[],[f356,f7118]) ).
fof(f7118,plain,
( spl0_756
<=> ! [X2] : c_0 = c_Divides_Oop_Amod(X2,X2,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
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(f7116,plain,
spl0_755,
inference(avatar_split_clause,[],[f354,f7114]) ).
fof(f7114,plain,
( spl0_755
<=> ! [X2] : c_0 = c_Divides_Oop_Amod(X2,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
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(f7112,plain,
spl0_754,
inference(avatar_split_clause,[],[f339,f7110]) ).
fof(f7110,plain,
( spl0_754
<=> ! [X7] : c_0 = c_div(c_0,X7,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
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(f7108,plain,
spl0_753,
inference(avatar_split_clause,[],[f331,f7106]) ).
fof(f7106,plain,
( spl0_753
<=> ! [X8] : c_div(X8,c_1,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
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(f7104,plain,
spl0_752,
inference(avatar_split_clause,[],[f329,f7102]) ).
fof(f7102,plain,
( spl0_752
<=> ! [X43] : c_1 = c_Nat_Opower(X43,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
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(f7100,plain,
spl0_751,
inference(avatar_split_clause,[],[f297,f7098]) ).
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(f7096,plain,
spl0_750,
inference(avatar_split_clause,[],[f229,f7094]) ).
fof(f7094,plain,
( spl0_750
<=> ! [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_750])]) ).
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(f7092,plain,
spl0_749,
inference(avatar_split_clause,[],[f228,f7090]) ).
fof(f7090,plain,
( spl0_749
<=> ! [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_749])]) ).
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(f7088,plain,
spl0_748,
inference(avatar_split_clause,[],[f223,f7086]) ).
fof(f7086,plain,
( spl0_748
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_1,c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
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(f7084,plain,
spl0_747,
inference(avatar_split_clause,[],[f222,f7082]) ).
fof(f7082,plain,
( spl0_747
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_0,c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
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(f7080,plain,
spl0_746,
inference(avatar_split_clause,[],[f215,f7077]) ).
fof(f7077,plain,
( spl0_746
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
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(f7075,plain,
spl0_745,
inference(avatar_split_clause,[],[f112,f7073]) ).
fof(f7073,plain,
( spl0_745
<=> ! [X6,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X6,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f112,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__empty_1) ).
fof(f7071,plain,
spl0_744,
inference(avatar_split_clause,[],[f106,f7069]) ).
fof(f7069,plain,
( spl0_744
<=> ! [X19] : c_0 = c_Divides_Oop_Amod(X19,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
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(f7067,plain,
spl0_743,
inference(avatar_split_clause,[],[f95,f7065]) ).
fof(f7065,plain,
( spl0_743
<=> ! [X30] : c_0 = c_Divides_Oop_Amod(c_0,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
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(f7063,plain,
spl0_742,
inference(avatar_split_clause,[],[f78,f7061]) ).
fof(f7061,plain,
( spl0_742
<=> ! [X30] : c_0 = c_div(c_0,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
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(f7059,plain,
spl0_741,
inference(avatar_split_clause,[],[f77,f7057]) ).
fof(f7057,plain,
( spl0_741
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
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(f7055,plain,
spl0_740,
inference(avatar_split_clause,[],[f76,f7053]) ).
fof(f7053,plain,
( spl0_740
<=> ! [X2] : c_0 = c_div(X2,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
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(f7051,plain,
spl0_739,
inference(avatar_split_clause,[],[f48,f7049]) ).
fof(f7049,plain,
( spl0_739
<=> ! [X5,X8] : c_Datatype_Ounit_Ounit__rec(X8,c_Product__Type_OUnity,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
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(f7047,plain,
spl0_738,
inference(avatar_split_clause,[],[f47,f7045]) ).
fof(f7045,plain,
( spl0_738
<=> ! [X5,X8] : c_Datatype_Ounit_Ounit__case(X8,c_Product__Type_OUnity,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
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(f7043,plain,
spl0_737,
inference(avatar_split_clause,[],[f41,f7041]) ).
fof(f7041,plain,
( spl0_737
<=> ! [X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
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(f7039,plain,
spl0_736,
inference(avatar_split_clause,[],[f15,f7036]) ).
fof(f7036,plain,
( spl0_736
<=> 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_736])]) ).
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(f7032,plain,
( spl0_735
| ~ spl0_116
| ~ spl0_675 ),
inference(avatar_split_clause,[],[f7016,f6756,f3744,f7029]) ).
fof(f7029,plain,
( spl0_735
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f6756,plain,
( spl0_675
<=> ! [X19] : c_lessequals(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f7016,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_675 ),
inference(superposition,[],[f6757,f3746]) ).
fof(f6757,plain,
( ! [X19] : c_lessequals(c_0,c_IntDef_Oint(X19),tc_IntDef_Oint)
| ~ spl0_675 ),
inference(avatar_component_clause,[],[f6756]) ).
fof(f7027,plain,
( ~ spl0_734
| ~ spl0_117
| ~ spl0_673 ),
inference(avatar_split_clause,[],[f7013,f6748,f3749,f7024]) ).
fof(f7024,plain,
( spl0_734
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f6748,plain,
( spl0_673
<=> ! [X18] : ~ c_less(c_IntDef_Oint(X18),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f7013,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_117
| ~ spl0_673 ),
inference(superposition,[],[f6749,f3751]) ).
fof(f6749,plain,
( ! [X18] : ~ c_less(c_IntDef_Oint(X18),c_0,tc_IntDef_Oint)
| ~ spl0_673 ),
inference(avatar_component_clause,[],[f6748]) ).
fof(f7022,plain,
( ~ spl0_733
| ~ spl0_116
| ~ spl0_673 ),
inference(avatar_split_clause,[],[f7012,f6748,f3744,f7019]) ).
fof(f7019,plain,
( spl0_733
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f7012,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_673 ),
inference(superposition,[],[f6749,f3746]) ).
fof(f7011,plain,
spl0_732,
inference(avatar_split_clause,[],[f2992,f7008]) ).
fof(f7008,plain,
( spl0_732
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
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(f7006,plain,
spl0_731,
inference(avatar_split_clause,[],[f2987,f7004]) ).
fof(f7004,plain,
( spl0_731
<=> ! [X8] : c_Binomial_Obinomial(X8,c_1) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2987,plain,
! [X8] : c_Binomial_Obinomial(X8,c_1) = X8,
inference(forward_demodulation,[],[f2780,f2764]) ).
fof(f2780,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(f7002,plain,
spl0_730,
inference(avatar_split_clause,[],[f2763,f6999]) ).
fof(f6997,plain,
spl0_729,
inference(avatar_split_clause,[],[f1842,f6995]) ).
fof(f6995,plain,
( spl0_729
<=> ! [X92] :
( ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_set(X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
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(f6993,plain,
spl0_728,
inference(avatar_split_clause,[],[f1720,f6991]) ).
fof(f6991,plain,
( spl0_728
<=> ! [X92] :
( ~ class_Finite__Set_Ofinite(X92)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
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(f6989,plain,
spl0_727,
inference(avatar_split_clause,[],[f1704,f6987]) ).
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(f6985,plain,
spl0_726,
inference(avatar_split_clause,[],[f1693,f6983]) ).
fof(f6983,plain,
( spl0_726
<=> ! [X5,X1] : c_lessequals(c_emptyset,X1,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
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(f6981,plain,
spl0_725,
inference(avatar_split_clause,[],[f1636,f6979]) ).
fof(f6979,plain,
( spl0_725
<=> ! [X5,X44] : c_List_Odistinct(c_List_Oremdups(X44,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
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(f6977,plain,
spl0_724,
inference(avatar_split_clause,[],[f1620,f6975]) ).
fof(f6975,plain,
( spl0_724
<=> ! [X5] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
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(f6973,plain,
spl0_723,
inference(avatar_split_clause,[],[f1579,f6971]) ).
fof(f6971,plain,
( spl0_723
<=> ! [X5] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
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(f6969,plain,
spl0_722,
inference(avatar_split_clause,[],[f1563,f6967]) ).
fof(f6967,plain,
( spl0_722
<=> ! [X5,X1] : c_lessequals(X1,c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
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(f6965,plain,
spl0_721,
inference(avatar_split_clause,[],[f1556,f6963]) ).
fof(f6963,plain,
( spl0_721
<=> ! [X5,X1] : ~ c_less(X1,c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
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(f6961,plain,
spl0_720,
inference(avatar_split_clause,[],[f1516,f6959]) ).
fof(f6959,plain,
( spl0_720
<=> ! [X5] : c_emptyset = c_Union(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1516,axiom,
! [X5] : c_emptyset = c_Union(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f6957,plain,
spl0_719,
inference(avatar_split_clause,[],[f1514,f6955]) ).
fof(f6955,plain,
( spl0_719
<=> ! [X5] : c_UNIV = c_Union(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f1514,axiom,
! [X5] : c_UNIV = c_Union(c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f6953,plain,
spl0_718,
inference(avatar_split_clause,[],[f1490,f6951]) ).
fof(f6951,plain,
( spl0_718
<=> ! [X5] : c_UNIV = c_Pow(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1490,axiom,
! [X5] : c_UNIV = c_Pow(c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f6949,plain,
spl0_717,
inference(avatar_split_clause,[],[f1484,f6947]) ).
fof(f6947,plain,
( spl0_717
<=> ! [X5] : c_UNIV = c_Inter(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1484,axiom,
! [X5] : c_UNIV = c_Inter(c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f6945,plain,
spl0_716,
inference(avatar_split_clause,[],[f1477,f6943]) ).
fof(f6943,plain,
( spl0_716
<=> ! [X5] : c_emptyset = c_Inter(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1477,axiom,
! [X5] : c_emptyset = c_Inter(c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f6941,plain,
spl0_715,
inference(avatar_split_clause,[],[f1432,f6938]) ).
fof(f6938,plain,
( spl0_715
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
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(f6936,plain,
spl0_714,
inference(avatar_split_clause,[],[f1393,f6933]) ).
fof(f6933,plain,
( spl0_714
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
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(f6931,plain,
spl0_713,
inference(avatar_split_clause,[],[f1251,f6929]) ).
fof(f6927,plain,
spl0_712,
inference(avatar_split_clause,[],[f1029,f6924]) ).
fof(f6924,plain,
( spl0_712
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
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(f6922,plain,
spl0_711,
inference(avatar_split_clause,[],[f1028,f6919]) ).
fof(f6919,plain,
( spl0_711
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
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(f6917,plain,
spl0_710,
inference(avatar_split_clause,[],[f1017,f6915]) ).
fof(f6915,plain,
( spl0_710
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
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(f6913,plain,
spl0_709,
inference(avatar_split_clause,[],[f1016,f6911]) ).
fof(f6911,plain,
( spl0_709
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
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(f6909,plain,
spl0_708,
inference(avatar_split_clause,[],[f1000,f6907]) ).
fof(f6907,plain,
( spl0_708
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_IntDef_Oiszero(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
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(f6905,plain,
spl0_707,
inference(avatar_split_clause,[],[f995,f6903]) ).
fof(f6903,plain,
( spl0_707
<=> ! [X39] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X39) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
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(f6901,plain,
spl0_706,
inference(avatar_split_clause,[],[f980,f6899]) ).
fof(f6899,plain,
( spl0_706
<=> ! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f6897,plain,
spl0_705,
inference(avatar_split_clause,[],[f979,f6895]) ).
fof(f6893,plain,
spl0_704,
inference(avatar_split_clause,[],[f971,f6890]) ).
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(f6888,plain,
spl0_703,
inference(avatar_split_clause,[],[f970,f6885]) ).
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(f6883,plain,
spl0_702,
inference(avatar_split_clause,[],[f731,f6880]) ).
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(f6878,plain,
spl0_701,
inference(avatar_split_clause,[],[f650,f6876]) ).
fof(f6876,plain,
( spl0_701
<=> ! [X29] : c_List_Olist_ONil = c_List_Oupt(X29,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
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(f6874,plain,
spl0_700,
inference(avatar_split_clause,[],[f643,f6872]) ).
fof(f6872,plain,
( spl0_700
<=> ! [X21] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
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(f6870,plain,
spl0_699,
inference(avatar_split_clause,[],[f618,f6868]) ).
fof(f6868,plain,
( spl0_699
<=> ! [X5] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f618,axiom,
! [X5] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
fof(f6866,plain,
spl0_698,
inference(avatar_split_clause,[],[f601,f6864]) ).
fof(f6864,plain,
( spl0_698
<=> ! [X5] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
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(f6862,plain,
spl0_697,
inference(avatar_split_clause,[],[f594,f6860]) ).
fof(f6860,plain,
( spl0_697
<=> ! [X5] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f6858,plain,
spl0_696,
inference(avatar_split_clause,[],[f581,f6856]) ).
fof(f6856,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(f6854,plain,
spl0_695,
inference(avatar_split_clause,[],[f553,f6851]) ).
fof(f6851,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(f6849,plain,
spl0_694,
inference(avatar_split_clause,[],[f552,f6846]) ).
fof(f6846,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(f6844,plain,
spl0_693,
inference(avatar_split_clause,[],[f551,f6841]) ).
fof(f6841,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(f6839,plain,
spl0_692,
inference(avatar_split_clause,[],[f550,f6836]) ).
fof(f6836,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(f6834,plain,
spl0_691,
inference(avatar_split_clause,[],[f549,f6831]) ).
fof(f6831,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(f6829,plain,
spl0_690,
inference(avatar_split_clause,[],[f548,f6826]) ).
fof(f6826,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(f6824,plain,
spl0_689,
inference(avatar_split_clause,[],[f547,f6821]) ).
fof(f6821,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(f6819,plain,
spl0_688,
inference(avatar_split_clause,[],[f546,f6816]) ).
fof(f6816,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(f6814,plain,
spl0_687,
inference(avatar_split_clause,[],[f545,f6811]) ).
fof(f6811,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(f6809,plain,
spl0_686,
inference(avatar_split_clause,[],[f544,f6806]) ).
fof(f6806,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(f6804,plain,
spl0_685,
inference(avatar_split_clause,[],[f543,f6801]) ).
fof(f6801,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(f6799,plain,
spl0_684,
inference(avatar_split_clause,[],[f542,f6796]) ).
fof(f6796,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(f6794,plain,
spl0_683,
inference(avatar_split_clause,[],[f541,f6791]) ).
fof(f6791,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(f6789,plain,
spl0_682,
inference(avatar_split_clause,[],[f540,f6786]) ).
fof(f6786,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(f6784,plain,
spl0_681,
inference(avatar_split_clause,[],[f539,f6781]) ).
fof(f6781,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(f6779,plain,
spl0_680,
inference(avatar_split_clause,[],[f538,f6776]) ).
fof(f6776,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(f6774,plain,
spl0_679,
inference(avatar_split_clause,[],[f503,f6772]) ).
fof(f6772,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(f6770,plain,
spl0_678,
inference(avatar_split_clause,[],[f432,f6768]) ).
fof(f6768,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(f6766,plain,
spl0_677,
inference(avatar_split_clause,[],[f408,f6764]) ).
fof(f6764,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(f6762,plain,
spl0_676,
inference(avatar_split_clause,[],[f401,f6760]) ).
fof(f6760,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(f6758,plain,
spl0_675,
inference(avatar_split_clause,[],[f289,f6756]) ).
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(f6754,plain,
spl0_674,
inference(avatar_split_clause,[],[f249,f6752]) ).
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(f6750,plain,
spl0_673,
inference(avatar_split_clause,[],[f243,f6748]) ).
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(f6746,plain,
~ spl0_672,
inference(avatar_split_clause,[],[f174,f6743]) ).
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(f6741,plain,
spl0_671,
inference(avatar_split_clause,[],[f161,f6739]) ).
fof(f6739,plain,
( spl0_671
<=> ! [X5,X8] : c_Fun_Oid(X8,X5) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f161,axiom,
! [X8,X5] : c_Fun_Oid(X8,X5) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6737,plain,
spl0_670,
inference(avatar_split_clause,[],[f160,f6735]) ).
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(f6733,plain,
spl0_669,
inference(avatar_split_clause,[],[f143,f6731]) ).
fof(f6731,plain,
( spl0_669
<=> ! [X5] : c_0 = c_Finite__Set_Ocard(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
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(f6729,plain,
spl0_668,
inference(avatar_split_clause,[],[f120,f6726]) ).
fof(f6726,plain,
( spl0_668
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
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(f6724,plain,
spl0_667,
inference(avatar_split_clause,[],[f119,f6721]) ).
fof(f6721,plain,
( spl0_667
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
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(f6719,plain,
spl0_666,
inference(avatar_split_clause,[],[f49,f6716]) ).
fof(f6716,plain,
( spl0_666
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
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(f6714,plain,
spl0_665,
inference(avatar_split_clause,[],[f38,f6712]) ).
fof(f6712,plain,
( spl0_665
<=> ! [X22,X5] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X22,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
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(f6710,plain,
spl0_664,
inference(avatar_split_clause,[],[f37,f6708]) ).
fof(f6708,plain,
( spl0_664
<=> ! [X5] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
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(f6706,plain,
spl0_663,
inference(avatar_split_clause,[],[f30,f6704]) ).
fof(f6704,plain,
( spl0_663
<=> ! [X19] : c_1 = c_Binomial_Obinomial(X19,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
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(f6702,plain,
spl0_662,
inference(avatar_split_clause,[],[f29,f6700]) ).
fof(f6700,plain,
( spl0_662
<=> ! [X19] : c_Binomial_Obinomial(X19,c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
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(f5942,plain,
( ~ spl0_661
| ~ spl0_117
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f5928,f3759,f3749,f5939]) ).
fof(f5939,plain,
( spl0_661
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f3759,plain,
( spl0_119
<=> ! [X19] : ~ c_IntDef_Oneg(c_IntDef_Oint(X19),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f5928,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_117
| ~ spl0_119 ),
inference(superposition,[],[f3760,f3751]) ).
fof(f3760,plain,
( ! [X19] : ~ c_IntDef_Oneg(c_IntDef_Oint(X19),tc_IntDef_Oint)
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f3759]) ).
fof(f5933,plain,
( ~ spl0_660
| ~ spl0_116
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f5927,f3759,f3744,f5930]) ).
fof(f5930,plain,
( spl0_660
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f5927,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_119 ),
inference(superposition,[],[f3760,f3746]) ).
fof(f5926,plain,
spl0_659,
inference(avatar_split_clause,[],[f3002,f5923]) ).
fof(f5923,plain,
( spl0_659
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
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(f5921,plain,
spl0_658,
inference(avatar_split_clause,[],[f2983,f5919]) ).
fof(f5919,plain,
( spl0_658
<=> ! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f2983,plain,
! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_nat),
inference(forward_demodulation,[],[f2769,f2764]) ).
fof(f2769,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(f5917,plain,
spl0_657,
inference(avatar_split_clause,[],[f2982,f5914]) ).
fof(f5914,plain,
( spl0_657
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2982,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(f5912,plain,
spl0_656,
inference(avatar_split_clause,[],[f2981,f5909]) ).
fof(f5909,plain,
( spl0_656
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2981,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2766,f2764]) ).
fof(f2766,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(f5907,plain,
spl0_655,
inference(avatar_split_clause,[],[f2751,f5905]) ).
fof(f5905,plain,
( spl0_655
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
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(f5903,plain,
spl0_654,
inference(avatar_split_clause,[],[f2750,f5901]) ).
fof(f5901,plain,
( spl0_654
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
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(f5899,plain,
spl0_653,
inference(avatar_split_clause,[],[f2749,f5897]) ).
fof(f5897,plain,
( spl0_653
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
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(f5895,plain,
spl0_652,
inference(avatar_split_clause,[],[f2748,f5893]) ).
fof(f5893,plain,
( spl0_652
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
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(f5891,plain,
spl0_651,
inference(avatar_split_clause,[],[f2747,f5889]) ).
fof(f5889,plain,
( spl0_651
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
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(f5887,plain,
spl0_650,
inference(avatar_split_clause,[],[f2746,f5885]) ).
fof(f5885,plain,
( spl0_650
<=> ! [X94] :
( ~ class_Wellfounded__Recursion_Owellorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
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(f5883,plain,
spl0_649,
inference(avatar_split_clause,[],[f2745,f5881]) ).
fof(f5881,plain,
( spl0_649
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
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(f5879,plain,
spl0_648,
inference(avatar_split_clause,[],[f2740,f5877]) ).
fof(f5877,plain,
( spl0_648
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
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(f5875,plain,
spl0_647,
inference(avatar_split_clause,[],[f2739,f5873]) ).
fof(f5873,plain,
( spl0_647
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
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(f5871,plain,
spl0_646,
inference(avatar_split_clause,[],[f2738,f5869]) ).
fof(f5869,plain,
( spl0_646
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
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(f5867,plain,
spl0_645,
inference(avatar_split_clause,[],[f2737,f5865]) ).
fof(f5865,plain,
( spl0_645
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
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(f5863,plain,
spl0_644,
inference(avatar_split_clause,[],[f2736,f5861]) ).
fof(f5861,plain,
( spl0_644
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
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(f5859,plain,
spl0_643,
inference(avatar_split_clause,[],[f2735,f5857]) ).
fof(f5857,plain,
( spl0_643
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
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(f5855,plain,
spl0_642,
inference(avatar_split_clause,[],[f2732,f5853]) ).
fof(f5853,plain,
( spl0_642
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
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(f5851,plain,
spl0_641,
inference(avatar_split_clause,[],[f2731,f5849]) ).
fof(f5849,plain,
( spl0_641
<=> ! [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_641])]) ).
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(f5847,plain,
spl0_640,
inference(avatar_split_clause,[],[f2730,f5845]) ).
fof(f5845,plain,
( spl0_640
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
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(f5843,plain,
spl0_639,
inference(avatar_split_clause,[],[f2727,f5841]) ).
fof(f5841,plain,
( spl0_639
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
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(f5839,plain,
spl0_638,
inference(avatar_split_clause,[],[f2724,f5837]) ).
fof(f5837,plain,
( spl0_638
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
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(f5835,plain,
spl0_637,
inference(avatar_split_clause,[],[f2723,f5833]) ).
fof(f5833,plain,
( spl0_637
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
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(f5831,plain,
spl0_636,
inference(avatar_split_clause,[],[f2722,f5829]) ).
fof(f5829,plain,
( spl0_636
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
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(f5827,plain,
spl0_635,
inference(avatar_split_clause,[],[f2721,f5825]) ).
fof(f5825,plain,
( spl0_635
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
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(f5823,plain,
spl0_634,
inference(avatar_split_clause,[],[f2718,f5821]) ).
fof(f5821,plain,
( spl0_634
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
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(f5819,plain,
spl0_633,
inference(avatar_split_clause,[],[f2717,f5817]) ).
fof(f5817,plain,
( spl0_633
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
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(f5815,plain,
spl0_632,
inference(avatar_split_clause,[],[f2712,f5813]) ).
fof(f5813,plain,
( spl0_632
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
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(f5811,plain,
spl0_631,
inference(avatar_split_clause,[],[f2709,f5809]) ).
fof(f5809,plain,
( spl0_631
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
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(f5807,plain,
spl0_630,
inference(avatar_split_clause,[],[f2708,f5805]) ).
fof(f5805,plain,
( spl0_630
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
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(f5803,plain,
spl0_629,
inference(avatar_split_clause,[],[f2707,f5801]) ).
fof(f5801,plain,
( spl0_629
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
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(f5799,plain,
spl0_628,
inference(avatar_split_clause,[],[f2705,f5797]) ).
fof(f5797,plain,
( spl0_628
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
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(f5795,plain,
spl0_627,
inference(avatar_split_clause,[],[f2699,f5793]) ).
fof(f5793,plain,
( spl0_627
<=> ! [X94] :
( ~ class_Ring__and__Field_Osemiring__0(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
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(f5791,plain,
spl0_626,
inference(avatar_split_clause,[],[f2691,f5789]) ).
fof(f5789,plain,
( spl0_626
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
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(f5787,plain,
spl0_625,
inference(avatar_split_clause,[],[f2690,f5785]) ).
fof(f5785,plain,
( spl0_625
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
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(f5783,plain,
spl0_624,
inference(avatar_split_clause,[],[f2689,f5781]) ).
fof(f5781,plain,
( spl0_624
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
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(f5779,plain,
spl0_623,
inference(avatar_split_clause,[],[f2688,f5777]) ).
fof(f5777,plain,
( spl0_623
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
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(f5775,plain,
spl0_622,
inference(avatar_split_clause,[],[f2687,f5773]) ).
fof(f5773,plain,
( spl0_622
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
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(f5771,plain,
spl0_621,
inference(avatar_split_clause,[],[f2685,f5769]) ).
fof(f5769,plain,
( spl0_621
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
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(f5767,plain,
spl0_620,
inference(avatar_split_clause,[],[f2684,f5765]) ).
fof(f5765,plain,
( spl0_620
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
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(f5763,plain,
spl0_619,
inference(avatar_split_clause,[],[f2683,f5761]) ).
fof(f5761,plain,
( spl0_619
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
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(f5759,plain,
spl0_618,
inference(avatar_split_clause,[],[f2682,f5757]) ).
fof(f5757,plain,
( spl0_618
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
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(f5755,plain,
spl0_617,
inference(avatar_split_clause,[],[f2681,f5753]) ).
fof(f5753,plain,
( spl0_617
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
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(f5751,plain,
spl0_616,
inference(avatar_split_clause,[],[f2676,f5749]) ).
fof(f5749,plain,
( spl0_616
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
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(f5747,plain,
spl0_615,
inference(avatar_split_clause,[],[f2675,f5745]) ).
fof(f5745,plain,
( spl0_615
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
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(f5743,plain,
spl0_614,
inference(avatar_split_clause,[],[f2674,f5741]) ).
fof(f5741,plain,
( spl0_614
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring__1(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
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(f5739,plain,
spl0_613,
inference(avatar_split_clause,[],[f2672,f5737]) ).
fof(f5737,plain,
( spl0_613
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
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(f5735,plain,
spl0_612,
inference(avatar_split_clause,[],[f2670,f5733]) ).
fof(f5733,plain,
( spl0_612
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
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(f5731,plain,
spl0_611,
inference(avatar_split_clause,[],[f2665,f5729]) ).
fof(f5729,plain,
( spl0_611
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
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(f5727,plain,
spl0_610,
inference(avatar_split_clause,[],[f2664,f5725]) ).
fof(f5725,plain,
( spl0_610
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
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(f5723,plain,
spl0_609,
inference(avatar_split_clause,[],[f2663,f5721]) ).
fof(f5721,plain,
( spl0_609
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
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(f5719,plain,
spl0_608,
inference(avatar_split_clause,[],[f2662,f5717]) ).
fof(f5717,plain,
( spl0_608
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
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(f5715,plain,
spl0_607,
inference(avatar_split_clause,[],[f2660,f5713]) ).
fof(f5713,plain,
( spl0_607
<=> ! [X94] :
( ~ class_Ring__and__Field_Oring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
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(f5711,plain,
spl0_606,
inference(avatar_split_clause,[],[f2659,f5709]) ).
fof(f5709,plain,
( spl0_606
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
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(f5707,plain,
spl0_605,
inference(avatar_split_clause,[],[f2654,f5705]) ).
fof(f5705,plain,
( spl0_605
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
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(f5703,plain,
spl0_604,
inference(avatar_split_clause,[],[f2651,f5701]) ).
fof(f5701,plain,
( spl0_604
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
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(f5699,plain,
spl0_603,
inference(avatar_split_clause,[],[f2650,f5697]) ).
fof(f5697,plain,
( spl0_603
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
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(f5695,plain,
spl0_602,
inference(avatar_split_clause,[],[f2649,f5693]) ).
fof(f5693,plain,
( spl0_602
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
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(f5691,plain,
spl0_601,
inference(avatar_split_clause,[],[f2648,f5689]) ).
fof(f5689,plain,
( spl0_601
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
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(f5687,plain,
spl0_600,
inference(avatar_split_clause,[],[f2645,f5685]) ).
fof(f5685,plain,
( spl0_600
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
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(f5683,plain,
spl0_599,
inference(avatar_split_clause,[],[f2644,f5681]) ).
fof(f5681,plain,
( spl0_599
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
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(f5679,plain,
spl0_598,
inference(avatar_split_clause,[],[f2643,f5677]) ).
fof(f5677,plain,
( spl0_598
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
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(f5675,plain,
spl0_597,
inference(avatar_split_clause,[],[f2642,f5673]) ).
fof(f5673,plain,
( spl0_597
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
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(f5671,plain,
spl0_596,
inference(avatar_split_clause,[],[f2641,f5669]) ).
fof(f5669,plain,
( spl0_596
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
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(f5667,plain,
spl0_595,
inference(avatar_split_clause,[],[f2640,f5665]) ).
fof(f5665,plain,
( spl0_595
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
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(f5663,plain,
spl0_594,
inference(avatar_split_clause,[],[f2639,f5661]) ).
fof(f5661,plain,
( spl0_594
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
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(f5659,plain,
spl0_593,
inference(avatar_split_clause,[],[f2638,f5657]) ).
fof(f5657,plain,
( spl0_593
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
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(f5655,plain,
spl0_592,
inference(avatar_split_clause,[],[f2636,f5653]) ).
fof(f5653,plain,
( spl0_592
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
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(f5651,plain,
spl0_591,
inference(avatar_split_clause,[],[f2635,f5649]) ).
fof(f5649,plain,
( spl0_591
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
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(f5647,plain,
spl0_590,
inference(avatar_split_clause,[],[f2634,f5645]) ).
fof(f5645,plain,
( spl0_590
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
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(f5643,plain,
spl0_589,
inference(avatar_split_clause,[],[f2633,f5641]) ).
fof(f5641,plain,
( spl0_589
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
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(f5639,plain,
spl0_588,
inference(avatar_split_clause,[],[f2632,f5637]) ).
fof(f5637,plain,
( spl0_588
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
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(f5635,plain,
spl0_587,
inference(avatar_split_clause,[],[f2627,f5633]) ).
fof(f5633,plain,
( spl0_587
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
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(f5631,plain,
spl0_586,
inference(avatar_split_clause,[],[f2626,f5629]) ).
fof(f5629,plain,
( spl0_586
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
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(f5627,plain,
spl0_585,
inference(avatar_split_clause,[],[f2625,f5625]) ).
fof(f5625,plain,
( spl0_585
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
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(f5623,plain,
spl0_584,
inference(avatar_split_clause,[],[f2622,f5621]) ).
fof(f5621,plain,
( spl0_584
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
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(f5619,plain,
spl0_583,
inference(avatar_split_clause,[],[f2619,f5617]) ).
fof(f5617,plain,
( spl0_583
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
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(f5615,plain,
spl0_582,
inference(avatar_split_clause,[],[f2618,f5613]) ).
fof(f5613,plain,
( spl0_582
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
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(f5611,plain,
spl0_581,
inference(avatar_split_clause,[],[f2616,f5609]) ).
fof(f5609,plain,
( spl0_581
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
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(f5607,plain,
spl0_580,
inference(avatar_split_clause,[],[f2615,f5605]) ).
fof(f5605,plain,
( spl0_580
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
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(f5603,plain,
spl0_579,
inference(avatar_split_clause,[],[f2614,f5601]) ).
fof(f5601,plain,
( spl0_579
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
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(f5599,plain,
spl0_578,
inference(avatar_split_clause,[],[f2613,f5597]) ).
fof(f5597,plain,
( spl0_578
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
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(f5595,plain,
spl0_577,
inference(avatar_split_clause,[],[f2610,f5593]) ).
fof(f5593,plain,
( spl0_577
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
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(f5591,plain,
spl0_576,
inference(avatar_split_clause,[],[f2609,f5589]) ).
fof(f5589,plain,
( spl0_576
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
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(f5587,plain,
spl0_575,
inference(avatar_split_clause,[],[f2581,f5585]) ).
fof(f5585,plain,
( spl0_575
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
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(f5583,plain,
spl0_574,
inference(avatar_split_clause,[],[f2579,f5581]) ).
fof(f5581,plain,
( spl0_574
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
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(f5579,plain,
spl0_573,
inference(avatar_split_clause,[],[f2576,f5577]) ).
fof(f5577,plain,
( spl0_573
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
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(f5575,plain,
spl0_572,
inference(avatar_split_clause,[],[f2575,f5573]) ).
fof(f5573,plain,
( spl0_572
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
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(f5571,plain,
spl0_571,
inference(avatar_split_clause,[],[f2574,f5569]) ).
fof(f5569,plain,
( spl0_571
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
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(f5567,plain,
spl0_570,
inference(avatar_split_clause,[],[f2573,f5565]) ).
fof(f5565,plain,
( spl0_570
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
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(f5563,plain,
spl0_569,
inference(avatar_split_clause,[],[f2572,f5561]) ).
fof(f5561,plain,
( spl0_569
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
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(f5559,plain,
spl0_568,
inference(avatar_split_clause,[],[f2571,f5557]) ).
fof(f5557,plain,
( spl0_568
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
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(f5555,plain,
spl0_567,
inference(avatar_split_clause,[],[f2569,f5553]) ).
fof(f5553,plain,
( spl0_567
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
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(f5551,plain,
spl0_566,
inference(avatar_split_clause,[],[f2568,f5549]) ).
fof(f5549,plain,
( spl0_566
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
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(f5547,plain,
spl0_565,
inference(avatar_split_clause,[],[f2566,f5545]) ).
fof(f5545,plain,
( spl0_565
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
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(f5543,plain,
spl0_564,
inference(avatar_split_clause,[],[f2563,f5541]) ).
fof(f5541,plain,
( spl0_564
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
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(f5539,plain,
spl0_563,
inference(avatar_split_clause,[],[f2562,f5537]) ).
fof(f5537,plain,
( spl0_563
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
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(f5535,plain,
spl0_562,
inference(avatar_split_clause,[],[f2560,f5533]) ).
fof(f5533,plain,
( spl0_562
<=> ! [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_562])]) ).
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(f5531,plain,
spl0_561,
inference(avatar_split_clause,[],[f2559,f5529]) ).
fof(f5529,plain,
( spl0_561
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
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(f5527,plain,
spl0_560,
inference(avatar_split_clause,[],[f2558,f5525]) ).
fof(f5525,plain,
( spl0_560
<=> ! [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_560])]) ).
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(f5523,plain,
spl0_559,
inference(avatar_split_clause,[],[f2557,f5521]) ).
fof(f5521,plain,
( spl0_559
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
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(f5519,plain,
spl0_558,
inference(avatar_split_clause,[],[f2556,f5517]) ).
fof(f5517,plain,
( spl0_558
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
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(f5515,plain,
spl0_557,
inference(avatar_split_clause,[],[f2555,f5513]) ).
fof(f5513,plain,
( spl0_557
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
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(f5511,plain,
spl0_556,
inference(avatar_split_clause,[],[f2554,f5509]) ).
fof(f5509,plain,
( spl0_556
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
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(f5507,plain,
spl0_555,
inference(avatar_split_clause,[],[f2553,f5505]) ).
fof(f5505,plain,
( spl0_555
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
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(f5503,plain,
spl0_554,
inference(avatar_split_clause,[],[f2549,f5501]) ).
fof(f5501,plain,
( spl0_554
<=> ! [X94] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
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(f5499,plain,
spl0_553,
inference(avatar_split_clause,[],[f2548,f5497]) ).
fof(f5497,plain,
( spl0_553
<=> ! [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_553])]) ).
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(f5495,plain,
spl0_552,
inference(avatar_split_clause,[],[f2547,f5493]) ).
fof(f5493,plain,
( spl0_552
<=> ! [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_552])]) ).
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(f5491,plain,
spl0_551,
inference(avatar_split_clause,[],[f2546,f5489]) ).
fof(f5489,plain,
( spl0_551
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
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(f5487,plain,
spl0_550,
inference(avatar_split_clause,[],[f2541,f5485]) ).
fof(f5485,plain,
( spl0_550
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
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(f5483,plain,
spl0_549,
inference(avatar_split_clause,[],[f2539,f5481]) ).
fof(f5481,plain,
( spl0_549
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
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(f5479,plain,
spl0_548,
inference(avatar_split_clause,[],[f2538,f5477]) ).
fof(f5477,plain,
( spl0_548
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
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(f5475,plain,
spl0_547,
inference(avatar_split_clause,[],[f2537,f5473]) ).
fof(f5473,plain,
( spl0_547
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
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(f5471,plain,
spl0_546,
inference(avatar_split_clause,[],[f2536,f5469]) ).
fof(f5469,plain,
( spl0_546
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
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(f5467,plain,
spl0_545,
inference(avatar_split_clause,[],[f2534,f5465]) ).
fof(f5465,plain,
( spl0_545
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
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(f5463,plain,
spl0_544,
inference(avatar_split_clause,[],[f2533,f5461]) ).
fof(f5461,plain,
( spl0_544
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
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(f5459,plain,
spl0_543,
inference(avatar_split_clause,[],[f2532,f5457]) ).
fof(f5457,plain,
( spl0_543
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
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(f5455,plain,
spl0_542,
inference(avatar_split_clause,[],[f2531,f5453]) ).
fof(f5453,plain,
( spl0_542
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
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(f5451,plain,
spl0_541,
inference(avatar_split_clause,[],[f2530,f5449]) ).
fof(f5449,plain,
( spl0_541
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
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(f5447,plain,
spl0_540,
inference(avatar_split_clause,[],[f2529,f5445]) ).
fof(f5445,plain,
( spl0_540
<=> ! [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_540])]) ).
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(f5443,plain,
spl0_539,
inference(avatar_split_clause,[],[f2528,f5441]) ).
fof(f5441,plain,
( spl0_539
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
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(f5439,plain,
spl0_538,
inference(avatar_split_clause,[],[f2527,f5437]) ).
fof(f5437,plain,
( spl0_538
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
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(f5435,plain,
spl0_537,
inference(avatar_split_clause,[],[f2526,f5433]) ).
fof(f5433,plain,
( spl0_537
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
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(f5431,plain,
spl0_536,
inference(avatar_split_clause,[],[f2525,f5429]) ).
fof(f5429,plain,
( spl0_536
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
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(f5427,plain,
spl0_535,
inference(avatar_split_clause,[],[f2524,f5425]) ).
fof(f5425,plain,
( spl0_535
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
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(f5423,plain,
spl0_534,
inference(avatar_split_clause,[],[f2523,f5421]) ).
fof(f5421,plain,
( spl0_534
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
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(f5419,plain,
spl0_533,
inference(avatar_split_clause,[],[f2522,f5417]) ).
fof(f5417,plain,
( spl0_533
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
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(f5415,plain,
spl0_532,
inference(avatar_split_clause,[],[f2521,f5413]) ).
fof(f5413,plain,
( spl0_532
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
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(f5411,plain,
spl0_531,
inference(avatar_split_clause,[],[f2520,f5409]) ).
fof(f5409,plain,
( spl0_531
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
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(f5407,plain,
spl0_530,
inference(avatar_split_clause,[],[f2519,f5405]) ).
fof(f5405,plain,
( spl0_530
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
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(f5403,plain,
spl0_529,
inference(avatar_split_clause,[],[f2518,f5401]) ).
fof(f5401,plain,
( spl0_529
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
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(f5399,plain,
spl0_528,
inference(avatar_split_clause,[],[f2517,f5397]) ).
fof(f5397,plain,
( spl0_528
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
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(f5395,plain,
spl0_527,
inference(avatar_split_clause,[],[f2516,f5393]) ).
fof(f5393,plain,
( spl0_527
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
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(f5391,plain,
spl0_526,
inference(avatar_split_clause,[],[f2515,f5389]) ).
fof(f5389,plain,
( spl0_526
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
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(f5387,plain,
spl0_525,
inference(avatar_split_clause,[],[f2514,f5385]) ).
fof(f5385,plain,
( spl0_525
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
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(f5383,plain,
spl0_524,
inference(avatar_split_clause,[],[f2513,f5381]) ).
fof(f5381,plain,
( spl0_524
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
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(f5379,plain,
spl0_523,
inference(avatar_split_clause,[],[f2512,f5377]) ).
fof(f5377,plain,
( spl0_523
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
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(f5375,plain,
spl0_522,
inference(avatar_split_clause,[],[f2511,f5373]) ).
fof(f5373,plain,
( spl0_522
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
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(f5371,plain,
spl0_521,
inference(avatar_split_clause,[],[f2510,f5369]) ).
fof(f5369,plain,
( spl0_521
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
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(f5367,plain,
spl0_520,
inference(avatar_split_clause,[],[f2509,f5365]) ).
fof(f5365,plain,
( spl0_520
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
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(f5363,plain,
spl0_519,
inference(avatar_split_clause,[],[f2508,f5361]) ).
fof(f5361,plain,
( spl0_519
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
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(f5359,plain,
spl0_518,
inference(avatar_split_clause,[],[f2507,f5357]) ).
fof(f5357,plain,
( spl0_518
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
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(f5355,plain,
spl0_517,
inference(avatar_split_clause,[],[f2506,f5353]) ).
fof(f5353,plain,
( spl0_517
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
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(f5351,plain,
spl0_516,
inference(avatar_split_clause,[],[f2505,f5349]) ).
fof(f5349,plain,
( spl0_516
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
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(f5347,plain,
spl0_515,
inference(avatar_split_clause,[],[f2504,f5345]) ).
fof(f5345,plain,
( spl0_515
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
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(f5343,plain,
spl0_514,
inference(avatar_split_clause,[],[f2503,f5341]) ).
fof(f5341,plain,
( spl0_514
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
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(f5339,plain,
spl0_513,
inference(avatar_split_clause,[],[f2502,f5337]) ).
fof(f5337,plain,
( spl0_513
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
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(f5335,plain,
spl0_512,
inference(avatar_split_clause,[],[f2501,f5333]) ).
fof(f5333,plain,
( spl0_512
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
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(f5331,plain,
spl0_511,
inference(avatar_split_clause,[],[f2500,f5329]) ).
fof(f5329,plain,
( spl0_511
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
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(f5327,plain,
spl0_510,
inference(avatar_split_clause,[],[f2497,f5325]) ).
fof(f5325,plain,
( spl0_510
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
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(f5323,plain,
spl0_509,
inference(avatar_split_clause,[],[f2495,f5321]) ).
fof(f5321,plain,
( spl0_509
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
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(f5319,plain,
spl0_508,
inference(avatar_split_clause,[],[f2494,f5317]) ).
fof(f5317,plain,
( spl0_508
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
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(f5315,plain,
spl0_507,
inference(avatar_split_clause,[],[f2492,f5313]) ).
fof(f5313,plain,
( spl0_507
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
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(f5311,plain,
spl0_506,
inference(avatar_split_clause,[],[f2489,f5309]) ).
fof(f5309,plain,
( spl0_506
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
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(f5307,plain,
spl0_505,
inference(avatar_split_clause,[],[f2488,f5305]) ).
fof(f5305,plain,
( spl0_505
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
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(f5303,plain,
spl0_504,
inference(avatar_split_clause,[],[f2487,f5301]) ).
fof(f5301,plain,
( spl0_504
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
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(f5299,plain,
spl0_503,
inference(avatar_split_clause,[],[f2485,f5297]) ).
fof(f5297,plain,
( spl0_503
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
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(f5295,plain,
spl0_502,
inference(avatar_split_clause,[],[f2484,f5293]) ).
fof(f5293,plain,
( spl0_502
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
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(f5291,plain,
spl0_501,
inference(avatar_split_clause,[],[f2483,f5289]) ).
fof(f5289,plain,
( spl0_501
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__semidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
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(f5287,plain,
spl0_500,
inference(avatar_split_clause,[],[f2480,f5285]) ).
fof(f5285,plain,
( spl0_500
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
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(f5283,plain,
spl0_499,
inference(avatar_split_clause,[],[f2479,f5281]) ).
fof(f5281,plain,
( spl0_499
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
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(f5279,plain,
spl0_498,
inference(avatar_split_clause,[],[f2478,f5277]) ).
fof(f5277,plain,
( spl0_498
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
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(f5275,plain,
spl0_497,
inference(avatar_split_clause,[],[f2477,f5273]) ).
fof(f5273,plain,
( spl0_497
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
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(f5271,plain,
spl0_496,
inference(avatar_split_clause,[],[f2475,f5269]) ).
fof(f5269,plain,
( spl0_496
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
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(f5267,plain,
spl0_495,
inference(avatar_split_clause,[],[f2474,f5265]) ).
fof(f5265,plain,
( spl0_495
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
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(f5263,plain,
spl0_494,
inference(avatar_split_clause,[],[f2473,f5261]) ).
fof(f5261,plain,
( spl0_494
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
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(f5259,plain,
spl0_493,
inference(avatar_split_clause,[],[f2472,f5257]) ).
fof(f5257,plain,
( spl0_493
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
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(f5255,plain,
spl0_492,
inference(avatar_split_clause,[],[f2471,f5253]) ).
fof(f5253,plain,
( spl0_492
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Olordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
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(f5251,plain,
spl0_491,
inference(avatar_split_clause,[],[f2470,f5249]) ).
fof(f5249,plain,
( spl0_491
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
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(f5247,plain,
spl0_490,
inference(avatar_split_clause,[],[f2469,f5245]) ).
fof(f5245,plain,
( spl0_490
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
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(f5243,plain,
spl0_489,
inference(avatar_split_clause,[],[f2468,f5241]) ).
fof(f5241,plain,
( spl0_489
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
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(f5239,plain,
spl0_488,
inference(avatar_split_clause,[],[f2467,f5237]) ).
fof(f5237,plain,
( spl0_488
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oaxclass__abs__if(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
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(f5235,plain,
spl0_487,
inference(avatar_split_clause,[],[f2466,f5233]) ).
fof(f5233,plain,
( spl0_487
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
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(f5231,plain,
spl0_486,
inference(avatar_split_clause,[],[f2465,f5229]) ).
fof(f5229,plain,
( spl0_486
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
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(f5227,plain,
spl0_485,
inference(avatar_split_clause,[],[f2464,f5225]) ).
fof(f5225,plain,
( spl0_485
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
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(f5223,plain,
spl0_484,
inference(avatar_split_clause,[],[f2463,f5221]) ).
fof(f5221,plain,
( spl0_484
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
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(f5219,plain,
spl0_483,
inference(avatar_split_clause,[],[f2462,f5217]) ).
fof(f5217,plain,
( spl0_483
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
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(f5215,plain,
spl0_482,
inference(avatar_split_clause,[],[f2461,f5213]) ).
fof(f5213,plain,
( spl0_482
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
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(f5211,plain,
spl0_481,
inference(avatar_split_clause,[],[f2460,f5209]) ).
fof(f5209,plain,
( spl0_481
<=> ! [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_481])]) ).
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(f5207,plain,
spl0_480,
inference(avatar_split_clause,[],[f2459,f5205]) ).
fof(f5205,plain,
( spl0_480
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
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(f5203,plain,
spl0_479,
inference(avatar_split_clause,[],[f2457,f5201]) ).
fof(f5201,plain,
( spl0_479
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
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(f5199,plain,
spl0_478,
inference(avatar_split_clause,[],[f2456,f5197]) ).
fof(f5197,plain,
( spl0_478
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
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(f5195,plain,
spl0_477,
inference(avatar_split_clause,[],[f2455,f5193]) ).
fof(f5193,plain,
( spl0_477
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
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(f5191,plain,
spl0_476,
inference(avatar_split_clause,[],[f2454,f5189]) ).
fof(f5189,plain,
( spl0_476
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
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(f5187,plain,
spl0_475,
inference(avatar_split_clause,[],[f2453,f5185]) ).
fof(f5185,plain,
( spl0_475
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
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(f5183,plain,
spl0_474,
inference(avatar_split_clause,[],[f2448,f5181]) ).
fof(f5181,plain,
( spl0_474
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
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(f5179,plain,
spl0_473,
inference(avatar_split_clause,[],[f2447,f5177]) ).
fof(f5177,plain,
( spl0_473
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
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(f5175,plain,
spl0_472,
inference(avatar_split_clause,[],[f2446,f5173]) ).
fof(f5173,plain,
( spl0_472
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
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(f5171,plain,
spl0_471,
inference(avatar_split_clause,[],[f2445,f5169]) ).
fof(f5169,plain,
( spl0_471
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
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(f5167,plain,
spl0_470,
inference(avatar_split_clause,[],[f2444,f5165]) ).
fof(f5165,plain,
( spl0_470
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
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(f5163,plain,
spl0_469,
inference(avatar_split_clause,[],[f2443,f5161]) ).
fof(f5161,plain,
( spl0_469
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
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(f5159,plain,
spl0_468,
inference(avatar_split_clause,[],[f2442,f5157]) ).
fof(f5157,plain,
( spl0_468
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
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(f5155,plain,
spl0_467,
inference(avatar_split_clause,[],[f2441,f5153]) ).
fof(f5153,plain,
( spl0_467
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oidom(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
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(f5151,plain,
spl0_466,
inference(avatar_split_clause,[],[f2439,f5149]) ).
fof(f5149,plain,
( spl0_466
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__semidom(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
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(f5147,plain,
spl0_465,
inference(avatar_split_clause,[],[f2438,f5145]) ).
fof(f5145,plain,
( spl0_465
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
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(f5143,plain,
spl0_464,
inference(avatar_split_clause,[],[f2437,f5141]) ).
fof(f5141,plain,
( spl0_464
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
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(f5139,plain,
spl0_463,
inference(avatar_split_clause,[],[f2436,f5137]) ).
fof(f5137,plain,
( spl0_463
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
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(f5135,plain,
spl0_462,
inference(avatar_split_clause,[],[f2435,f5133]) ).
fof(f5133,plain,
( spl0_462
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
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(f5131,plain,
spl0_461,
inference(avatar_split_clause,[],[f2434,f5129]) ).
fof(f5129,plain,
( spl0_461
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
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(f5127,plain,
spl0_460,
inference(avatar_split_clause,[],[f2432,f5125]) ).
fof(f5125,plain,
( spl0_460
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
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(f5123,plain,
spl0_459,
inference(avatar_split_clause,[],[f2431,f5121]) ).
fof(f5121,plain,
( spl0_459
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Olordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
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(f5119,plain,
spl0_458,
inference(avatar_split_clause,[],[f2430,f5117]) ).
fof(f5117,plain,
( spl0_458
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__ring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
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(f5115,plain,
spl0_457,
inference(avatar_split_clause,[],[f2429,f5113]) ).
fof(f5113,plain,
( spl0_457
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oaxclass__abs__if(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
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(f5111,plain,
spl0_456,
inference(avatar_split_clause,[],[f2428,f5109]) ).
fof(f5109,plain,
( spl0_456
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
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(f5107,plain,
spl0_455,
inference(avatar_split_clause,[],[f2427,f5105]) ).
fof(f5105,plain,
( spl0_455
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
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(f5103,plain,
spl0_454,
inference(avatar_split_clause,[],[f2426,f5101]) ).
fof(f5101,plain,
( spl0_454
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
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(f5099,plain,
spl0_453,
inference(avatar_split_clause,[],[f2425,f5097]) ).
fof(f5097,plain,
( spl0_453
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
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(f5095,plain,
spl0_452,
inference(avatar_split_clause,[],[f2424,f5093]) ).
fof(f5093,plain,
( spl0_452
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
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(f5091,plain,
spl0_451,
inference(avatar_split_clause,[],[f2423,f5089]) ).
fof(f5089,plain,
( spl0_451
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
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(f5087,plain,
spl0_450,
inference(avatar_split_clause,[],[f2422,f5085]) ).
fof(f5085,plain,
( spl0_450
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
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(f5083,plain,
spl0_449,
inference(avatar_split_clause,[],[f2421,f5081]) ).
fof(f5081,plain,
( spl0_449
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
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(f5079,plain,
spl0_448,
inference(avatar_split_clause,[],[f2420,f5077]) ).
fof(f5077,plain,
( spl0_448
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
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(f5075,plain,
spl0_447,
inference(avatar_split_clause,[],[f2419,f5073]) ).
fof(f5073,plain,
( spl0_447
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
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(f5071,plain,
spl0_446,
inference(avatar_split_clause,[],[f2418,f5069]) ).
fof(f5069,plain,
( spl0_446
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
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(f5067,plain,
spl0_445,
inference(avatar_split_clause,[],[f2417,f5065]) ).
fof(f5065,plain,
( spl0_445
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
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(f5063,plain,
spl0_444,
inference(avatar_split_clause,[],[f2416,f5061]) ).
fof(f5061,plain,
( spl0_444
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
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(f5059,plain,
spl0_443,
inference(avatar_split_clause,[],[f2415,f5057]) ).
fof(f5057,plain,
( spl0_443
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
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(f5055,plain,
spl0_442,
inference(avatar_split_clause,[],[f2414,f5053]) ).
fof(f5053,plain,
( spl0_442
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
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(f5051,plain,
spl0_441,
inference(avatar_split_clause,[],[f2413,f5049]) ).
fof(f5049,plain,
( spl0_441
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
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(f5047,plain,
spl0_440,
inference(avatar_split_clause,[],[f2412,f5045]) ).
fof(f5045,plain,
( spl0_440
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
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(f5043,plain,
spl0_439,
inference(avatar_split_clause,[],[f2411,f5041]) ).
fof(f5041,plain,
( spl0_439
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
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(f5039,plain,
spl0_438,
inference(avatar_split_clause,[],[f2408,f5037]) ).
fof(f5037,plain,
( spl0_438
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
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(f5035,plain,
spl0_437,
inference(avatar_split_clause,[],[f2406,f5033]) ).
fof(f5033,plain,
( spl0_437
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
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(f5031,plain,
spl0_436,
inference(avatar_split_clause,[],[f2404,f5029]) ).
fof(f5029,plain,
( spl0_436
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
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(f5027,plain,
spl0_435,
inference(avatar_split_clause,[],[f2401,f5025]) ).
fof(f5025,plain,
( spl0_435
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
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(f5023,plain,
spl0_434,
inference(avatar_split_clause,[],[f2400,f5021]) ).
fof(f5021,plain,
( spl0_434
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
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(f5019,plain,
spl0_433,
inference(avatar_split_clause,[],[f2399,f5017]) ).
fof(f5017,plain,
( spl0_433
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
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(f5015,plain,
spl0_432,
inference(avatar_split_clause,[],[f2398,f5013]) ).
fof(f5013,plain,
( spl0_432
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
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(f5011,plain,
spl0_431,
inference(avatar_split_clause,[],[f2396,f5009]) ).
fof(f5009,plain,
( spl0_431
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
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(f5007,plain,
spl0_430,
inference(avatar_split_clause,[],[f2395,f5005]) ).
fof(f5005,plain,
( spl0_430
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
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(f5003,plain,
spl0_429,
inference(avatar_split_clause,[],[f2394,f5001]) ).
fof(f5001,plain,
( spl0_429
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
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(f4999,plain,
spl0_428,
inference(avatar_split_clause,[],[f2393,f4997]) ).
fof(f4997,plain,
( spl0_428
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
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(f4995,plain,
spl0_427,
inference(avatar_split_clause,[],[f2392,f4993]) ).
fof(f4993,plain,
( spl0_427
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
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(f4991,plain,
spl0_426,
inference(avatar_split_clause,[],[f2391,f4989]) ).
fof(f4989,plain,
( spl0_426
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
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(f4987,plain,
spl0_425,
inference(avatar_split_clause,[],[f2390,f4985]) ).
fof(f4985,plain,
( spl0_425
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
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(f4983,plain,
spl0_424,
inference(avatar_split_clause,[],[f2389,f4981]) ).
fof(f4981,plain,
( spl0_424
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
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(f4979,plain,
spl0_423,
inference(avatar_split_clause,[],[f2388,f4977]) ).
fof(f4977,plain,
( spl0_423
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__idom(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
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(f4975,plain,
spl0_422,
inference(avatar_split_clause,[],[f2324,f4973]) ).
fof(f4973,plain,
( spl0_422
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
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(f4971,plain,
spl0_421,
inference(avatar_split_clause,[],[f2321,f4969]) ).
fof(f4969,plain,
( spl0_421
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
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(f4967,plain,
spl0_420,
inference(avatar_split_clause,[],[f2320,f4965]) ).
fof(f4965,plain,
( spl0_420
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
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(f4963,plain,
spl0_419,
inference(avatar_split_clause,[],[f2319,f4961]) ).
fof(f4961,plain,
( spl0_419
<=> ! [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_419])]) ).
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(f4959,plain,
spl0_418,
inference(avatar_split_clause,[],[f2318,f4957]) ).
fof(f4957,plain,
( spl0_418
<=> ! [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_418])]) ).
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(f4955,plain,
spl0_417,
inference(avatar_split_clause,[],[f2317,f4953]) ).
fof(f4953,plain,
( spl0_417
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
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(f4951,plain,
spl0_416,
inference(avatar_split_clause,[],[f2316,f4949]) ).
fof(f4949,plain,
( spl0_416
<=> ! [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_416])]) ).
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(f4947,plain,
spl0_415,
inference(avatar_split_clause,[],[f2315,f4945]) ).
fof(f4945,plain,
( spl0_415
<=> ! [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_415])]) ).
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(f4943,plain,
spl0_414,
inference(avatar_split_clause,[],[f2314,f4941]) ).
fof(f4941,plain,
( spl0_414
<=> ! [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_414])]) ).
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(f4939,plain,
spl0_413,
inference(avatar_split_clause,[],[f2313,f4937]) ).
fof(f4937,plain,
( spl0_413
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
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(f4935,plain,
spl0_412,
inference(avatar_split_clause,[],[f2312,f4933]) ).
fof(f4933,plain,
( spl0_412
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
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(f4931,plain,
spl0_411,
inference(avatar_split_clause,[],[f2311,f4929]) ).
fof(f4929,plain,
( spl0_411
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
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(f4927,plain,
spl0_410,
inference(avatar_split_clause,[],[f2310,f4925]) ).
fof(f4925,plain,
( spl0_410
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
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(f4923,plain,
spl0_409,
inference(avatar_split_clause,[],[f2308,f4921]) ).
fof(f4921,plain,
( spl0_409
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
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(f4919,plain,
spl0_408,
inference(avatar_split_clause,[],[f2307,f4917]) ).
fof(f4917,plain,
( spl0_408
<=> ! [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_408])]) ).
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(f4915,plain,
spl0_407,
inference(avatar_split_clause,[],[f2306,f4913]) ).
fof(f4913,plain,
( spl0_407
<=> ! [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_407])]) ).
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(f4911,plain,
spl0_406,
inference(avatar_split_clause,[],[f2305,f4909]) ).
fof(f4909,plain,
( spl0_406
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
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(f4907,plain,
spl0_405,
inference(avatar_split_clause,[],[f2304,f4905]) ).
fof(f4905,plain,
( spl0_405
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
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(f4903,plain,
spl0_404,
inference(avatar_split_clause,[],[f2303,f4901]) ).
fof(f4901,plain,
( spl0_404
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
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(f4899,plain,
spl0_403,
inference(avatar_split_clause,[],[f2302,f4897]) ).
fof(f4897,plain,
( spl0_403
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
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(f4895,plain,
spl0_402,
inference(avatar_split_clause,[],[f2301,f4893]) ).
fof(f4893,plain,
( spl0_402
<=> ! [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_402])]) ).
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(f4891,plain,
spl0_401,
inference(avatar_split_clause,[],[f2298,f4889]) ).
fof(f4889,plain,
( spl0_401
<=> ! [X94] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
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(f4887,plain,
spl0_400,
inference(avatar_split_clause,[],[f2297,f4885]) ).
fof(f4885,plain,
( spl0_400
<=> ! [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_400])]) ).
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(f4883,plain,
spl0_399,
inference(avatar_split_clause,[],[f2296,f4881]) ).
fof(f4881,plain,
( spl0_399
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
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(f4879,plain,
spl0_398,
inference(avatar_split_clause,[],[f2295,f4877]) ).
fof(f4877,plain,
( spl0_398
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
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(f4875,plain,
spl0_397,
inference(avatar_split_clause,[],[f2294,f4873]) ).
fof(f4873,plain,
( spl0_397
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__cancel__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
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(f4871,plain,
spl0_396,
inference(avatar_split_clause,[],[f2293,f4869]) ).
fof(f4869,plain,
( spl0_396
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
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(f4867,plain,
spl0_395,
inference(avatar_split_clause,[],[f2292,f4865]) ).
fof(f4865,plain,
( spl0_395
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
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(f4863,plain,
spl0_394,
inference(avatar_split_clause,[],[f2290,f4861]) ).
fof(f4861,plain,
( spl0_394
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__join(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
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(f4859,plain,
spl0_393,
inference(avatar_split_clause,[],[f2289,f4857]) ).
fof(f4857,plain,
( spl0_393
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
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(f4855,plain,
spl0_392,
inference(avatar_split_clause,[],[f2288,f4853]) ).
fof(f4853,plain,
( spl0_392
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__meet(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
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(f4851,plain,
spl0_391,
inference(avatar_split_clause,[],[f2287,f4849]) ).
fof(f4849,plain,
( spl0_391
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
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(f4847,plain,
spl0_390,
inference(avatar_split_clause,[],[f2286,f4845]) ).
fof(f4845,plain,
( spl0_390
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
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(f4843,plain,
spl0_389,
inference(avatar_split_clause,[],[f2285,f4841]) ).
fof(f4841,plain,
( spl0_389
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
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(f4839,plain,
spl0_388,
inference(avatar_split_clause,[],[f2284,f4837]) ).
fof(f4837,plain,
( spl0_388
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
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(f4835,plain,
spl0_387,
inference(avatar_split_clause,[],[f2283,f4833]) ).
fof(f4833,plain,
( spl0_387
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Olordered__ab__group__abs(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
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(f4831,plain,
spl0_386,
inference(avatar_split_clause,[],[f2280,f4829]) ).
fof(f4829,plain,
( spl0_386
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
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(f4827,plain,
spl0_385,
inference(avatar_split_clause,[],[f2278,f4825]) ).
fof(f4825,plain,
( spl0_385
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
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(f4823,plain,
spl0_384,
inference(avatar_split_clause,[],[f2277,f4821]) ).
fof(f4821,plain,
( spl0_384
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
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(f4819,plain,
spl0_383,
inference(avatar_split_clause,[],[f2275,f4817]) ).
fof(f4817,plain,
( spl0_383
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
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(f4815,plain,
spl0_382,
inference(avatar_split_clause,[],[f2272,f4813]) ).
fof(f4813,plain,
( spl0_382
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
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(f4811,plain,
spl0_381,
inference(avatar_split_clause,[],[f2271,f4809]) ).
fof(f4809,plain,
( spl0_381
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
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(f4807,plain,
spl0_380,
inference(avatar_split_clause,[],[f2270,f4805]) ).
fof(f4805,plain,
( spl0_380
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
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(f4803,plain,
spl0_379,
inference(avatar_split_clause,[],[f2269,f4801]) ).
fof(f4801,plain,
( spl0_379
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
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(f4799,plain,
spl0_378,
inference(avatar_split_clause,[],[f2268,f4797]) ).
fof(f4797,plain,
( spl0_378
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
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(f4795,plain,
spl0_377,
inference(avatar_split_clause,[],[f2267,f4793]) ).
fof(f4793,plain,
( spl0_377
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
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(f4791,plain,
spl0_376,
inference(avatar_split_clause,[],[f2266,f4789]) ).
fof(f4789,plain,
( spl0_376
<=> ! [X94] :
( ~ class_Ring__and__Field_Olordered__ring(X94)
| class_Ring__and__Field_Opordered__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
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(f4787,plain,
spl0_375,
inference(avatar_split_clause,[],[f2265,f4785]) ).
fof(f4785,plain,
( spl0_375
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
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(f4783,plain,
spl0_374,
inference(avatar_split_clause,[],[f2264,f4781]) ).
fof(f4781,plain,
( spl0_374
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
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(f4779,plain,
spl0_373,
inference(avatar_split_clause,[],[f2263,f4777]) ).
fof(f4777,plain,
( spl0_373
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
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(f4775,plain,
spl0_372,
inference(avatar_split_clause,[],[f2262,f4773]) ).
fof(f4773,plain,
( spl0_372
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
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(f4771,plain,
spl0_371,
inference(avatar_split_clause,[],[f2260,f4769]) ).
fof(f4769,plain,
( spl0_371
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
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(f4767,plain,
spl0_370,
inference(avatar_split_clause,[],[f2258,f4765]) ).
fof(f4765,plain,
( spl0_370
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
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(f4763,plain,
spl0_369,
inference(avatar_split_clause,[],[f2255,f4761]) ).
fof(f4761,plain,
( spl0_369
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
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(f4759,plain,
spl0_368,
inference(avatar_split_clause,[],[f2253,f4757]) ).
fof(f4757,plain,
( spl0_368
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
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(f4755,plain,
spl0_367,
inference(avatar_split_clause,[],[f2251,f4753]) ).
fof(f4753,plain,
( spl0_367
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
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(f4751,plain,
spl0_366,
inference(avatar_split_clause,[],[f2248,f4749]) ).
fof(f4749,plain,
( spl0_366
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
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(f4747,plain,
spl0_365,
inference(avatar_split_clause,[],[f2247,f4745]) ).
fof(f4745,plain,
( spl0_365
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
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(f4743,plain,
spl0_364,
inference(avatar_split_clause,[],[f2246,f4741]) ).
fof(f4741,plain,
( spl0_364
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
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(f4739,plain,
spl0_363,
inference(avatar_split_clause,[],[f2245,f4737]) ).
fof(f4737,plain,
( spl0_363
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
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(f4735,plain,
spl0_362,
inference(avatar_split_clause,[],[f2243,f4733]) ).
fof(f4733,plain,
( spl0_362
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
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(f4731,plain,
spl0_361,
inference(avatar_split_clause,[],[f2242,f4729]) ).
fof(f4729,plain,
( spl0_361
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
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(f4727,plain,
spl0_360,
inference(avatar_split_clause,[],[f2241,f4725]) ).
fof(f4725,plain,
( spl0_360
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
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(f4723,plain,
spl0_359,
inference(avatar_split_clause,[],[f2240,f4721]) ).
fof(f4721,plain,
( spl0_359
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
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(f4719,plain,
spl0_358,
inference(avatar_split_clause,[],[f2239,f4717]) ).
fof(f4717,plain,
( spl0_358
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
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(f4715,plain,
spl0_357,
inference(avatar_split_clause,[],[f2238,f4713]) ).
fof(f4713,plain,
( spl0_357
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
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(f4711,plain,
spl0_356,
inference(avatar_split_clause,[],[f2237,f4709]) ).
fof(f4709,plain,
( spl0_356
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
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(f4707,plain,
spl0_355,
inference(avatar_split_clause,[],[f2236,f4705]) ).
fof(f4705,plain,
( spl0_355
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
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(f4703,plain,
spl0_354,
inference(avatar_split_clause,[],[f2235,f4701]) ).
fof(f4701,plain,
( spl0_354
<=> ! [X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
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(f4699,plain,
spl0_353,
inference(avatar_split_clause,[],[f2199,f4697]) ).
fof(f4697,plain,
( spl0_353
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
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(f4695,plain,
spl0_352,
inference(avatar_split_clause,[],[f2198,f4693]) ).
fof(f4693,plain,
( spl0_352
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
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(f4691,plain,
spl0_351,
inference(avatar_split_clause,[],[f2197,f4689]) ).
fof(f4689,plain,
( spl0_351
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
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(f4687,plain,
spl0_350,
inference(avatar_split_clause,[],[f2196,f4685]) ).
fof(f4685,plain,
( spl0_350
<=> ! [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_350])]) ).
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(f4683,plain,
spl0_349,
inference(avatar_split_clause,[],[f2195,f4681]) ).
fof(f4681,plain,
( spl0_349
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
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(f4679,plain,
spl0_348,
inference(avatar_split_clause,[],[f2193,f4677]) ).
fof(f4677,plain,
( spl0_348
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
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(f4675,plain,
spl0_347,
inference(avatar_split_clause,[],[f2192,f4673]) ).
fof(f4673,plain,
( spl0_347
<=> ! [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_347])]) ).
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(f4671,plain,
spl0_346,
inference(avatar_split_clause,[],[f2191,f4669]) ).
fof(f4669,plain,
( spl0_346
<=> ! [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_346])]) ).
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(f4667,plain,
spl0_345,
inference(avatar_split_clause,[],[f2190,f4665]) ).
fof(f4665,plain,
( spl0_345
<=> ! [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_345])]) ).
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(f4663,plain,
spl0_344,
inference(avatar_split_clause,[],[f2189,f4661]) ).
fof(f4661,plain,
( spl0_344
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
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(f4659,plain,
spl0_343,
inference(avatar_split_clause,[],[f2188,f4657]) ).
fof(f4657,plain,
( spl0_343
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
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(f4655,plain,
spl0_342,
inference(avatar_split_clause,[],[f2187,f4653]) ).
fof(f4653,plain,
( spl0_342
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
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(f4651,plain,
spl0_341,
inference(avatar_split_clause,[],[f2184,f4649]) ).
fof(f4649,plain,
( spl0_341
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
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(f4647,plain,
spl0_340,
inference(avatar_split_clause,[],[f2183,f4645]) ).
fof(f4645,plain,
( spl0_340
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
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(f4643,plain,
spl0_339,
inference(avatar_split_clause,[],[f2178,f4641]) ).
fof(f4641,plain,
( spl0_339
<=> ! [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_339])]) ).
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(f4639,plain,
spl0_338,
inference(avatar_split_clause,[],[f2177,f4637]) ).
fof(f4637,plain,
( spl0_338
<=> ! [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_338])]) ).
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(f4635,plain,
spl0_337,
inference(avatar_split_clause,[],[f2174,f4633]) ).
fof(f4633,plain,
( spl0_337
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
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(f4631,plain,
spl0_336,
inference(avatar_split_clause,[],[f2173,f4629]) ).
fof(f4629,plain,
( spl0_336
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
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(f4627,plain,
spl0_335,
inference(avatar_split_clause,[],[f2171,f4625]) ).
fof(f4625,plain,
( spl0_335
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
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(f4623,plain,
spl0_334,
inference(avatar_split_clause,[],[f2170,f4621]) ).
fof(f4621,plain,
( spl0_334
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
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(f4619,plain,
spl0_333,
inference(avatar_split_clause,[],[f2169,f4617]) ).
fof(f4617,plain,
( spl0_333
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
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(f4615,plain,
spl0_332,
inference(avatar_split_clause,[],[f2168,f4613]) ).
fof(f4613,plain,
( spl0_332
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
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(f4611,plain,
spl0_331,
inference(avatar_split_clause,[],[f2167,f4609]) ).
fof(f4609,plain,
( spl0_331
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
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(f4607,plain,
spl0_330,
inference(avatar_split_clause,[],[f2166,f4605]) ).
fof(f4605,plain,
( spl0_330
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
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(f4603,plain,
spl0_329,
inference(avatar_split_clause,[],[f2162,f4601]) ).
fof(f4601,plain,
( spl0_329
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
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(f4599,plain,
spl0_328,
inference(avatar_split_clause,[],[f2160,f4597]) ).
fof(f4597,plain,
( spl0_328
<=> ! [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_328])]) ).
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(f4595,plain,
spl0_327,
inference(avatar_split_clause,[],[f2157,f4593]) ).
fof(f4593,plain,
( spl0_327
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
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(f4591,plain,
spl0_326,
inference(avatar_split_clause,[],[f2154,f4589]) ).
fof(f4589,plain,
( spl0_326
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
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(f4587,plain,
spl0_325,
inference(avatar_split_clause,[],[f2153,f4585]) ).
fof(f4585,plain,
( spl0_325
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
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(f4583,plain,
spl0_324,
inference(avatar_split_clause,[],[f2151,f4581]) ).
fof(f4581,plain,
( spl0_324
<=> ! [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_324])]) ).
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(f4579,plain,
spl0_323,
inference(avatar_split_clause,[],[f2150,f4577]) ).
fof(f4577,plain,
( spl0_323
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
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(f4575,plain,
spl0_322,
inference(avatar_split_clause,[],[f2149,f4573]) ).
fof(f4573,plain,
( spl0_322
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
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(f4571,plain,
spl0_321,
inference(avatar_split_clause,[],[f2146,f4569]) ).
fof(f4569,plain,
( spl0_321
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
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(f4567,plain,
spl0_320,
inference(avatar_split_clause,[],[f2145,f4565]) ).
fof(f4565,plain,
( spl0_320
<=> ! [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_320])]) ).
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(f4563,plain,
spl0_319,
inference(avatar_split_clause,[],[f2143,f4561]) ).
fof(f4561,plain,
( spl0_319
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
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(f4559,plain,
spl0_318,
inference(avatar_split_clause,[],[f2137,f4557]) ).
fof(f4557,plain,
( spl0_318
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
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(f4555,plain,
spl0_317,
inference(avatar_split_clause,[],[f2136,f4553]) ).
fof(f4553,plain,
( spl0_317
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
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(f4551,plain,
spl0_316,
inference(avatar_split_clause,[],[f2134,f4549]) ).
fof(f4549,plain,
( spl0_316
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
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(f4547,plain,
spl0_315,
inference(avatar_split_clause,[],[f2133,f4545]) ).
fof(f4545,plain,
( spl0_315
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__semiring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
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(f4543,plain,
spl0_314,
inference(avatar_split_clause,[],[f2126,f4541]) ).
fof(f4541,plain,
( spl0_314
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
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(f4539,plain,
spl0_313,
inference(avatar_split_clause,[],[f2125,f4537]) ).
fof(f4537,plain,
( spl0_313
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
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(f4535,plain,
spl0_312,
inference(avatar_split_clause,[],[f2123,f4533]) ).
fof(f4533,plain,
( spl0_312
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
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(f4531,plain,
spl0_311,
inference(avatar_split_clause,[],[f2122,f4529]) ).
fof(f4529,plain,
( spl0_311
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
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(f4527,plain,
spl0_310,
inference(avatar_split_clause,[],[f2121,f4525]) ).
fof(f4525,plain,
( spl0_310
<=> ! [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_310])]) ).
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(f4523,plain,
spl0_309,
inference(avatar_split_clause,[],[f2119,f4521]) ).
fof(f4521,plain,
( spl0_309
<=> ! [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_309])]) ).
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(f4519,plain,
spl0_308,
inference(avatar_split_clause,[],[f2118,f4517]) ).
fof(f4517,plain,
( spl0_308
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
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(f4515,plain,
spl0_307,
inference(avatar_split_clause,[],[f2117,f4513]) ).
fof(f4513,plain,
( spl0_307
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
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(f4511,plain,
spl0_306,
inference(avatar_split_clause,[],[f2116,f4509]) ).
fof(f4509,plain,
( spl0_306
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
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(f4507,plain,
spl0_305,
inference(avatar_split_clause,[],[f2115,f4505]) ).
fof(f4505,plain,
( spl0_305
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
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(f4503,plain,
spl0_304,
inference(avatar_split_clause,[],[f2114,f4501]) ).
fof(f4501,plain,
( spl0_304
<=> ! [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_304])]) ).
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(f4499,plain,
spl0_303,
inference(avatar_split_clause,[],[f2113,f4497]) ).
fof(f4497,plain,
( spl0_303
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
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(f4495,plain,
spl0_302,
inference(avatar_split_clause,[],[f2112,f4493]) ).
fof(f4493,plain,
( spl0_302
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
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(f4491,plain,
spl0_301,
inference(avatar_split_clause,[],[f2111,f4489]) ).
fof(f4489,plain,
( spl0_301
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
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(f4487,plain,
spl0_300,
inference(avatar_split_clause,[],[f2110,f4485]) ).
fof(f4485,plain,
( spl0_300
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
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(f4483,plain,
spl0_299,
inference(avatar_split_clause,[],[f2107,f4481]) ).
fof(f4481,plain,
( spl0_299
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
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(f4479,plain,
spl0_298,
inference(avatar_split_clause,[],[f2105,f4477]) ).
fof(f4477,plain,
( spl0_298
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
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(f4475,plain,
spl0_297,
inference(avatar_split_clause,[],[f2103,f4473]) ).
fof(f4473,plain,
( spl0_297
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
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(f4471,plain,
spl0_296,
inference(avatar_split_clause,[],[f2100,f4469]) ).
fof(f4469,plain,
( spl0_296
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
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(f4467,plain,
spl0_295,
inference(avatar_split_clause,[],[f2099,f4465]) ).
fof(f4465,plain,
( spl0_295
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
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(f4463,plain,
spl0_294,
inference(avatar_split_clause,[],[f2098,f4461]) ).
fof(f4461,plain,
( spl0_294
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
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(f4459,plain,
spl0_293,
inference(avatar_split_clause,[],[f2095,f4457]) ).
fof(f4457,plain,
( spl0_293
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
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(f4455,plain,
spl0_292,
inference(avatar_split_clause,[],[f2092,f4453]) ).
fof(f4453,plain,
( spl0_292
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
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(f4451,plain,
spl0_291,
inference(avatar_split_clause,[],[f2091,f4449]) ).
fof(f4449,plain,
( spl0_291
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
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(f4447,plain,
spl0_290,
inference(avatar_split_clause,[],[f2089,f4445]) ).
fof(f4445,plain,
( spl0_290
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
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(f4443,plain,
spl0_289,
inference(avatar_split_clause,[],[f2088,f4441]) ).
fof(f4441,plain,
( spl0_289
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
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(f4439,plain,
spl0_288,
inference(avatar_split_clause,[],[f2087,f4437]) ).
fof(f4437,plain,
( spl0_288
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
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(f4435,plain,
spl0_287,
inference(avatar_split_clause,[],[f2086,f4433]) ).
fof(f4433,plain,
( spl0_287
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
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(f4431,plain,
spl0_286,
inference(avatar_split_clause,[],[f2085,f4429]) ).
fof(f4429,plain,
( spl0_286
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
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(f4427,plain,
spl0_285,
inference(avatar_split_clause,[],[f2083,f4425]) ).
fof(f4425,plain,
( spl0_285
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
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(f4423,plain,
spl0_284,
inference(avatar_split_clause,[],[f2080,f4421]) ).
fof(f4421,plain,
( spl0_284
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
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(f4419,plain,
spl0_283,
inference(avatar_split_clause,[],[f2079,f4417]) ).
fof(f4417,plain,
( spl0_283
<=> ! [X94] :
( ~ class_Ring__and__Field_Ocomm__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
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(f4415,plain,
spl0_282,
inference(avatar_split_clause,[],[f2075,f4413]) ).
fof(f4413,plain,
( spl0_282
<=> ! [X94] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
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(f4411,plain,
spl0_281,
inference(avatar_split_clause,[],[f2073,f4409]) ).
fof(f4409,plain,
( spl0_281
<=> ! [X94] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
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(f4407,plain,
spl0_280,
inference(avatar_split_clause,[],[f2065,f4405]) ).
fof(f4405,plain,
( spl0_280
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
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(f4403,plain,
spl0_279,
inference(avatar_split_clause,[],[f2064,f4401]) ).
fof(f4401,plain,
( spl0_279
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
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(f4399,plain,
spl0_278,
inference(avatar_split_clause,[],[f2063,f4397]) ).
fof(f4397,plain,
( spl0_278
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
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(f4395,plain,
spl0_277,
inference(avatar_split_clause,[],[f2062,f4393]) ).
fof(f4393,plain,
( spl0_277
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
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(f4391,plain,
spl0_276,
inference(avatar_split_clause,[],[f2061,f4389]) ).
fof(f4389,plain,
( spl0_276
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
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(f4387,plain,
spl0_275,
inference(avatar_split_clause,[],[f2060,f4385]) ).
fof(f4385,plain,
( spl0_275
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
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(f4383,plain,
spl0_274,
inference(avatar_split_clause,[],[f2059,f4381]) ).
fof(f4381,plain,
( spl0_274
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2059,axiom,
! [X94] :
( ~ class_Power_Orecpower(X94)
| class_HOL_Oone(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4379,plain,
spl0_273,
inference(avatar_split_clause,[],[f2058,f4377]) ).
fof(f4377,plain,
( spl0_273
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
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(f4375,plain,
spl0_272,
inference(avatar_split_clause,[],[f2057,f4373]) ).
fof(f4373,plain,
( spl0_272
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
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(f4371,plain,
spl0_271,
inference(avatar_split_clause,[],[f2056,f4369]) ).
fof(f4369,plain,
( spl0_271
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
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(f4367,plain,
spl0_270,
inference(avatar_split_clause,[],[f2055,f4365]) ).
fof(f4365,plain,
( spl0_270
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
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(f4363,plain,
spl0_269,
inference(avatar_split_clause,[],[f2054,f4361]) ).
fof(f4361,plain,
( spl0_269
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
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(f4359,plain,
spl0_268,
inference(avatar_split_clause,[],[f2053,f4357]) ).
fof(f4357,plain,
( spl0_268
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
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(f4355,plain,
spl0_267,
inference(avatar_split_clause,[],[f2052,f4353]) ).
fof(f4353,plain,
( spl0_267
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
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(f4351,plain,
spl0_266,
inference(avatar_split_clause,[],[f2051,f4349]) ).
fof(f4349,plain,
( spl0_266
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
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(f4347,plain,
spl0_265,
inference(avatar_split_clause,[],[f2050,f4345]) ).
fof(f4345,plain,
( spl0_265
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
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(f4343,plain,
spl0_264,
inference(avatar_split_clause,[],[f2049,f4341]) ).
fof(f4341,plain,
( spl0_264
<=> ! [X94] :
( ~ class_Power_Orecpower(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
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(f4339,plain,
spl0_263,
inference(avatar_split_clause,[],[f2046,f4337]) ).
fof(f4337,plain,
( spl0_263
<=> ! [X94] :
( ~ class_Orderings_Oorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2046,axiom,
! [X94] :
( ~ class_Orderings_Oorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4335,plain,
spl0_262,
inference(avatar_split_clause,[],[f2045,f4333]) ).
fof(f4333,plain,
( spl0_262
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2045,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4331,plain,
spl0_261,
inference(avatar_split_clause,[],[f2044,f4329]) ).
fof(f4329,plain,
( spl0_261
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2044,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4327,plain,
spl0_260,
inference(avatar_split_clause,[],[f2043,f4325]) ).
fof(f4325,plain,
( spl0_260
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
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(f4323,plain,
spl0_259,
inference(avatar_split_clause,[],[f2042,f4321]) ).
fof(f4321,plain,
( spl0_259
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
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(f4319,plain,
spl0_258,
inference(avatar_split_clause,[],[f2041,f4317]) ).
fof(f4317,plain,
( spl0_258
<=> ! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2041,axiom,
! [X94] :
( ~ class_Orderings_Olinorder(X94)
| class_LOrder_Olorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4315,plain,
spl0_257,
inference(avatar_split_clause,[],[f2038,f4313]) ).
fof(f4313,plain,
( spl0_257
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
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(f4311,plain,
spl0_256,
inference(avatar_split_clause,[],[f2037,f4309]) ).
fof(f4309,plain,
( spl0_256
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
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(f4307,plain,
spl0_255,
inference(avatar_split_clause,[],[f2033,f4305]) ).
fof(f4305,plain,
( spl0_255
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
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(f4303,plain,
spl0_254,
inference(avatar_split_clause,[],[f2032,f4301]) ).
fof(f4301,plain,
( spl0_254
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
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(f4299,plain,
spl0_253,
inference(avatar_split_clause,[],[f2031,f4297]) ).
fof(f4297,plain,
( spl0_253
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
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(f4295,plain,
spl0_252,
inference(avatar_split_clause,[],[f2028,f4293]) ).
fof(f4293,plain,
( spl0_252
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
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(f4291,plain,
spl0_251,
inference(avatar_split_clause,[],[f2026,f4289]) ).
fof(f4289,plain,
( spl0_251
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
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(f4287,plain,
spl0_250,
inference(avatar_split_clause,[],[f2025,f4285]) ).
fof(f4285,plain,
( spl0_250
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
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(f4283,plain,
spl0_249,
inference(avatar_split_clause,[],[f2024,f4281]) ).
fof(f4281,plain,
( spl0_249
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
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(f4279,plain,
spl0_248,
inference(avatar_split_clause,[],[f2023,f4277]) ).
fof(f4277,plain,
( spl0_248
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
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(f4275,plain,
spl0_247,
inference(avatar_split_clause,[],[f2022,f4273]) ).
fof(f4273,plain,
( spl0_247
<=> ! [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_247])]) ).
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(f4271,plain,
spl0_246,
inference(avatar_split_clause,[],[f2018,f4269]) ).
fof(f4269,plain,
( spl0_246
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
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(f4267,plain,
spl0_245,
inference(avatar_split_clause,[],[f2017,f4265]) ).
fof(f4265,plain,
( spl0_245
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
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(f4263,plain,
spl0_244,
inference(avatar_split_clause,[],[f2016,f4261]) ).
fof(f4261,plain,
( spl0_244
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
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(f4259,plain,
spl0_243,
inference(avatar_split_clause,[],[f2013,f4257]) ).
fof(f4257,plain,
( spl0_243
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
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(f4255,plain,
spl0_242,
inference(avatar_split_clause,[],[f2011,f4253]) ).
fof(f4253,plain,
( spl0_242
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
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(f4251,plain,
spl0_241,
inference(avatar_split_clause,[],[f2009,f4249]) ).
fof(f4249,plain,
( spl0_241
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
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(f4247,plain,
spl0_240,
inference(avatar_split_clause,[],[f2008,f4245]) ).
fof(f4245,plain,
( spl0_240
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
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(f4243,plain,
spl0_239,
inference(avatar_split_clause,[],[f2007,f4241]) ).
fof(f4241,plain,
( spl0_239
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
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(f4239,plain,
spl0_238,
inference(avatar_split_clause,[],[f2006,f4237]) ).
fof(f4237,plain,
( spl0_238
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
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(f4235,plain,
spl0_237,
inference(avatar_split_clause,[],[f2005,f4233]) ).
fof(f4233,plain,
( spl0_237
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
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(f4231,plain,
spl0_236,
inference(avatar_split_clause,[],[f2003,f4229]) ).
fof(f4229,plain,
( spl0_236
<=> ! [X94] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
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(f4227,plain,
spl0_235,
inference(avatar_split_clause,[],[f2002,f4225]) ).
fof(f4225,plain,
( spl0_235
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Olinorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
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(f4223,plain,
spl0_234,
inference(avatar_split_clause,[],[f1999,f4221]) ).
fof(f4221,plain,
( spl0_234
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
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(f4219,plain,
spl0_233,
inference(avatar_split_clause,[],[f1997,f4217]) ).
fof(f4217,plain,
( spl0_233
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
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(f4215,plain,
spl0_232,
inference(avatar_split_clause,[],[f1996,f4213]) ).
fof(f4213,plain,
( spl0_232
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
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(f4211,plain,
spl0_231,
inference(avatar_split_clause,[],[f1995,f4209]) ).
fof(f4209,plain,
( spl0_231
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
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(f4207,plain,
spl0_230,
inference(avatar_split_clause,[],[f1994,f4205]) ).
fof(f4205,plain,
( spl0_230
<=> ! [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_230])]) ).
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(f4203,plain,
spl0_229,
inference(avatar_split_clause,[],[f1993,f4201]) ).
fof(f4201,plain,
( spl0_229
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
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(f4199,plain,
spl0_228,
inference(avatar_split_clause,[],[f1992,f4197]) ).
fof(f4197,plain,
( spl0_228
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
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(f4195,plain,
spl0_227,
inference(avatar_split_clause,[],[f1991,f4193]) ).
fof(f4193,plain,
( spl0_227
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
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(f4191,plain,
spl0_226,
inference(avatar_split_clause,[],[f1990,f4189]) ).
fof(f4189,plain,
( spl0_226
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
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(f4187,plain,
spl0_225,
inference(avatar_split_clause,[],[f1989,f4185]) ).
fof(f4185,plain,
( spl0_225
<=> ! [X94] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
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(f4183,plain,
spl0_224,
inference(avatar_split_clause,[],[f1986,f4181]) ).
fof(f4181,plain,
( spl0_224
<=> ! [X94] :
( ~ class_OrderedGroup_Omonoid__mult(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
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(f4179,plain,
spl0_223,
inference(avatar_split_clause,[],[f1985,f4177]) ).
fof(f4177,plain,
( spl0_223
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
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(f4175,plain,
spl0_222,
inference(avatar_split_clause,[],[f1984,f4173]) ).
fof(f4173,plain,
( spl0_222
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
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(f4171,plain,
spl0_221,
inference(avatar_split_clause,[],[f1983,f4169]) ).
fof(f4169,plain,
( spl0_221
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
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(f4167,plain,
spl0_220,
inference(avatar_split_clause,[],[f1982,f4165]) ).
fof(f4165,plain,
( spl0_220
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
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(f4163,plain,
spl0_219,
inference(avatar_split_clause,[],[f1981,f4161]) ).
fof(f4161,plain,
( spl0_219
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
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(f4159,plain,
spl0_218,
inference(avatar_split_clause,[],[f1979,f4157]) ).
fof(f4157,plain,
( spl0_218
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
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(f4155,plain,
spl0_217,
inference(avatar_split_clause,[],[f1977,f4153]) ).
fof(f4153,plain,
( spl0_217
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
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(f4151,plain,
spl0_216,
inference(avatar_split_clause,[],[f1976,f4149]) ).
fof(f4149,plain,
( spl0_216
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
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(f4147,plain,
spl0_215,
inference(avatar_split_clause,[],[f1975,f4145]) ).
fof(f4145,plain,
( spl0_215
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
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(f4143,plain,
spl0_214,
inference(avatar_split_clause,[],[f1974,f4141]) ).
fof(f4141,plain,
( spl0_214
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
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(f4139,plain,
spl0_213,
inference(avatar_split_clause,[],[f1971,f4137]) ).
fof(f4137,plain,
( spl0_213
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
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(f4135,plain,
spl0_212,
inference(avatar_split_clause,[],[f1969,f4133]) ).
fof(f4133,plain,
( spl0_212
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
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(f4131,plain,
spl0_211,
inference(avatar_split_clause,[],[f1968,f4129]) ).
fof(f4129,plain,
( spl0_211
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
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(f4127,plain,
spl0_210,
inference(avatar_split_clause,[],[f1967,f4125]) ).
fof(f4125,plain,
( spl0_210
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
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(f4123,plain,
spl0_209,
inference(avatar_split_clause,[],[f1966,f4121]) ).
fof(f4121,plain,
( spl0_209
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
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(f4119,plain,
spl0_208,
inference(avatar_split_clause,[],[f1965,f4117]) ).
fof(f4117,plain,
( spl0_208
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
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(f4115,plain,
spl0_207,
inference(avatar_split_clause,[],[f1964,f4113]) ).
fof(f4113,plain,
( spl0_207
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
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(f4111,plain,
spl0_206,
inference(avatar_split_clause,[],[f1963,f4109]) ).
fof(f4109,plain,
( spl0_206
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
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(f4107,plain,
spl0_205,
inference(avatar_split_clause,[],[f1962,f4105]) ).
fof(f4105,plain,
( spl0_205
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
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(f4103,plain,
spl0_204,
inference(avatar_split_clause,[],[f1960,f4101]) ).
fof(f4101,plain,
( spl0_204
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
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(f4099,plain,
spl0_203,
inference(avatar_split_clause,[],[f1958,f4097]) ).
fof(f4097,plain,
( spl0_203
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
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(f4095,plain,
spl0_202,
inference(avatar_split_clause,[],[f1957,f4093]) ).
fof(f4093,plain,
( spl0_202
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
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(f4091,plain,
spl0_201,
inference(avatar_split_clause,[],[f1956,f4089]) ).
fof(f4089,plain,
( spl0_201
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
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(f4087,plain,
spl0_200,
inference(avatar_split_clause,[],[f1955,f4085]) ).
fof(f4085,plain,
( spl0_200
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
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(f4083,plain,
spl0_199,
inference(avatar_split_clause,[],[f1952,f4081]) ).
fof(f4081,plain,
( spl0_199
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
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(f4079,plain,
spl0_198,
inference(avatar_split_clause,[],[f1950,f4077]) ).
fof(f4077,plain,
( spl0_198
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
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(f4075,plain,
spl0_197,
inference(avatar_split_clause,[],[f1949,f4073]) ).
fof(f4073,plain,
( spl0_197
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
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(f4071,plain,
spl0_196,
inference(avatar_split_clause,[],[f1948,f4069]) ).
fof(f4069,plain,
( spl0_196
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
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(f4067,plain,
spl0_195,
inference(avatar_split_clause,[],[f1947,f4065]) ).
fof(f4065,plain,
( spl0_195
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
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(f4063,plain,
spl0_194,
inference(avatar_split_clause,[],[f1946,f4061]) ).
fof(f4061,plain,
( spl0_194
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
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(f4059,plain,
spl0_193,
inference(avatar_split_clause,[],[f1945,f4057]) ).
fof(f4057,plain,
( spl0_193
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
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(f4055,plain,
spl0_192,
inference(avatar_split_clause,[],[f1944,f4053]) ).
fof(f4053,plain,
( spl0_192
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
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(f4051,plain,
spl0_191,
inference(avatar_split_clause,[],[f1942,f4049]) ).
fof(f4049,plain,
( spl0_191
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
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(f4047,plain,
spl0_190,
inference(avatar_split_clause,[],[f1940,f4045]) ).
fof(f4045,plain,
( spl0_190
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
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(f4043,plain,
spl0_189,
inference(avatar_split_clause,[],[f1939,f4041]) ).
fof(f4041,plain,
( spl0_189
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
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(f4039,plain,
spl0_188,
inference(avatar_split_clause,[],[f1938,f4037]) ).
fof(f4037,plain,
( spl0_188
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
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(f4035,plain,
spl0_187,
inference(avatar_split_clause,[],[f1937,f4033]) ).
fof(f4033,plain,
( spl0_187
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
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(f4031,plain,
spl0_186,
inference(avatar_split_clause,[],[f1936,f4029]) ).
fof(f4029,plain,
( spl0_186
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
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(f4027,plain,
spl0_185,
inference(avatar_split_clause,[],[f1935,f4025]) ).
fof(f4025,plain,
( spl0_185
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
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(f4023,plain,
spl0_184,
inference(avatar_split_clause,[],[f1932,f4021]) ).
fof(f4021,plain,
( spl0_184
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
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(f4019,plain,
spl0_183,
inference(avatar_split_clause,[],[f1930,f4017]) ).
fof(f4017,plain,
( spl0_183
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
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(f4015,plain,
spl0_182,
inference(avatar_split_clause,[],[f1929,f4013]) ).
fof(f4013,plain,
( spl0_182
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X94)
| class_OrderedGroup_Olordered__ab__group(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
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(f4011,plain,
spl0_181,
inference(avatar_split_clause,[],[f1928,f4009]) ).
fof(f4009,plain,
( spl0_181
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
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(f4007,plain,
spl0_180,
inference(avatar_split_clause,[],[f1927,f4005]) ).
fof(f4005,plain,
( spl0_180
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
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(f4003,plain,
spl0_179,
inference(avatar_split_clause,[],[f1926,f4001]) ).
fof(f4001,plain,
( spl0_179
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
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(f3999,plain,
spl0_178,
inference(avatar_split_clause,[],[f1925,f3997]) ).
fof(f3997,plain,
( spl0_178
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
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(f3995,plain,
spl0_177,
inference(avatar_split_clause,[],[f1924,f3993]) ).
fof(f3993,plain,
( spl0_177
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
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(f3991,plain,
spl0_176,
inference(avatar_split_clause,[],[f1922,f3989]) ).
fof(f3989,plain,
( spl0_176
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
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(f3987,plain,
spl0_175,
inference(avatar_split_clause,[],[f1920,f3985]) ).
fof(f3985,plain,
( spl0_175
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
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(f3983,plain,
spl0_174,
inference(avatar_split_clause,[],[f1919,f3981]) ).
fof(f3981,plain,
( spl0_174
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
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(f3979,plain,
spl0_173,
inference(avatar_split_clause,[],[f1918,f3977]) ).
fof(f3977,plain,
( spl0_173
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_LOrder_Olorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
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(f3975,plain,
spl0_172,
inference(avatar_split_clause,[],[f1915,f3973]) ).
fof(f3973,plain,
( spl0_172
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
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(f3971,plain,
spl0_171,
inference(avatar_split_clause,[],[f1913,f3969]) ).
fof(f3969,plain,
( spl0_171
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
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(f3967,plain,
spl0_170,
inference(avatar_split_clause,[],[f1912,f3965]) ).
fof(f3965,plain,
( spl0_170
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
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(f3963,plain,
spl0_169,
inference(avatar_split_clause,[],[f1911,f3961]) ).
fof(f3961,plain,
( spl0_169
<=> ! [X94] :
( ~ class_OrderedGroup_Olordered__ab__group(X94)
| class_OrderedGroup_Opordered__ab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
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(f3959,plain,
spl0_168,
inference(avatar_split_clause,[],[f1910,f3957]) ).
fof(f3957,plain,
( spl0_168
<=> ! [X94] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
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(f3955,plain,
spl0_167,
inference(avatar_split_clause,[],[f1906,f3953]) ).
fof(f3953,plain,
( spl0_167
<=> ! [X94] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
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(f3951,plain,
spl0_166,
inference(avatar_split_clause,[],[f1899,f3949]) ).
fof(f3949,plain,
( spl0_166
<=> ! [X94] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
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(f3947,plain,
spl0_165,
inference(avatar_split_clause,[],[f1891,f3945]) ).
fof(f3945,plain,
( spl0_165
<=> ! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
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(f3943,plain,
spl0_164,
inference(avatar_split_clause,[],[f1890,f3941]) ).
fof(f3941,plain,
( spl0_164
<=> ! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
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(f3939,plain,
spl0_163,
inference(avatar_split_clause,[],[f1885,f3937]) ).
fof(f3937,plain,
( spl0_163
<=> ! [X94] :
( ~ class_OrderedGroup_Oab__group__add(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
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(f3935,plain,
spl0_162,
inference(avatar_split_clause,[],[f1883,f3933]) ).
fof(f3933,plain,
( spl0_162
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocomm__monoid__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
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(f3931,plain,
spl0_161,
inference(avatar_split_clause,[],[f1881,f3929]) ).
fof(f3929,plain,
( spl0_161
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
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(f3927,plain,
spl0_160,
inference(avatar_split_clause,[],[f1880,f3925]) ).
fof(f3925,plain,
( spl0_160
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
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(f3923,plain,
spl0_159,
inference(avatar_split_clause,[],[f1877,f3921]) ).
fof(f3921,plain,
( spl0_159
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Numeral_Onumber(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
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(f3919,plain,
spl0_158,
inference(avatar_split_clause,[],[f1875,f3917]) ).
fof(f3917,plain,
( spl0_158
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__ring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
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(f3915,plain,
spl0_157,
inference(avatar_split_clause,[],[f1874,f3913]) ).
fof(f3913,plain,
( spl0_157
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
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(f3911,plain,
spl0_156,
inference(avatar_split_clause,[],[f1873,f3909]) ).
fof(f3909,plain,
( spl0_156
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
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(f3907,plain,
spl0_155,
inference(avatar_split_clause,[],[f1872,f3905]) ).
fof(f3905,plain,
( spl0_155
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__1__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
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(f3903,plain,
spl0_154,
inference(avatar_split_clause,[],[f1871,f3901]) ).
fof(f3901,plain,
( spl0_154
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
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(f3899,plain,
spl0_153,
inference(avatar_split_clause,[],[f1870,f3897]) ).
fof(f3897,plain,
( spl0_153
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
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(f3895,plain,
spl0_152,
inference(avatar_split_clause,[],[f1869,f3893]) ).
fof(f3893,plain,
( spl0_152
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocomm__monoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
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(f3891,plain,
spl0_151,
inference(avatar_split_clause,[],[f1868,f3889]) ).
fof(f3889,plain,
( spl0_151
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Omonoid__mult(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
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(f3887,plain,
spl0_150,
inference(avatar_split_clause,[],[f1867,f3885]) ).
fof(f3885,plain,
( spl0_150
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oaxclass__0__neq__1(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
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(f3883,plain,
spl0_149,
inference(avatar_split_clause,[],[f1866,f3881]) ).
fof(f3881,plain,
( spl0_149
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_HOL_Oone(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
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(f3879,plain,
spl0_148,
inference(avatar_split_clause,[],[f1864,f3877]) ).
fof(f3877,plain,
( spl0_148
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__ring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
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(f3875,plain,
spl0_147,
inference(avatar_split_clause,[],[f1863,f3873]) ).
fof(f3873,plain,
( spl0_147
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
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(f3871,plain,
spl0_146,
inference(avatar_split_clause,[],[f1862,f3869]) ).
fof(f3869,plain,
( spl0_146
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Oring(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
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(f3867,plain,
spl0_145,
inference(avatar_split_clause,[],[f1861,f3865]) ).
fof(f3865,plain,
( spl0_145
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__0__cancel(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
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(f3863,plain,
spl0_144,
inference(avatar_split_clause,[],[f1860,f3861]) ).
fof(f3861,plain,
( spl0_144
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Oab__group__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
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(f3859,plain,
spl0_143,
inference(avatar_split_clause,[],[f1859,f3857]) ).
fof(f3857,plain,
( spl0_143
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
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(f3855,plain,
spl0_142,
inference(avatar_split_clause,[],[f1858,f3853]) ).
fof(f3853,plain,
( spl0_142
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_OrderedGroup_Ocancel__semigroup__add(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
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(f3851,plain,
spl0_141,
inference(avatar_split_clause,[],[f1856,f3849]) ).
fof(f3849,plain,
( spl0_141
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Ocomm__semiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
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(f3847,plain,
spl0_140,
inference(avatar_split_clause,[],[f1855,f3845]) ).
fof(f3845,plain,
( spl0_140
<=> ! [X94] :
( ~ class_Numeral_Onumber__ring(X94)
| class_Ring__and__Field_Osemiring__0(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
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(f3843,plain,
spl0_139,
inference(avatar_split_clause,[],[f1852,f3841]) ).
fof(f3841,plain,
( spl0_139
<=> ! [X94] :
( ~ class_LOrder_Omeet__semilorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
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(f3839,plain,
spl0_138,
inference(avatar_split_clause,[],[f1851,f3837]) ).
fof(f3837,plain,
( spl0_138
<=> ! [X94] :
( ~ class_LOrder_Omeet__semilorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
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(f3835,plain,
spl0_137,
inference(avatar_split_clause,[],[f1850,f3833]) ).
fof(f3833,plain,
( spl0_137
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_LOrder_Ojoin__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
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(f3831,plain,
spl0_136,
inference(avatar_split_clause,[],[f1849,f3829]) ).
fof(f3829,plain,
( spl0_136
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1849,axiom,
! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oorder(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3827,plain,
spl0_135,
inference(avatar_split_clause,[],[f1848,f3825]) ).
fof(f3825,plain,
( spl0_135
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1848,axiom,
! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_Orderings_Oord(X94) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3823,plain,
spl0_134,
inference(avatar_split_clause,[],[f1847,f3821]) ).
fof(f3821,plain,
( spl0_134
<=> ! [X94] :
( ~ class_LOrder_Olorder(X94)
| class_LOrder_Omeet__semilorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
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(f3819,plain,
spl0_133,
inference(avatar_split_clause,[],[f1846,f3817]) ).
fof(f3817,plain,
( spl0_133
<=> ! [X94] :
( ~ class_LOrder_Ojoin__semilorder(X94)
| class_Orderings_Oorder(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
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(f3815,plain,
spl0_132,
inference(avatar_split_clause,[],[f1845,f3813]) ).
fof(f3813,plain,
( spl0_132
<=> ! [X94] :
( ~ class_LOrder_Ojoin__semilorder(X94)
| class_Orderings_Oord(X94) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
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(f3811,plain,
spl0_131,
inference(avatar_split_clause,[],[f1690,f3809]) ).
fof(f1690,axiom,
! [X4,X5] : c_in(X4,c_UNIV,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3807,plain,
spl0_130,
inference(avatar_split_clause,[],[f1658,f3805]) ).
fof(f3805,plain,
( spl0_130
<=> ! [X19] : ~ c_less(X19,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1658,axiom,
! [X19] : ~ c_less(X19,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3803,plain,
spl0_129,
inference(avatar_split_clause,[],[f1656,f3801]) ).
fof(f3801,plain,
( spl0_129
<=> ! [X19] : c_lessequals(c_0,X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1656,axiom,
! [X19] : c_lessequals(c_0,X19,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3799,plain,
spl0_128,
inference(avatar_split_clause,[],[f1632,f3797]) ).
fof(f3797,plain,
( spl0_128
<=> ! [X30] : c_Divides_Oop_Advd(c_1,X30,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
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(f3795,plain,
spl0_127,
inference(avatar_split_clause,[],[f1631,f3793]) ).
fof(f3793,plain,
( spl0_127
<=> ! [X30] : c_Divides_Oop_Advd(X30,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
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(f3791,plain,
spl0_126,
inference(avatar_split_clause,[],[f1615,f3789]) ).
fof(f3789,plain,
( spl0_126
<=> ! [X30] : c_Divides_Oop_Advd(X30,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
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(f3787,plain,
spl0_125,
inference(avatar_split_clause,[],[f1537,f3785]) ).
fof(f3785,plain,
( spl0_125
<=> ! [X5,X31] : ~ c_in(X31,c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1537,axiom,
! [X31,X5] : ~ c_in(X31,c_emptyset,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3783,plain,
spl0_124,
inference(avatar_split_clause,[],[f1020,f3780]) ).
fof(f3780,plain,
( spl0_124
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
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(f3778,plain,
spl0_123,
inference(avatar_split_clause,[],[f956,f3776]) ).
fof(f3776,plain,
( spl0_123
<=> ! [X19] : ~ c_less(X19,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f956,axiom,
! [X19] : ~ c_less(X19,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3774,plain,
spl0_122,
inference(avatar_split_clause,[],[f914,f3771]) ).
fof(f3771,plain,
( spl0_122
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f914,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3769,plain,
spl0_121,
inference(avatar_split_clause,[],[f574,f3767]) ).
fof(f3767,plain,
( spl0_121
<=> ! [X4,X21] : ~ c_List_Oop_Amem(X4,c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
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(f3765,plain,
spl0_120,
inference(avatar_split_clause,[],[f347,f3763]) ).
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(f3761,plain,
spl0_119,
inference(avatar_split_clause,[],[f258,f3759]) ).
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(f3757,plain,
spl0_118,
inference(avatar_split_clause,[],[f251,f3754]) ).
fof(f3754,plain,
( spl0_118
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f251,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3752,plain,
spl0_117,
inference(avatar_split_clause,[],[f239,f3749]) ).
fof(f3747,plain,
spl0_116,
inference(avatar_split_clause,[],[f236,f3744]) ).
fof(f236,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3742,plain,
spl0_115,
inference(avatar_split_clause,[],[f94,f3740]) ).
fof(f3740,plain,
( spl0_115
<=> ! [X30] : c_Divides_Oop_Advd(X30,X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
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(f3738,plain,
spl0_114,
inference(avatar_split_clause,[],[f1841,f3736]) ).
fof(f1841,axiom,
! [X92] : class_Orderings_Oorder(tc_set(X92)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3734,plain,
spl0_113,
inference(avatar_split_clause,[],[f1840,f3732]) ).
fof(f3732,plain,
( spl0_113
<=> ! [X92] : class_Orderings_Oord(tc_set(X92)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1840,axiom,
! [X92] : class_Orderings_Oord(tc_set(X92)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3730,plain,
spl0_112,
inference(avatar_split_clause,[],[f1718,f3727]) ).
fof(f3727,plain,
( spl0_112
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
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(f3725,plain,
spl0_111,
inference(avatar_split_clause,[],[f1716,f3722]) ).
fof(f3722,plain,
( spl0_111
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
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(f3720,plain,
spl0_110,
inference(avatar_split_clause,[],[f1715,f3718]) ).
fof(f3718,plain,
( spl0_110
<=> ! [X5] : c_Wellfounded__Recursion_Owf(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
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(f3716,plain,
~ spl0_109,
inference(avatar_split_clause,[],[f1494,f3713]) ).
fof(f3713,plain,
( spl0_109
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1494,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3711,plain,
~ spl0_108,
inference(avatar_split_clause,[],[f1175,f3708]) ).
fof(f3708,plain,
( spl0_108
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1175,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3706,plain,
spl0_107,
inference(avatar_split_clause,[],[f1168,f3703]) ).
fof(f3703,plain,
( spl0_107
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1168,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3701,plain,
spl0_106,
inference(avatar_split_clause,[],[f1155,f3698]) ).
fof(f3698,plain,
( spl0_106
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1155,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3696,plain,
~ spl0_105,
inference(avatar_split_clause,[],[f1024,f3693]) ).
fof(f3693,plain,
( spl0_105
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1024,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3691,plain,
spl0_104,
inference(avatar_split_clause,[],[f571,f3689]) ).
fof(f3689,plain,
( spl0_104
<=> ! [X21] : c_List_Onull(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
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(f3687,plain,
spl0_103,
inference(avatar_split_clause,[],[f416,f3685]) ).
fof(f3685,plain,
( spl0_103
<=> ! [X21] : c_List_Odistinct(c_List_Olist_ONil,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
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(f3683,plain,
~ spl0_102,
inference(avatar_split_clause,[],[f235,f3680]) ).
fof(f3680,plain,
( spl0_102
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f235,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3678,plain,
~ spl0_101,
inference(avatar_split_clause,[],[f115,f3675]) ).
fof(f3675,plain,
( spl0_101
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f115,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3673,plain,
~ spl0_100,
inference(avatar_split_clause,[],[f2759,f3670]) ).
fof(f2759,axiom,
~ c_in(c_Pair(v_x,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
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,[],[f2756,f3195]) ).
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(f3193,plain,
spl0_4,
inference(avatar_split_clause,[],[f2758,f3190]) ).
fof(f2758,axiom,
c_in(v_x,v_S,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
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
% 0.06/0.11 % Problem : LAT272-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n021.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 12:35:28 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (19894)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.43 % (19897)WARNING: value z3 for option sas not known
% 0.18/0.44 % (19897)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.18/0.44 % (19896)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.44 % (19899)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)
% 0.18/0.44 % (19898)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.44 % (19895)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.44 % (19901)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)
% 0.18/0.44 % (19900)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)
% 1.92/0.71 TRYING [1]
% 5.21/1.19 TRYING [2]
% 8.07/1.56 TRYING [1]
% 8.07/1.61 % (19899)First to succeed.
% 8.90/1.71 % (19899)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19894"
% 8.90/1.72 % (19899)Refutation found. Thanks to Tanya!
% 8.90/1.72 % SZS status Unsatisfiable for theBenchmark
% 8.90/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 9.29/1.78 % (19899)------------------------------
% 9.29/1.78 % (19899)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 9.29/1.78 % (19899)Termination reason: Refutation
% 9.29/1.78
% 9.29/1.78 % (19899)Memory used [KB]: 18456
% 9.29/1.78 % (19899)Time elapsed: 1.277 s
% 9.29/1.78 % (19899)Instructions burned: 2271 (million)
% 9.29/1.78 % (19894)Success in time 1.433 s
%------------------------------------------------------------------------------