%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV353-1 : 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 : n007.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 : Tue Apr 30 16:45:42 EDT 2024

% Result   : Unsatisfiable 7.19s 1.49s
% Output   : Refutation 7.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      : 4840
% Syntax   : Number of formulae    : 8688 (3073 unt;   0 def)
%            Number of atoms       : 19366 (3578 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives : 18521 (7843   ~;8079   |;   0   &)
%                                         (2599 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Maximal term depth    :   10 (   1 avg)
%            Number of predicates  : 2670 (2668 usr;2600 prp; 0-3 aty)
%            Number of functors    :  281 ( 281 usr;  65 con; 0-18 aty)
%            Number of variables   : 12880 (12880   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f34315,plain,
    $false,
    inference(avatar_sat_refutation,[],[f3437,f3442,f3447,f3452,f3457,f3462,f3467,f3472,f3477,f3482,f3487,f3492,f3497,f3502,f3507,f3512,f3517,f3522,f3527,f3532,f3537,f3542,f3547,f3552,f3557,f3562,f3567,f3572,f3577,f3582,f3587,f3592,f3597,f3602,f3607,f3612,f3617,f3622,f3627,f3632,f3637,f3642,f3647,f3652,f3657,f3662,f3667,f3672,f3677,f3682,f3687,f3692,f3697,f3702,f3707,f3712,f3717,f3722,f3727,f3732,f3737,f3742,f3747,f3752,f3757,f3762,f3767,f3772,f3777,f3782,f3787,f3792,f3797,f3802,f3807,f3812,f3817,f3822,f3827,f3832,f3837,f3842,f3847,f3852,f3857,f3862,f3867,f3872,f3877,f3882,f3887,f3892,f3897,f3902,f3907,f3912,f3917,f3921,f3926,f3931,f3935,f3939,f3944,f3949,f3953,f3957,f3962,f3967,f3972,f3977,f3982,f3987,f3992,f3996,f4000,f4004,f4008,f4012,f4016,f4020,f4024,f4028,f4032,f4036,f4040,f4044,f4048,f4052,f4056,f4060,f4064,f4068,f4072,f4076,f4080,f4084,f4088,f4092,f4096,f4100,f4104,f4108,f4112,f4116,f4120,f4124,f4128,f4132,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4212,f4216,f4220,f4224,f4228,f4232,f4236,f4240,f4244,f4248,f4252,f4256,f4260,f4264,f4268,f4272,f4276,f4280,f4284,f4288,f4292,f4296,f4300,f4304,f4308,f4312,f4316,f4320,f4324,f4328,f4332,f4336,f4340,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4372,f4376,f4380,f4384,f4388,f4392,f4396,f4400,f4404,f4408,f4412,f4416,f4420,f4424,f4428,f4432,f4436,f4440,f4444,f4448,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4524,f4528,f4532,f4536,f4540,f4544,f4548,f4552,f4556,f4560,f4564,f4568,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4600,f4604,f4608,f4612,f4616,f4620,f4624,f4628,f4632,f4636,f4640,f4644,f4648,f4652,f4656,f4660,f4664,f4668,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4700,f4704,f4708,f4712,f4716,f4720,f4724,f4728,f4732,f4736,f4740,f4744,f4748,f4752,f4756,f4760,f4764,f4768,f4772,f4776,f4780,f4784,f4788,f4792,f4796,f4800,f4804,f4808,f4812,f4816,f4820,f4824,f4828,f4832,f4836,f4840,f4844,f4848,f4852,f4856,f4860,f4864,f4868,f4872,f4876,f4880,f4884,f4888,f4892,f4896,f4900,f4904,f4908,f4912,f4916,f4920,f4924,f4928,f4932,f4936,f4940,f4944,f4948,f4952,f4956,f4960,f4964,f4968,f4972,f4976,f4980,f4984,f4988,f4992,f4996,f5000,f5004,f5008,f5012,f5016,f5020,f5024,f5028,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5092,f5096,f5100,f5104,f5108,f5112,f5116,f5120,f5124,f5128,f5132,f5136,f5140,f5144,f5148,f5152,f5156,f5160,f5164,f5168,f5172,f5176,f5180,f5184,f5188,f5192,f5196,f5200,f5204,f5208,f5212,f5216,f5220,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5252,f5256,f5260,f5264,f5268,f5272,f5276,f5280,f5284,f5288,f5292,f5296,f5300,f5304,f5308,f5312,f5316,f5320,f5324,f5328,f5332,f5336,f5340,f5344,f5348,f5352,f5356,f5360,f5364,f5368,f5372,f5376,f5380,f5384,f5388,f5392,f5396,f5400,f5404,f5408,f5412,f5416,f5420,f5424,f5428,f5432,f5436,f5440,f5444,f5448,f5452,f5456,f5460,f5464,f5468,f5472,f5476,f5480,f5484,f5488,f5492,f5496,f5500,f5504,f5508,f5512,f5516,f5520,f5524,f5528,f5532,f5536,f5540,f5544,f5548,f5552,f5556,f5560,f5564,f5568,f5572,f5576,f5580,f5584,f5588,f5592,f5596,f5600,f5604,f5608,f5612,f5616,f5620,f5624,f5628,f5632,f5636,f5640,f5644,f5648,f5652,f5656,f5660,f5664,f5668,f5672,f5676,f5680,f5684,f5688,f5692,f5696,f5700,f5704,f5708,f5712,f5716,f5720,f5724,f5728,f5732,f5736,f5740,f5744,f5748,f5752,f5756,f5760,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5792,f5796,f5800,f5804,f5808,f5812,f5816,f5820,f5824,f5828,f5832,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5872,f5876,f5880,f5884,f5888,f5892,f5896,f5900,f5904,f5908,f5912,f5916,f5920,f5924,f5928,f5932,f5936,f5940,f5944,f5948,f5952,f5956,f5960,f5964,f5968,f5972,f5976,f5980,f5984,f5988,f5992,f5996,f6000,f6004,f6008,f6012,f6016,f6020,f6024,f6028,f6032,f6036,f6040,f6044,f6048,f6052,f6056,f6060,f6064,f6068,f6072,f6076,f6080,f6084,f6088,f6092,f6096,f6100,f6104,f6108,f6112,f6116,f6120,f6125,f6130,f6135,f6139,f6143,f6147,f6152,f6156,f6161,f6165,f6169,f6173,f6178,f6183,f6188,f6193,f6198,f6203,f6207,f6212,f6217,f6984,f6989,f6993,f6997,f7001,f7005,f7009,f7013,f7017,f7021,f7025,f7029,f7034,f7039,f7044,f7048,f7052,f7056,f7061,f7065,f7069,f7073,f7077,f7081,f7085,f7089,f7093,f7098,f7103,f7108,f7113,f7118,f7123,f7128,f7133,f7138,f7143,f7148,f7153,f7158,f7163,f7168,f7173,f7177,f7181,f7185,f7189,f7193,f7198,f7203,f7208,f7212,f7216,f7220,f7224,f7228,f7232,f7237,f7242,f7246,f7251,f7256,f7260,f7264,f7268,f7272,f7276,f7280,f7284,f7288,f7293,f7298,f7302,f7307,f7312,f7316,f7321,f7325,f7330,f7337,f7346,f7353,f7358,f7363,f7367,f7371,f7375,f7379,f7383,f7387,f7391,f7395,f7399,f7403,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,f7557,f7561,f7565,f7569,f7573,f7577,f7581,f7585,f7589,f7593,f7597,f7601,f7605,f7609,f7613,f7617,f7621,f7625,f7629,f7633,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7673,f7677,f7681,f7685,f7689,f7693,f7698,f7702,f7707,f7711,f7716,f7720,f7734,f7738,f7742,f7746,f7750,f7754,f7758,f7762,f7766,f7770,f7774,f7778,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f7834,f7838,f7842,f7846,f7850,f7854,f7858,f7862,f7866,f7870,f7874,f7878,f7882,f7886,f7890,f7894,f7898,f7902,f7906,f7910,f7914,f7918,f7922,f7926,f7930,f7934,f7938,f7942,f7946,f7950,f7954,f7958,f7962,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8015,f8019,f8024,f8028,f8032,f8036,f8064,f8098,f8109,f8116,f8121,f8130,f8134,f8138,f8142,f8147,f8151,f8155,f8159,f8163,f8167,f8171,f8175,f8179,f8183,f8188,f8193,f8197,f8201,f8205,f8209,f8213,f8217,f8221,f8225,f8229,f8233,f8242,f8246,f8250,f8254,f8258,f8262,f8266,f8270,f8274,f8278,f8282,f8286,f8290,f8294,f8298,f8302,f8306,f8310,f8314,f8318,f8322,f8326,f8330,f8334,f8338,f8342,f8346,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8382,f8386,f8390,f8394,f8398,f8402,f8407,f8411,f8415,f8419,f8423,f8427,f8431,f8435,f8439,f8444,f8448,f8453,f8457,f8461,f8465,f8469,f8473,f8477,f8481,f8485,f8489,f8493,f8498,f8502,f8506,f8510,f8514,f8518,f8522,f8526,f8530,f8534,f8538,f8543,f8547,f8672,f8684,f8688,f8692,f8697,f8701,f8705,f8709,f8713,f8717,f8721,f8725,f8729,f8733,f8737,f8741,f8745,f8749,f8753,f8757,f8761,f8765,f8769,f8773,f8777,f8782,f8786,f8790,f8794,f8798,f8802,f8806,f8810,f8814,f8818,f8822,f8826,f8830,f8834,f8838,f8842,f8846,f8850,f8854,f8858,f8862,f8866,f8870,f8874,f8878,f8882,f8886,f8890,f8894,f8898,f8902,f8906,f8910,f8914,f8918,f8922,f8926,f8930,f8934,f8938,f8942,f8946,f8950,f8954,f8958,f8962,f8966,f8970,f8974,f8978,f8982,f8986,f8990,f8994,f8998,f9002,f9006,f9010,f9014,f9018,f9022,f9026,f9030,f9034,f9038,f9042,f9046,f9050,f9054,f9058,f9062,f9066,f9070,f9074,f9078,f9082,f9086,f9090,f9094,f9118,f9175,f9203,f9221,f9269,f9295,f9308,f9343,f9347,f9351,f9355,f9359,f9363,f9367,f9371,f9375,f9379,f9383,f9387,f9391,f9396,f9400,f9404,f9408,f9412,f9416,f9420,f9424,f9428,f9432,f9436,f9440,f9444,f9448,f9452,f9456,f9460,f9464,f9468,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9501,f9505,f9509,f9513,f9517,f9521,f9525,f9529,f9533,f9537,f9541,f9545,f9549,f9553,f9557,f9561,f9565,f9569,f9573,f9577,f9581,f9585,f9589,f9593,f9597,f9601,f9605,f9609,f9613,f9617,f9621,f9625,f9629,f9633,f9637,f9641,f9645,f9649,f9653,f9657,f9661,f9665,f9669,f9673,f9677,f9681,f9685,f9689,f9694,f9698,f9702,f9706,f9711,f9718,f9722,f9726,f9730,f9734,f9738,f9743,f9747,f9800,f9856,f9881,f9921,f9947,f9955,f9985,f10004,f10008,f10012,f10016,f10020,f10024,f10028,f10032,f10037,f10041,f10045,f10049,f10053,f10057,f10061,f10065,f10069,f10073,f10077,f10081,f10085,f10089,f10093,f10097,f10101,f10105,f10109,f10113,f10117,f10121,f10125,f10129,f10133,f10138,f10142,f10146,f10150,f10154,f10158,f10162,f10166,f10170,f10174,f10178,f10183,f10187,f10191,f10195,f10199,f10203,f10207,f10211,f10215,f10219,f10223,f10232,f10236,f10240,f10244,f10248,f10252,f10256,f10260,f10264,f10268,f10278,f10282,f10286,f10290,f10294,f10298,f10302,f10306,f10311,f10325,f10329,f10333,f10337,f10341,f10345,f10349,f10383,f10536,f10659,f10747,f10751,f10755,f10759,f10763,f10767,f10771,f10775,f10779,f10783,f10787,f10791,f10795,f10799,f10803,f10807,f10811,f10815,f10823,f10827,f10831,f10835,f10839,f10843,f10847,f10851,f10855,f10859,f10863,f10867,f10872,f10877,f10881,f10885,f10889,f10893,f10897,f10901,f10906,f10910,f10914,f10918,f10922,f10926,f10930,f10934,f10938,f10942,f10946,f10954,f10958,f10962,f10966,f10970,f10974,f10978,f10982,f10986,f10990,f10995,f10999,f11003,f11007,f11011,f11015,f11019,f11023,f11027,f11031,f11038,f11042,f11046,f11050,f11054,f11058,f11062,f11066,f11070,f11074,f11084,f11088,f11092,f11096,f11100,f11104,f11108,f11112,f11116,f11120,f11137,f11141,f11145,f11149,f11153,f11157,f11161,f11165,f11169,f11173,f11183,f11187,f11191,f11195,f11199,f11203,f11207,f11211,f11215,f11219,f11236,f11240,f11244,f11248,f11252,f11256,f11260,f11264,f11268,f11272,f11276,f11280,f11284,f11288,f11292,f11296,f11300,f11304,f11308,f11312,f11316,f11320,f11324,f11328,f11332,f11336,f11340,f11344,f11348,f11352,f11356,f11360,f11424,f11612,f11822,f11919,f12380,f12384,f12388,f12392,f12396,f12411,f12415,f12419,f12423,f12427,f12431,f12435,f12439,f12443,f12447,f12452,f12456,f12460,f12464,f12468,f12472,f12476,f12480,f12484,f12488,f12492,f12502,f12506,f12510,f12514,f12518,f12522,f12526,f12530,f12534,f12538,f12547,f12551,f12555,f12559,f12563,f12567,f12571,f12575,f12579,f12583,f12591,f12595,f12599,f12603,f12607,f12611,f12615,f12619,f12623,f12627,f12636,f12640,f12644,f12648,f12652,f12656,f12660,f12664,f12668,f12672,f12680,f12684,f12688,f12692,f12696,f12700,f12704,f12708,f12712,f12716,f12720,f12724,f12728,f12732,f12736,f12740,f12744,f12748,f12752,f12756,f12760,f12767,f12771,f12775,f12779,f12783,f12787,f12791,f12795,f12799,f12803,f12811,f12815,f12819,f12823,f12827,f12831,f12835,f12839,f12843,f12847,f12851,f12856,f12863,f12867,f12871,f12875,f12880,f12888,f12892,f12903,f12934,f12938,f12942,f12946,f12950,f12954,f12958,f13165,f13297,f13599,f13800,f13902,f14044,f14166,f14261,f14265,f14269,f14273,f14277,f14281,f14285,f14289,f14293,f14297,f14301,f14305,f14309,f14313,f14317,f14321,f14325,f14329,f14333,f14337,f14341,f14345,f14349,f14353,f14357,f14361,f14365,f14369,f14373,f14377,f14381,f14385,f14389,f14393,f14397,f14401,f14405,f14409,f14413,f14417,f14421,f14425,f14429,f14433,f14437,f14441,f14445,f14449,f14453,f14457,f14461,f14465,f14469,f14473,f14477,f14481,f14485,f14489,f14493,f14498,f14502,f14506,f14510,f14514,f14518,f14522,f14526,f14530,f14534,f14538,f14542,f14546,f14550,f14554,f14558,f14562,f14566,f14570,f14574,f14578,f14582,f14609,f14618,f14622,f14626,f14630,f15540,f15619,f15672,f15676,f15680,f15684,f15688,f15692,f15696,f15700,f15704,f15708,f15712,f15716,f15720,f15724,f15728,f15732,f15736,f15740,f15744,f15748,f15752,f15756,f15760,f15764,f15768,f15772,f15776,f15780,f15784,f15788,f15792,f15796,f15800,f15804,f15808,f15812,f15816,f15820,f15824,f15828,f15832,f15836,f15840,f15844,f15848,f15852,f15856,f15860,f15864,f15868,f15872,f15876,f15880,f15884,f15888,f15892,f15896,f15900,f15904,f15908,f15916,f15920,f15924,f15928,f15933,f15957,f15962,f15980,f15985,f16005,f16009,f16013,f16017,f16021,f16025,f16029,f16033,f16037,f16042,f16046,f16050,f16142,f16339,f16582,f16848,f17029,f17033,f17037,f17041,f17045,f17049,f17053,f17057,f17061,f17065,f17070,f17074,f17078,f17082,f17086,f17090,f17094,f17098,f17102,f17106,f17110,f17114,f17119,f17123,f17127,f17131,f17135,f17139,f17143,f17147,f17151,f17155,f17159,f17163,f17167,f17171,f17175,f17179,f17183,f17187,f17191,f17195,f17199,f17203,f17207,f17211,f17215,f17219,f17223,f17227,f17231,f17235,f17239,f17296,f17300,f17304,f17308,f17312,f17316,f17320,f17324,f17328,f17332,f17351,f17355,f17360,f17388,f17393,f17451,f17456,f17552,f17556,f17561,f17660,f17665,f17702,f17707,f17725,f17730,f17734,f17742,f17747,f17755,f17759,f17763,f17767,f17773,f17779,f17783,f17789,f17795,f17799,f17803,f17807,f17811,f17817,f17850,f17854,f17868,f18013,f18142,f18325,f18726,f18932,f19130,f19148,f19152,f19156,f19160,f19164,f19168,f19172,f19176,f19180,f19193,f19197,f19201,f19205,f19209,f19213,f19217,f19221,f19225,f19229,f19242,f19246,f19250,f19254,f19258,f19262,f19266,f19270,f19274,f19278,f19295,f19299,f19303,f19307,f19311,f19315,f19319,f19323,f19327,f19331,f19336,f19340,f19344,f19348,f19352,f19356,f19360,f19364,f19368,f19372,f19376,f19391,f19395,f19399,f19403,f19407,f19411,f19417,f19443,f19449,f19454,f19539,f19544,f19569,f19573,f19577,f19582,f19587,f19600,f19605,f19610,f19615,f19619,f19623,f19627,f19632,f19636,f19658,f19662,f19666,f19670,f19675,f19680,f19685,f19691,f19695,f19700,f19706,f19711,f19724,f19728,f19733,f19749,f19753,f19757,f19761,f19765,f19954,f20078,f20333,f20807,f20811,f20815,f20819,f20823,f20827,f20831,f20837,f20841,f20847,f20851,f20855,f20859,f20863,f20867,f20871,f20875,f20879,f20883,f20887,f20891,f20895,f20899,f20903,f20907,f20911,f20915,f20919,f20923,f20940,f20944,f20948,f20952,f20956,f20960,f20964,f20968,f20972,f20976,f20993,f20997,f21001,f21005,f21009,f21013,f21017,f21021,f21027,f21177,f21355,f21359,f21724,f22078,f22219,f22328,f22332,f22336,f22340,f22367,f22372,f22376,f22380,f22385,f22389,f22393,f22397,f22401,f22405,f22432,f22436,f22440,f22444,f22448,f22452,f22456,f22488,f22518,f22553,f22791,f22959,f22963,f22967,f22971,f22975,f22979,f22983,f22987,f22991,f22995,f22999,f23003,f23007,f23011,f23015,f23019,f23023,f23027,f23031,f23035,f23039,f23043,f23059,f23064,f23070,f23091,f23096,f23109,f23113,f23117,f23135,f23156,f23161,f23182,f23186,f23190,f23195,f23212,f23528,f23543,f23644,f23648,f23652,f23669,f23673,f23677,f23681,f23685,f23689,f23693,f23697,f23701,f23705,f23709,f23713,f23717,f23721,f23725,f23729,f23733,f23737,f23741,f23745,f23749,f23760,f23764,f23768,f23772,f23776,f23780,f23784,f23788,f23792,f23796,f23800,f23804,f23808,f23812,f23816,f23820,f23824,f23828,f23832,f23836,f23840,f23844,f23848,f23852,f23856,f23860,f23864,f23868,f23872,f23876,f23880,f23884,f23900,f23904,f23908,f23912,f23916,f23920,f23924,f23931,f23951,f23970,f23993,f23997,f24001,f24005,f24011,f24076,f24080,f24089,f24093,f24097,f24101,f24105,f24109,f24113,f24118,f24145,f24151,f24368,f24536,f24544,f24818,f25166,f25170,f25174,f25178,f25182,f25186,f25190,f25194,f25198,f25202,f25206,f25210,f25214,f25218,f25222,f25226,f25230,f25234,f25238,f25242,f25246,f25258,f25262,f25266,f25270,f25274,f25278,f25282,f25286,f25290,f25294,f25298,f25699,f26022,f26026,f26030,f26034,f26038,f26042,f26046,f26050,f26054,f26058,f26063,f26067,f26071,f26075,f26079,f26083,f26087,f26091,f26095,f26099,f26103,f26125,f26129,f26134,f26159,f26164,f26214,f26218,f26222,f26227,f26231,f26841,f27035,f27039,f27043,f27047,f27051,f27061,f27065,f27070,f27075,f27079,f27083,f27087,f27091,f27095,f27099,f27103,f27107,f27111,f27117,f27123,f27205,f27209,f27213,f27217,f27222,f27246,f27250,f27326,f27331,f27335,f27776,f27822,f27826,f27830,f27865,f27869,f27873,f27877,f27881,f27999,f28064,f28068,f28072,f28076,f28080,f28084,f28088,f28100,f28104,f28108,f28112,f28116,f28120,f28124,f28128,f28146,f28485,f28489,f28493,f28497,f28501,f28506,f28533,f28647,f28651,f28655,f28659,f28663,f28667,f28678,f28682,f28686,f28690,f28694,f28698,f28702,f28706,f28710,f28714,f28719,f28723,f28727,f28731,f28735,f28739,f28743,f28747,f28751,f28755,f28759,f28787,f28795,f28801,f28809,f28815,f28831,f28837,f28841,f28890,f28896,f28909,f28914,f29363,f29641,f29645,f29657,f29661,f29665,f29669,f29673,f29678,f29682,f29762,f29766,f29770,f29774,f29792,f29796,f29800,f30091,f30095,f30099,f30103,f30208,f30212,f30216,f30220,f30238,f30242,f30246,f30252,f30272,f30346,f30408,f30412,f30416,f30420,f30558,f30562,f30566,f30570,f30575,f30580,f30585,f30590,f30613,f30621,f30625,f30629,f30668,f30672,f30677,f30681,f30685,f30689,f30693,f30697,f30846,f30851,f30855,f30883,f30887,f30891,f30899,f30903,f30908,f30913,f30918,f30998,f31003,f31007,f31011,f31015,f31035,f31039,f31043,f31051,f31078,f31113,f31120,f31159,f31163,f31167,f31173,f31198,f31237,f31241,f31287,f31293,f31309,f31313,f31317,f31357,f31361,f31365,f31369,f31373,f31504,f31511,f31555,f31559,f31563,f31567,f31571,f31619,f31623,f31647,f31651,f31655,f31710,f31714,f31718,f31722,f31777,f31798,f31814,f31845,f31849,f31891,f31914,f31928,f31932,f31941,f31954,f31987,f31995,f32000,f32035,f32048,f32053,f32061,f32065,f32069,f32073,f32077,f32082,f32086,f32090,f32094,f32098,f32105,f32110,f32420,f32425,f32429,f32538,f32600,f32611,f32615,f32625,f32635,f32645,f32649,f32661,f32666,f32670,f32674,f32678,f32682,f32686,f32695,f32700,f32705,f32709,f32713,f32717,f32721,f32725,f32729,f32733,f32737,f32753,f32758,f32765,f32775,f32783,f32801,f32805,f32817,f32821,f32825,f32830,f32834,f32838,f32842,f32846,f32850,f32854,f32859,f32863,f32867,f32872,f32877,f32881,f32885,f32889,f32893,f32897,f32901,f32908,f32912,f32916,f32920,f32924,f32928,f32932,f32936,f32940,f32944,f32949,f32953,f32957,f32961,f32965,f32969,f32973,f33016,f33021,f33026,f33030,f33034,f33038,f33105,f33151,f33255,f33624,f34145,f34153,f34159,f34198,f34225,f34229,f34234,f34250,f34259,f34309,f34313,f34314]) ).

fof(f34314,plain,
    ( spl0_1
    | ~ spl0_2485
    | ~ spl0_2594 ),
    inference(avatar_split_clause,[],[f34239,f34227,f31997,f3434]) ).

fof(f3434,plain,
    ( spl0_1
  <=> v_NAa = v_NA ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f31997,plain,
    ( spl0_2485
  <=> c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2485])]) ).

fof(f34227,plain,
    ( spl0_2594
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_NA = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2594])]) ).

fof(f34239,plain,
    ( v_NAa = v_NA
    | ~ spl0_2485
    | ~ spl0_2594 ),
    inference(resolution,[],[f34228,f31999]) ).

fof(f31999,plain,
    ( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ spl0_2485 ),
    inference(avatar_component_clause,[],[f31997]) ).

fof(f34228,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_NA = X4 )
    | ~ spl0_2594 ),
    inference(avatar_component_clause,[],[f34227]) ).

fof(f34313,plain,
    ( spl0_2599
    | ~ spl0_855
    | ~ spl0_1035 ),
    inference(avatar_split_clause,[],[f9130,f8727,f7796,f34311]) ).

fof(f34311,plain,
    ( spl0_2599
  <=> ! [X0] :
        ( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
        | c_0 = c_IntDef_Oint(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2599])]) ).

fof(f7796,plain,
    ( spl0_855
  <=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).

fof(f8727,plain,
    ( spl0_1035
  <=> ! [X48] :
        ( c_0 = X48
        | ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f9130,plain,
    ( ! [X0] :
        ( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
        | c_0 = c_IntDef_Oint(X0) )
    | ~ spl0_855
    | ~ spl0_1035 ),
    inference(superposition,[],[f8728,f7797]) ).

fof(f7797,plain,
    ( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
    | ~ spl0_855 ),
    inference(avatar_component_clause,[],[f7796]) ).

fof(f8728,plain,
    ( ! [X48] :
        ( ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
        | c_0 = X48 )
    | ~ spl0_1035 ),
    inference(avatar_component_clause,[],[f8727]) ).

fof(f34309,plain,
    ( spl0_2598
    | ~ spl0_830
    | ~ spl0_1002 ),
    inference(avatar_split_clause,[],[f8662,f8463,f7683,f34307]) ).

fof(f34307,plain,
    ( spl0_2598
  <=> ! [X0,X1] :
        ( c_Public_OshrK(X0) != c_Message_OinvKey(X1)
        | c_Public_OshrK(X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2598])]) ).

fof(f7683,plain,
    ( spl0_830
  <=> ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f8463,plain,
    ( spl0_1002
  <=> ! [X92,X91] :
        ( X91 = X92
        | c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f8662,plain,
    ( ! [X0,X1] :
        ( c_Public_OshrK(X0) != c_Message_OinvKey(X1)
        | c_Public_OshrK(X0) = X1 )
    | ~ spl0_830
    | ~ spl0_1002 ),
    inference(superposition,[],[f8464,f7684]) ).

fof(f7684,plain,
    ( ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12))
    | ~ spl0_830 ),
    inference(avatar_component_clause,[],[f7683]) ).

fof(f8464,plain,
    ( ! [X91,X92] :
        ( c_Message_OinvKey(X91) != c_Message_OinvKey(X92)
        | X91 = X92 )
    | ~ spl0_1002 ),
    inference(avatar_component_clause,[],[f8463]) ).

fof(f34259,plain,
    ( spl0_2597
    | spl0_5
    | ~ spl0_4
    | ~ spl0_749
    | ~ spl0_2466 ),
    inference(avatar_split_clause,[],[f31694,f31653,f7355,f3449,f3454,f34257]) ).

fof(f34257,plain,
    ( spl0_2597
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_B = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2597])]) ).

fof(f3454,plain,
    ( spl0_5
  <=> c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f3449,plain,
    ( spl0_4
  <=> c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f7355,plain,
    ( spl0_749
  <=> c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f31653,plain,
    ( spl0_2466
  <=> ! [X12,X113,X111,X118,X119,X116,X117,X86,X107,X22,X102,X32,X13] :
        ( X13 = X117
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2466])]) ).

fof(f31694,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_B = X2 )
    | ~ spl0_749
    | ~ spl0_2466 ),
    inference(resolution,[],[f31654,f7357]) ).

fof(f7357,plain,
    ( c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ spl0_749 ),
    inference(avatar_component_clause,[],[f7355]) ).

fof(f31654,plain,
    ( ! [X113,X111,X118,X119,X116,X117,X86,X107,X22,X12,X32,X13,X102] :
        ( ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | X13 = X117 )
    | ~ spl0_2466 ),
    inference(avatar_component_clause,[],[f31653]) ).

fof(f34250,plain,
    ( spl0_2596
    | spl0_5
    | ~ spl0_4
    | ~ spl0_749
    | ~ spl0_2465 ),
    inference(avatar_split_clause,[],[f31681,f31649,f7355,f3449,f3454,f34248]) ).

fof(f34248,plain,
    ( spl0_2596
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_A = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2596])]) ).

fof(f31649,plain,
    ( spl0_2465
  <=> ! [X119,X113,X111,X118,X12,X116,X117,X86,X107,X22,X102,X32,X13] :
        ( X12 = X111
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2465])]) ).

fof(f31681,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_A = X3 )
    | ~ spl0_749
    | ~ spl0_2465 ),
    inference(resolution,[],[f31650,f7357]) ).

fof(f31650,plain,
    ( ! [X113,X111,X118,X119,X116,X117,X86,X107,X22,X12,X32,X13,X102] :
        ( ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | X12 = X111 )
    | ~ spl0_2465 ),
    inference(avatar_component_clause,[],[f31649]) ).

fof(f34234,plain,
    ( spl0_2595
    | ~ spl0_742
    | ~ spl0_2590 ),
    inference(avatar_split_clause,[],[f34160,f34150,f7314,f34231]) ).

fof(f34231,plain,
    ( spl0_2595
  <=> c_in(v_K,c_Message_OsymKeys,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2595])]) ).

fof(f7314,plain,
    ( spl0_742
  <=> ! [X86] : c_in(c_Public_OshrK(X86),c_Message_OsymKeys,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f34150,plain,
    ( spl0_2590
  <=> v_K = c_Public_OshrK(v_sko__2VY(v_K)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2590])]) ).

fof(f34160,plain,
    ( c_in(v_K,c_Message_OsymKeys,tc_nat)
    | ~ spl0_742
    | ~ spl0_2590 ),
    inference(superposition,[],[f7315,f34152]) ).

fof(f34152,plain,
    ( v_K = c_Public_OshrK(v_sko__2VY(v_K))
    | ~ spl0_2590 ),
    inference(avatar_component_clause,[],[f34150]) ).

fof(f7315,plain,
    ( ! [X86] : c_in(c_Public_OshrK(X86),c_Message_OsymKeys,tc_nat)
    | ~ spl0_742 ),
    inference(avatar_component_clause,[],[f7314]) ).

fof(f34229,plain,
    ( spl0_2594
    | spl0_5
    | ~ spl0_4
    | ~ spl0_749
    | ~ spl0_2464 ),
    inference(avatar_split_clause,[],[f31668,f31645,f7355,f3449,f3454,f34227]) ).

fof(f31645,plain,
    ( spl0_2464
  <=> ! [X107,X113,X111,X118,X119,X116,X117,X86,X12,X22,X102,X32,X13] :
        ( X118 = X119
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2464])]) ).

fof(f31668,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_NA = X4 )
    | ~ spl0_749
    | ~ spl0_2464 ),
    inference(resolution,[],[f31646,f7357]) ).

fof(f31646,plain,
    ( ! [X113,X111,X118,X119,X116,X117,X86,X107,X22,X12,X32,X13,X102] :
        ( ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | X118 = X119 )
    | ~ spl0_2464 ),
    inference(avatar_component_clause,[],[f31645]) ).

fof(f34225,plain,
    ( spl0_2593
    | ~ spl0_750
    | ~ spl0_2012 ),
    inference(avatar_split_clause,[],[f22001,f20921,f7360,f34223]) ).

fof(f34223,plain,
    ( spl0_2593
  <=> ! [X0] : c_minus(X0,c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent)) = c_minus(c_insert(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),X0,tc_Event_Oevent),c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2593])]) ).

fof(f7360,plain,
    ( spl0_750
  <=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f20921,plain,
    ( spl0_2012
  <=> ! [X13,X0,X12,X1] :
        ( ~ c_in(X0,X13,X1)
        | c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).

fof(f22001,plain,
    ( ! [X0] : c_minus(X0,c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent)) = c_minus(c_insert(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),X0,tc_Event_Oevent),c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent))
    | ~ spl0_750
    | ~ spl0_2012 ),
    inference(resolution,[],[f20922,f7362]) ).

fof(f7362,plain,
    ( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ spl0_750 ),
    inference(avatar_component_clause,[],[f7360]) ).

fof(f20922,plain,
    ( ! [X0,X1,X12,X13] :
        ( ~ c_in(X0,X13,X1)
        | c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) )
    | ~ spl0_2012 ),
    inference(avatar_component_clause,[],[f20921]) ).

fof(f34198,plain,
    ( spl0_2592
    | ~ spl0_749
    | ~ spl0_2012 ),
    inference(avatar_split_clause,[],[f22000,f20921,f7355,f34196]) ).

fof(f34196,plain,
    ( spl0_2592
  <=> ! [X0] : c_minus(X0,c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent)) = c_minus(c_insert(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),X0,tc_Event_Oevent),c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2592])]) ).

fof(f22000,plain,
    ( ! [X0] : c_minus(X0,c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent)) = c_minus(c_insert(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),X0,tc_Event_Oevent),c_List_Oset(v_evso,tc_Event_Oevent),tc_set(tc_Event_Oevent))
    | ~ spl0_749
    | ~ spl0_2012 ),
    inference(resolution,[],[f20922,f7357]) ).

fof(f34159,plain,
    ( spl0_2591
    | spl0_2590
    | ~ spl0_4
    | ~ spl0_750
    | ~ spl0_2470 ),
    inference(avatar_split_clause,[],[f31761,f31720,f7360,f3449,f34150,f34157]) ).

fof(f34157,plain,
    ( spl0_2591
  <=> ! [X0] :
        ( ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
        | v_NB = X0
        | c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2591])]) ).

fof(f31720,plain,
    ( spl0_2470
  <=> ! [X112,X102,X121,X13,X12,X114,X122,X86] :
        ( X114 = X122
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_Public_OshrK(v_sko__2VY(X121)) = X121
        | ~ c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X121),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X121),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X122))))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2470])]) ).

fof(f31761,plain,
    ( ! [X0] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | v_K = c_Public_OshrK(v_sko__2VY(v_K))
        | ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
        | c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg)
        | v_NB = X0 )
    | ~ spl0_750
    | ~ spl0_2470 ),
    inference(resolution,[],[f31721,f7362]) ).

fof(f31721,plain,
    ( ! [X121,X86,X114,X12,X122,X13,X112,X102] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X121),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X122))))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_Public_OshrK(v_sko__2VY(X121)) = X121
        | ~ c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X121),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)),tc_Message_Omsg)
        | X114 = X122 )
    | ~ spl0_2470 ),
    inference(avatar_component_clause,[],[f31720]) ).

fof(f34153,plain,
    ( spl0_2589
    | spl0_2590
    | ~ spl0_4
    | ~ spl0_750
    | ~ spl0_2468 ),
    inference(avatar_split_clause,[],[f31748,f31712,f7360,f3449,f34150,f34147]) ).

fof(f34147,plain,
    ( spl0_2589
  <=> ! [X0] :
        ( c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
        | v_NB = X0
        | ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2589])]) ).

fof(f31712,plain,
    ( spl0_2468
  <=> ! [X112,X102,X121,X13,X12,X114,X122,X86] :
        ( X114 = X122
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_Public_OshrK(v_sko__2VY(X121)) = X121
        | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X121),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X121),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X122))))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2468])]) ).

fof(f31748,plain,
    ( ! [X0] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | v_K = c_Public_OshrK(v_sko__2VY(v_K))
        | c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg)
        | v_NB = X0 )
    | ~ spl0_750
    | ~ spl0_2468 ),
    inference(resolution,[],[f31713,f7362]) ).

fof(f31713,plain,
    ( ! [X121,X86,X114,X12,X122,X13,X112,X102] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X121),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X122))))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_Public_OshrK(v_sko__2VY(X121)) = X121
        | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X121),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)),tc_Message_Omsg)
        | X114 = X122 )
    | ~ spl0_2468 ),
    inference(avatar_component_clause,[],[f31712]) ).

fof(f34145,plain,
    ( spl0_2588
    | ~ spl0_1468
    | ~ spl0_2548 ),
    inference(avatar_split_clause,[],[f33429,f32844,f11422,f34142]) ).

fof(f34142,plain,
    ( spl0_2588
  <=> c_UNIV = c_IntDef_ONats ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2588])]) ).

fof(f11422,plain,
    ( spl0_1468
  <=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).

fof(f32844,plain,
    ( spl0_2548
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
        | c_UNIV = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2548])]) ).

fof(f33429,plain,
    ( c_UNIV = c_IntDef_ONats
    | ~ spl0_1468
    | ~ spl0_2548 ),
    inference(resolution,[],[f32845,f11423]) ).

fof(f11423,plain,
    ( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
    | ~ spl0_1468 ),
    inference(avatar_component_clause,[],[f11422]) ).

fof(f32845,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
        | c_UNIV = X0 )
    | ~ spl0_2548 ),
    inference(avatar_component_clause,[],[f32844]) ).

fof(f33624,plain,
    ( ~ spl0_2587
    | ~ spl0_1468
    | ~ spl0_1631
    | ~ spl0_1822
    | ~ spl0_2548
    | ~ spl0_2560 ),
    inference(avatar_split_clause,[],[f33619,f32895,f32844,f17197,f14363,f11422,f33621]) ).

fof(f33621,plain,
    ( spl0_2587
  <=> c_emptyset = c_IntDef_ONats ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2587])]) ).

fof(f14363,plain,
    ( spl0_1631
  <=> ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).

fof(f17197,plain,
    ( spl0_1822
  <=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).

fof(f32895,plain,
    ( spl0_2560
  <=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2560])]) ).

fof(f33619,plain,
    ( c_emptyset != c_IntDef_ONats
    | ~ spl0_1468
    | ~ spl0_1631
    | ~ spl0_1822
    | ~ spl0_2548
    | ~ spl0_2560 ),
    inference(forward_demodulation,[],[f33618,f33437]) ).

fof(f33437,plain,
    ( c_IntDef_ONats = c_Message_Oanalz(c_IntDef_ONats)
    | ~ spl0_1468
    | ~ spl0_1631
    | ~ spl0_2548 ),
    inference(forward_demodulation,[],[f33430,f33429]) ).

fof(f33430,plain,
    ( c_UNIV = c_Message_Oanalz(c_UNIV)
    | ~ spl0_1631
    | ~ spl0_2548 ),
    inference(resolution,[],[f32845,f14364]) ).

fof(f14364,plain,
    ( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
    | ~ spl0_1631 ),
    inference(avatar_component_clause,[],[f14363]) ).

fof(f33618,plain,
    ( c_emptyset != c_Message_Oanalz(c_IntDef_ONats)
    | ~ spl0_1468
    | ~ spl0_1822
    | ~ spl0_2548
    | ~ spl0_2560 ),
    inference(forward_demodulation,[],[f33613,f33429]) ).

fof(f33613,plain,
    ( c_emptyset != c_Message_Oanalz(c_UNIV)
    | ~ spl0_1822
    | ~ spl0_2560 ),
    inference(superposition,[],[f32896,f17198]) ).

fof(f17198,plain,
    ( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
    | ~ spl0_1822 ),
    inference(avatar_component_clause,[],[f17197]) ).

fof(f32896,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
    | ~ spl0_2560 ),
    inference(avatar_component_clause,[],[f32895]) ).

fof(f33255,plain,
    ( spl0_2586
    | ~ spl0_1565
    | ~ spl0_2503 ),
    inference(avatar_split_clause,[],[f32456,f32417,f12785,f33252]) ).

fof(f33252,plain,
    ( spl0_2586
  <=> c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)) = c_Message_Oparts(c_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2586])]) ).

fof(f12785,plain,
    ( spl0_1565
  <=> ! [X86,X88] :
        ( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
        | c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).

fof(f32417,plain,
    ( spl0_2503
  <=> c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2503])]) ).

fof(f32456,plain,
    ( c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)) = c_Message_Oparts(c_insert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg))
    | ~ spl0_1565
    | ~ spl0_2503 ),
    inference(resolution,[],[f32419,f12786]) ).

fof(f12786,plain,
    ( ! [X88,X86] :
        ( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
        | c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) )
    | ~ spl0_1565 ),
    inference(avatar_component_clause,[],[f12785]) ).

fof(f32419,plain,
    ( c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_2503 ),
    inference(avatar_component_clause,[],[f32417]) ).

fof(f33151,plain,
    ( spl0_2585
    | ~ spl0_14
    | ~ spl0_1249
    | ~ spl0_1915
    | ~ spl0_2523 ),
    inference(avatar_split_clause,[],[f32701,f32697,f19297,f10035,f3499,f33148]) ).

fof(f33148,plain,
    ( spl0_2585
  <=> c_IntDef_Oneg(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2585])]) ).

fof(f3499,plain,
    ( spl0_14
  <=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f10035,plain,
    ( spl0_1249
  <=> ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).

fof(f19297,plain,
    ( spl0_1915
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).

fof(f32697,plain,
    ( spl0_2523
  <=> c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2523])]) ).

fof(f32701,plain,
    ( c_IntDef_Oneg(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_14
    | ~ spl0_1249
    | ~ spl0_1915
    | ~ spl0_2523 ),
    inference(forward_demodulation,[],[f32699,f20108]) ).

fof(f20108,plain,
    ( ! [X0,X1] : c_uminus(c_plus(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
    | ~ spl0_14
    | ~ spl0_1249
    | ~ spl0_1915 ),
    inference(forward_demodulation,[],[f20107,f10036]) ).

fof(f10036,plain,
    ( ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint)
    | ~ spl0_1249 ),
    inference(avatar_component_clause,[],[f10035]) ).

fof(f20107,plain,
    ( ! [X0,X1] : c_uminus(c_plus(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_uminus(X0,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_14
    | ~ spl0_1915 ),
    inference(resolution,[],[f19298,f3501]) ).

fof(f3501,plain,
    ( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f3499]) ).

fof(f19298,plain,
    ( ! [X1,X18,X27] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) )
    | ~ spl0_1915 ),
    inference(avatar_component_clause,[],[f19297]) ).

fof(f32699,plain,
    ( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_2523 ),
    inference(avatar_component_clause,[],[f32697]) ).

fof(f33105,plain,
    ( ~ spl0_28
    | ~ spl0_55
    | ~ spl0_2578 ),
    inference(avatar_split_clause,[],[f33017,f32971,f3704,f3569]) ).

fof(f3569,plain,
    ( spl0_28
  <=> class_Orderings_Oorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f3704,plain,
    ( spl0_55
  <=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f32971,plain,
    ( spl0_2578
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2578])]) ).

fof(f33017,plain,
    ( ~ class_Orderings_Oorder(tc_IntDef_Oint)
    | ~ spl0_55
    | ~ spl0_2578 ),
    inference(resolution,[],[f32972,f3706]) ).

fof(f3706,plain,
    ( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f3704]) ).

fof(f32972,plain,
    ( ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_2578 ),
    inference(avatar_component_clause,[],[f32971]) ).

fof(f33038,plain,
    ( spl0_2584
    | ~ spl0_655
    | ~ spl0_2228 ),
    inference(avatar_split_clause,[],[f26316,f26028,f6163,f33036]) ).

fof(f33036,plain,
    ( spl0_2584
  <=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2584])]) ).

fof(f6163,plain,
    ( spl0_655
  <=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f26028,plain,
    ( spl0_2228
  <=> ! [X12,X5,X27,X2,X1] :
        ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
        | c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2228])]) ).

fof(f26316,plain,
    ( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3)
    | ~ spl0_655
    | ~ spl0_2228 ),
    inference(resolution,[],[f26029,f6164]) ).

fof(f6164,plain,
    ( ! [X1,X4] : ~ c_in(X4,c_emptyset,X1)
    | ~ spl0_655 ),
    inference(avatar_component_clause,[],[f6163]) ).

fof(f26029,plain,
    ( ! [X2,X1,X27,X5,X12] :
        ( c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1) )
    | ~ spl0_2228 ),
    inference(avatar_component_clause,[],[f26028]) ).

fof(f33034,plain,
    ( spl0_2583
    | ~ spl0_945
    | ~ spl0_1850
    | ~ spl0_1989 ),
    inference(avatar_split_clause,[],[f21351,f20825,f17549,f8231,f33032]) ).

fof(f33032,plain,
    ( spl0_2583
  <=> ! [X0] : c_Divides_Oop_Advd(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2583])]) ).

fof(f8231,plain,
    ( spl0_945
  <=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f17549,plain,
    ( spl0_1850
  <=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).

fof(f20825,plain,
    ( spl0_1989
  <=> ! [X0,X3] :
        ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1989])]) ).

fof(f21351,plain,
    ( ! [X0] : c_Divides_Oop_Advd(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_945
    | ~ spl0_1850
    | ~ spl0_1989 ),
    inference(forward_demodulation,[],[f21348,f17551]) ).

fof(f17551,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
    | ~ spl0_1850 ),
    inference(avatar_component_clause,[],[f17549]) ).

fof(f21348,plain,
    ( ! [X0] : c_Divides_Oop_Advd(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_945
    | ~ spl0_1989 ),
    inference(trivial_inequality_removal,[],[f21345]) ).

fof(f21345,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_Divides_Oop_Advd(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_945
    | ~ spl0_1989 ),
    inference(superposition,[],[f20826,f8232]) ).

fof(f8232,plain,
    ( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_945 ),
    inference(avatar_component_clause,[],[f8231]) ).

fof(f20826,plain,
    ( ! [X3,X0] :
        ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1989 ),
    inference(avatar_component_clause,[],[f20825]) ).

fof(f33030,plain,
    ( spl0_2582
    | ~ spl0_873
    | ~ spl0_1962 ),
    inference(avatar_split_clause,[],[f20664,f19660,f7868,f33028]) ).

fof(f33028,plain,
    ( spl0_2582
  <=> ! [X0,X1] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg),c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2582])]) ).

fof(f7868,plain,
    ( spl0_873
  <=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f19660,plain,
    ( spl0_1962
  <=> ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).

fof(f20664,plain,
    ( ! [X0,X1] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg),c_1,tc_nat)
    | ~ spl0_873
    | ~ spl0_1962 ),
    inference(superposition,[],[f7869,f19661]) ).

fof(f19661,plain,
    ( ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat)
    | ~ spl0_1962 ),
    inference(avatar_component_clause,[],[f19660]) ).

fof(f7869,plain,
    ( ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat)
    | ~ spl0_873 ),
    inference(avatar_component_clause,[],[f7868]) ).

fof(f33026,plain,
    ( spl0_2581
    | ~ spl0_788
    | ~ spl0_1760 ),
    inference(avatar_split_clause,[],[f15964,f15960,f7514,f33024]) ).

fof(f33024,plain,
    ( spl0_2581
  <=> ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2581])]) ).

fof(f7514,plain,
    ( spl0_788
  <=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f15960,plain,
    ( spl0_1760
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).

fof(f15964,plain,
    ( ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat)
    | ~ spl0_788
    | ~ spl0_1760 ),
    inference(superposition,[],[f15961,f7515]) ).

fof(f7515,plain,
    ( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
    | ~ spl0_788 ),
    inference(avatar_component_clause,[],[f7514]) ).

fof(f15961,plain,
    ( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
    | ~ spl0_1760 ),
    inference(avatar_component_clause,[],[f15960]) ).

fof(f33021,plain,
    ( spl0_2580
    | ~ spl0_119
    | ~ spl0_1618 ),
    inference(avatar_split_clause,[],[f14801,f14311,f4014,f33019]) ).

fof(f33019,plain,
    ( spl0_2580
  <=> ! [X0] :
        ( ~ c_less(c_0,X0,tc_IntDef_Oint)
        | ~ c_less(X0,X0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2580])]) ).

fof(f4014,plain,
    ( spl0_119
  <=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f14311,plain,
    ( spl0_1618
  <=> ! [X48,X11] :
        ( ~ c_less(X11,X48,tc_IntDef_Oint)
        | ~ c_less(c_0,X48,tc_IntDef_Oint)
        | c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).

fof(f14801,plain,
    ( ! [X0] :
        ( ~ c_less(c_0,X0,tc_IntDef_Oint)
        | ~ c_less(X0,X0,tc_IntDef_Oint) )
    | ~ spl0_119
    | ~ spl0_1618 ),
    inference(resolution,[],[f14312,f4015]) ).

fof(f4015,plain,
    ( ! [X21] : ~ c_less(X21,X21,tc_nat)
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f4014]) ).

fof(f14312,plain,
    ( ! [X48,X11] :
        ( c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
        | ~ c_less(c_0,X48,tc_IntDef_Oint)
        | ~ c_less(X11,X48,tc_IntDef_Oint) )
    | ~ spl0_1618 ),
    inference(avatar_component_clause,[],[f14311]) ).

fof(f33016,plain,
    ( spl0_2578
    | spl0_2579
    | ~ spl0_799
    | ~ spl0_1617 ),
    inference(avatar_split_clause,[],[f14786,f14307,f7559,f33014,f32971]) ).

fof(f33014,plain,
    ( spl0_2579
  <=> ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2579])]) ).

fof(f7559,plain,
    ( spl0_799
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_less(X0,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f14307,plain,
    ( spl0_1617
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(X11,X48,tc_IntDef_Oint)
        | c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).

fof(f14786,plain,
    ( ! [X0,X1] :
        ( ~ c_less(X0,X0,tc_IntDef_Oint)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_799
    | ~ spl0_1617 ),
    inference(resolution,[],[f14308,f7560]) ).

fof(f7560,plain,
    ( ! [X0,X1] :
        ( ~ c_less(X0,X0,X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_799 ),
    inference(avatar_component_clause,[],[f7559]) ).

fof(f14308,plain,
    ( ! [X48,X11,X1] :
        ( c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1)
        | ~ c_less(X11,X48,tc_IntDef_Oint)
        | ~ class_Ring__and__Field_Oordered__idom(X1) )
    | ~ spl0_1617 ),
    inference(avatar_component_clause,[],[f14307]) ).

fof(f32973,plain,
    ( spl0_2578
    | spl0_2501
    | ~ spl0_751
    | ~ spl0_1614 ),
    inference(avatar_split_clause,[],[f14756,f14295,f7365,f32103,f32971]) ).

fof(f32103,plain,
    ( spl0_2501
  <=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2501])]) ).

fof(f7365,plain,
    ( spl0_751
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X1)
        | c_lessequals(X0,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f14295,plain,
    ( spl0_1614
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(X11,X48,tc_IntDef_Oint)
        | ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).

fof(f14756,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,tc_IntDef_Oint)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_751
    | ~ spl0_1614 ),
    inference(resolution,[],[f14296,f7366]) ).

fof(f7366,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_751 ),
    inference(avatar_component_clause,[],[f7365]) ).

fof(f14296,plain,
    ( ! [X48,X11,X1] :
        ( ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1)
        | c_lessequals(X11,X48,tc_IntDef_Oint)
        | ~ class_Ring__and__Field_Oordered__idom(X1) )
    | ~ spl0_1614 ),
    inference(avatar_component_clause,[],[f14295]) ).

fof(f32969,plain,
    ( spl0_2577
    | ~ spl0_771
    | ~ spl0_1606 ),
    inference(avatar_split_clause,[],[f14661,f14263,f7446,f32967]) ).

fof(f32967,plain,
    ( spl0_2577
  <=> ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2577])]) ).

fof(f7446,plain,
    ( spl0_771
  <=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).

fof(f14263,plain,
    ( spl0_1606
  <=> ! [X17,X15] :
        ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
        | c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).

fof(f14661,plain,
    ( ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0
    | ~ spl0_771
    | ~ spl0_1606 ),
    inference(trivial_inequality_removal,[],[f14646]) ).

fof(f14646,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 )
    | ~ spl0_771
    | ~ spl0_1606 ),
    inference(superposition,[],[f14264,f7447]) ).

fof(f7447,plain,
    ( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint)
    | ~ spl0_771 ),
    inference(avatar_component_clause,[],[f7446]) ).

fof(f14264,plain,
    ( ! [X17,X15] :
        ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
        | c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 )
    | ~ spl0_1606 ),
    inference(avatar_component_clause,[],[f14263]) ).

fof(f32965,plain,
    ( spl0_2576
    | ~ spl0_770
    | ~ spl0_1606 ),
    inference(avatar_split_clause,[],[f14660,f14263,f7442,f32963]) ).

fof(f32963,plain,
    ( spl0_2576
  <=> ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2576])]) ).

fof(f7442,plain,
    ( spl0_770
  <=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f14660,plain,
    ( ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0
    | ~ spl0_770
    | ~ spl0_1606 ),
    inference(trivial_inequality_removal,[],[f14648]) ).

fof(f14648,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0 )
    | ~ spl0_770
    | ~ spl0_1606 ),
    inference(superposition,[],[f14264,f7443]) ).

fof(f7443,plain,
    ( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint)
    | ~ spl0_770 ),
    inference(avatar_component_clause,[],[f7442]) ).

fof(f32961,plain,
    ( spl0_2575
    | ~ spl0_772
    | ~ spl0_1606 ),
    inference(avatar_split_clause,[],[f14658,f14263,f7450,f32959]) ).

fof(f32959,plain,
    ( spl0_2575
  <=> ! [X0] : c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2575])]) ).

fof(f7450,plain,
    ( spl0_772
  <=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f14658,plain,
    ( ! [X0] : c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint)
    | ~ spl0_772
    | ~ spl0_1606 ),
    inference(trivial_inequality_removal,[],[f14650]) ).

fof(f14650,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint) )
    | ~ spl0_772
    | ~ spl0_1606 ),
    inference(superposition,[],[f14264,f7451]) ).

fof(f7451,plain,
    ( ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint)
    | ~ spl0_772 ),
    inference(avatar_component_clause,[],[f7450]) ).

fof(f32957,plain,
    ( spl0_2574
    | ~ spl0_759
    | ~ spl0_1605 ),
    inference(avatar_split_clause,[],[f14644,f14259,f7397,f32955]) ).

fof(f32955,plain,
    ( spl0_2574
  <=> ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2574])]) ).

fof(f7397,plain,
    ( spl0_759
  <=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f14259,plain,
    ( spl0_1605
  <=> ! [X17,X15] :
        ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
        | c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).

fof(f14644,plain,
    ( ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0
    | ~ spl0_759
    | ~ spl0_1605 ),
    inference(trivial_inequality_removal,[],[f14632]) ).

fof(f14632,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 )
    | ~ spl0_759
    | ~ spl0_1605 ),
    inference(superposition,[],[f14260,f7398]) ).

fof(f7398,plain,
    ( ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat)
    | ~ spl0_759 ),
    inference(avatar_component_clause,[],[f7397]) ).

fof(f14260,plain,
    ( ! [X17,X15] :
        ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
        | c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 )
    | ~ spl0_1605 ),
    inference(avatar_component_clause,[],[f14259]) ).

fof(f32953,plain,
    ( spl0_2573
    | ~ spl0_836
    | ~ spl0_1605 ),
    inference(avatar_split_clause,[],[f14643,f14259,f7709,f32951]) ).

fof(f32951,plain,
    ( spl0_2573
  <=> ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2573])]) ).

fof(f7709,plain,
    ( spl0_836
  <=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f14643,plain,
    ( ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0
    | ~ spl0_836
    | ~ spl0_1605 ),
    inference(trivial_inequality_removal,[],[f14633]) ).

fof(f14633,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0 )
    | ~ spl0_836
    | ~ spl0_1605 ),
    inference(superposition,[],[f14260,f7710]) ).

fof(f7710,plain,
    ( ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat)
    | ~ spl0_836 ),
    inference(avatar_component_clause,[],[f7709]) ).

fof(f32949,plain,
    ( spl0_2572
    | ~ spl0_1444
    | ~ spl0_2551 ),
    inference(avatar_split_clause,[],[f32902,f32856,f11266,f32946]) ).

fof(f32946,plain,
    ( spl0_2572
  <=> c_in(c_Message_Omsg_OAgent(v_B),c_Event_Oused(v_evso),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2572])]) ).

fof(f11266,plain,
    ( spl0_1444
  <=> ! [X102,X4] :
        ( c_in(X4,c_Event_Oused(X102),tc_Message_Omsg)
        | ~ c_in(X4,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).

fof(f32856,plain,
    ( spl0_2551
  <=> c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2551])]) ).

fof(f32902,plain,
    ( c_in(c_Message_Omsg_OAgent(v_B),c_Event_Oused(v_evso),tc_Message_Omsg)
    | ~ spl0_1444
    | ~ spl0_2551 ),
    inference(resolution,[],[f32858,f11267]) ).

fof(f11267,plain,
    ( ! [X4,X102] :
        ( ~ c_in(X4,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | c_in(X4,c_Event_Oused(X102),tc_Message_Omsg) )
    | ~ spl0_1444 ),
    inference(avatar_component_clause,[],[f11266]) ).

fof(f32858,plain,
    ( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_2551 ),
    inference(avatar_component_clause,[],[f32856]) ).

fof(f32944,plain,
    ( spl0_2571
    | ~ spl0_758
    | ~ spl0_1605 ),
    inference(avatar_split_clause,[],[f14642,f14259,f7393,f32942]) ).

fof(f32942,plain,
    ( spl0_2571
  <=> ! [X0] : c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2571])]) ).

fof(f7393,plain,
    ( spl0_758
  <=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f14642,plain,
    ( ! [X0] : c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat)
    | ~ spl0_758
    | ~ spl0_1605 ),
    inference(trivial_inequality_removal,[],[f14634]) ).

fof(f14634,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat) )
    | ~ spl0_758
    | ~ spl0_1605 ),
    inference(superposition,[],[f14260,f7394]) ).

fof(f7394,plain,
    ( ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat)
    | ~ spl0_758 ),
    inference(avatar_component_clause,[],[f7393]) ).

fof(f32940,plain,
    ( spl0_2570
    | ~ spl0_812
    | ~ spl0_1584 ),
    inference(avatar_split_clause,[],[f14177,f12865,f7611,f32938]) ).

fof(f32938,plain,
    ( spl0_2570
  <=> ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2570])]) ).

fof(f7611,plain,
    ( spl0_812
  <=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f12865,plain,
    ( spl0_1584
  <=> ! [X85,X1] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).

fof(f14177,plain,
    ( ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
    | ~ spl0_812
    | ~ spl0_1584 ),
    inference(superposition,[],[f12866,f7612]) ).

fof(f7612,plain,
    ( ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1)
    | ~ spl0_812 ),
    inference(avatar_component_clause,[],[f7611]) ).

fof(f12866,plain,
    ( ! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1)
    | ~ spl0_1584 ),
    inference(avatar_component_clause,[],[f12865]) ).

fof(f32936,plain,
    ( spl0_2569
    | ~ spl0_812
    | ~ spl0_1583 ),
    inference(avatar_split_clause,[],[f14169,f12861,f7611,f32934]) ).

fof(f32934,plain,
    ( spl0_2569
  <=> ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2569])]) ).

fof(f12861,plain,
    ( spl0_1583
  <=> ! [X85,X1] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).

fof(f14169,plain,
    ( ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
    | ~ spl0_812
    | ~ spl0_1583 ),
    inference(superposition,[],[f12862,f7612]) ).

fof(f12862,plain,
    ( ! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1)
    | ~ spl0_1583 ),
    inference(avatar_component_clause,[],[f12861]) ).

fof(f32932,plain,
    ( spl0_2568
    | ~ spl0_817
    | ~ spl0_1572 ),
    inference(avatar_split_clause,[],[f14117,f12813,f7631,f32930]) ).

fof(f32930,plain,
    ( spl0_2568
  <=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2568])]) ).

fof(f7631,plain,
    ( spl0_817
  <=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f12813,plain,
    ( spl0_1572
  <=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).

fof(f14117,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1572 ),
    inference(superposition,[],[f7632,f12814]) ).

fof(f12814,plain,
    ( ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg)
    | ~ spl0_1572 ),
    inference(avatar_component_clause,[],[f12813]) ).

fof(f7632,plain,
    ( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
    | ~ spl0_817 ),
    inference(avatar_component_clause,[],[f7631]) ).

fof(f32928,plain,
    ( spl0_2567
    | ~ spl0_817
    | ~ spl0_1569 ),
    inference(avatar_split_clause,[],[f14100,f12801,f7631,f32926]) ).

fof(f32926,plain,
    ( spl0_2567
  <=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2567])]) ).

fof(f12801,plain,
    ( spl0_1569
  <=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).

fof(f14100,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1569 ),
    inference(superposition,[],[f7632,f12802]) ).

fof(f12802,plain,
    ( ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg)
    | ~ spl0_1569 ),
    inference(avatar_component_clause,[],[f12801]) ).

fof(f32924,plain,
    ( spl0_2566
    | ~ spl0_817
    | ~ spl0_1568 ),
    inference(avatar_split_clause,[],[f14084,f12797,f7631,f32922]) ).

fof(f32922,plain,
    ( spl0_2566
  <=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2566])]) ).

fof(f12797,plain,
    ( spl0_1568
  <=> ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).

fof(f14084,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1568 ),
    inference(superposition,[],[f7632,f12798]) ).

fof(f12798,plain,
    ( ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg)
    | ~ spl0_1568 ),
    inference(avatar_component_clause,[],[f12797]) ).

fof(f32920,plain,
    ( spl0_2565
    | ~ spl0_817
    | ~ spl0_1567 ),
    inference(avatar_split_clause,[],[f14067,f12793,f7631,f32918]) ).

fof(f32918,plain,
    ( spl0_2565
  <=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2565])]) ).

fof(f12793,plain,
    ( spl0_1567
  <=> ! [X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).

fof(f14067,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1567 ),
    inference(superposition,[],[f7632,f12794]) ).

fof(f12794,plain,
    ( ! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg)
    | ~ spl0_1567 ),
    inference(avatar_component_clause,[],[f12793]) ).

fof(f32916,plain,
    ( spl0_2564
    | ~ spl0_817
    | ~ spl0_1566 ),
    inference(avatar_split_clause,[],[f14050,f12789,f7631,f32914]) ).

fof(f32914,plain,
    ( spl0_2564
  <=> ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2564])]) ).

fof(f12789,plain,
    ( spl0_1566
  <=> ! [X88,X110] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oparts(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).

fof(f14050,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1566 ),
    inference(superposition,[],[f7632,f12790]) ).

fof(f12790,plain,
    ( ! [X88,X110] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oparts(X88),tc_Message_Omsg)
    | ~ spl0_1566 ),
    inference(avatar_component_clause,[],[f12789]) ).

fof(f32912,plain,
    ( spl0_2563
    | ~ spl0_817
    | ~ spl0_1562 ),
    inference(avatar_split_clause,[],[f13991,f12773,f7631,f32910]) ).

fof(f32910,plain,
    ( spl0_2563
  <=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2563])]) ).

fof(f12773,plain,
    ( spl0_1562
  <=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).

fof(f13991,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1562 ),
    inference(superposition,[],[f7632,f12774]) ).

fof(f12774,plain,
    ( ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg)
    | ~ spl0_1562 ),
    inference(avatar_component_clause,[],[f12773]) ).

fof(f32908,plain,
    ( spl0_2562
    | ~ spl0_817
    | ~ spl0_1561 ),
    inference(avatar_split_clause,[],[f13971,f12769,f7631,f32906]) ).

fof(f32906,plain,
    ( spl0_2562
  <=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2562])]) ).

fof(f12769,plain,
    ( spl0_1561
  <=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).

fof(f13971,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1561 ),
    inference(superposition,[],[f7632,f12770]) ).

fof(f12770,plain,
    ( ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg)
    | ~ spl0_1561 ),
    inference(avatar_component_clause,[],[f12769]) ).

fof(f32901,plain,
    ( spl0_2561
    | ~ spl0_817
    | ~ spl0_1560 ),
    inference(avatar_split_clause,[],[f13951,f12765,f7631,f32899]) ).

fof(f32899,plain,
    ( spl0_2561
  <=> ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2561])]) ).

fof(f12765,plain,
    ( spl0_1560
  <=> ! [X86,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).

fof(f13951,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1560 ),
    inference(superposition,[],[f7632,f12766]) ).

fof(f12766,plain,
    ( ! [X88,X86] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg)
    | ~ spl0_1560 ),
    inference(avatar_component_clause,[],[f12765]) ).

fof(f32897,plain,
    ( spl0_2560
    | ~ spl0_817
    | ~ spl0_1559 ),
    inference(avatar_split_clause,[],[f13931,f12758,f7631,f32895]) ).

fof(f12758,plain,
    ( spl0_1559
  <=> ! [X88,X110] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).

fof(f13931,plain,
    ( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
    | ~ spl0_817
    | ~ spl0_1559 ),
    inference(superposition,[],[f7632,f12759]) ).

fof(f12759,plain,
    ( ! [X88,X110] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oanalz(X88),tc_Message_Omsg)
    | ~ spl0_1559 ),
    inference(avatar_component_clause,[],[f12758]) ).

fof(f32893,plain,
    ( spl0_2559
    | ~ spl0_672
    | ~ spl0_1557 ),
    inference(avatar_split_clause,[],[f13903,f12750,f7003,f32891]) ).

fof(f32891,plain,
    ( spl0_2559
  <=> ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2559])]) ).

fof(f7003,plain,
    ( spl0_672
  <=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f12750,plain,
    ( spl0_1557
  <=> ! [X13,X12,X0,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).

fof(f13903,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2))
    | ~ spl0_672
    | ~ spl0_1557 ),
    inference(resolution,[],[f12751,f7004]) ).

fof(f7004,plain,
    ( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
    | ~ spl0_672 ),
    inference(avatar_component_clause,[],[f7003]) ).

fof(f12751,plain,
    ( ! [X0,X1,X12,X13] :
        ( ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1))
        | c_lessequals(X12,X13,tc_set(X1)) )
    | ~ spl0_1557 ),
    inference(avatar_component_clause,[],[f12750]) ).

fof(f32889,plain,
    ( spl0_2558
    | ~ spl0_672
    | ~ spl0_1554 ),
    inference(avatar_split_clause,[],[f13878,f12738,f7003,f32887]) ).

fof(f32887,plain,
    ( spl0_2558
  <=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2558])]) ).

fof(f12738,plain,
    ( spl0_1554
  <=> ! [X13,X12,X32,X1] :
        ( c_lessequals(X13,X32,tc_set(X1))
        | ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).

fof(f13878,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
    | ~ spl0_672
    | ~ spl0_1554 ),
    inference(resolution,[],[f12739,f7004]) ).

fof(f12739,plain,
    ( ! [X1,X12,X32,X13] :
        ( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
        | c_lessequals(X13,X32,tc_set(X1)) )
    | ~ spl0_1554 ),
    inference(avatar_component_clause,[],[f12738]) ).

fof(f32885,plain,
    ( spl0_2557
    | ~ spl0_672
    | ~ spl0_1553 ),
    inference(avatar_split_clause,[],[f13862,f12734,f7003,f32883]) ).

fof(f32883,plain,
    ( spl0_2557
  <=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2557])]) ).

fof(f12734,plain,
    ( spl0_1553
  <=> ! [X13,X12,X32,X1] :
        ( c_lessequals(X12,X32,tc_set(X1))
        | ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).

fof(f13862,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
    | ~ spl0_672
    | ~ spl0_1553 ),
    inference(resolution,[],[f12735,f7004]) ).

fof(f12735,plain,
    ( ! [X1,X12,X32,X13] :
        ( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
        | c_lessequals(X12,X32,tc_set(X1)) )
    | ~ spl0_1553 ),
    inference(avatar_component_clause,[],[f12734]) ).

fof(f32881,plain,
    ( spl0_2556
    | ~ spl0_1024
    | ~ spl0_1537 ),
    inference(avatar_split_clause,[],[f13753,f12670,f8682,f32879]) ).

fof(f32879,plain,
    ( spl0_2556
  <=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2556])]) ).

fof(f8682,plain,
    ( spl0_1024
  <=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f12670,plain,
    ( spl0_1537
  <=> ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).

fof(f13753,plain,
    ( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat)
    | ~ spl0_1024
    | ~ spl0_1537 ),
    inference(superposition,[],[f8683,f12671]) ).

fof(f12671,plain,
    ( ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48
    | ~ spl0_1537 ),
    inference(avatar_component_clause,[],[f12670]) ).

fof(f8683,plain,
    ( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat)
    | ~ spl0_1024 ),
    inference(avatar_component_clause,[],[f8682]) ).

fof(f32877,plain,
    ( spl0_2555
    | ~ spl0_1025
    | ~ spl0_1537 ),
    inference(avatar_split_clause,[],[f13752,f12670,f8686,f32875]) ).

fof(f32875,plain,
    ( spl0_2555
  <=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2555])]) ).

fof(f8686,plain,
    ( spl0_1025
  <=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f13752,plain,
    ( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat)
    | ~ spl0_1025
    | ~ spl0_1537 ),
    inference(superposition,[],[f8687,f12671]) ).

fof(f8687,plain,
    ( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat)
    | ~ spl0_1025 ),
    inference(avatar_component_clause,[],[f8686]) ).

fof(f32872,plain,
    ( spl0_2554
    | ~ spl0_1024
    | ~ spl0_1536 ),
    inference(avatar_split_clause,[],[f13747,f12666,f8682,f32870]) ).

fof(f32870,plain,
    ( spl0_2554
  <=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2554])]) ).

fof(f12666,plain,
    ( spl0_1536
  <=> ! [X2,X1,X3] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).

fof(f13747,plain,
    ( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat)
    | ~ spl0_1024
    | ~ spl0_1536 ),
    inference(superposition,[],[f8683,f12667]) ).

fof(f12667,plain,
    ( ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3
    | ~ spl0_1536 ),
    inference(avatar_component_clause,[],[f12666]) ).

fof(f32867,plain,
    ( spl0_2553
    | ~ spl0_1025
    | ~ spl0_1536 ),
    inference(avatar_split_clause,[],[f13746,f12666,f8686,f32865]) ).

fof(f32865,plain,
    ( spl0_2553
  <=> ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2553])]) ).

fof(f13746,plain,
    ( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat)
    | ~ spl0_1025
    | ~ spl0_1536 ),
    inference(superposition,[],[f8687,f12667]) ).

fof(f32863,plain,
    ( spl0_2552
    | ~ spl0_817
    | ~ spl0_1501 ),
    inference(avatar_split_clause,[],[f13234,f12512,f7631,f32861]) ).

fof(f32861,plain,
    ( spl0_2552
  <=> ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2552])]) ).

fof(f12512,plain,
    ( spl0_1501
  <=> ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).

fof(f13234,plain,
    ( ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2)
    | ~ spl0_817
    | ~ spl0_1501 ),
    inference(superposition,[],[f7632,f12513]) ).

fof(f12513,plain,
    ( ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41)
    | ~ spl0_1501 ),
    inference(avatar_component_clause,[],[f12512]) ).

fof(f32859,plain,
    ( spl0_2551
    | ~ spl0_1214
    | ~ spl0_2535 ),
    inference(avatar_split_clause,[],[f32812,f32755,f9663,f32856]) ).

fof(f9663,plain,
    ( spl0_1214
  <=> ! [X86,X88] :
        ( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
        | c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).

fof(f32755,plain,
    ( spl0_2535
  <=> c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2535])]) ).

fof(f32812,plain,
    ( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_1214
    | ~ spl0_2535 ),
    inference(resolution,[],[f32757,f9664]) ).

fof(f9664,plain,
    ( ! [X88,X86] :
        ( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
        | c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) )
    | ~ spl0_1214 ),
    inference(avatar_component_clause,[],[f9663]) ).

fof(f32757,plain,
    ( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_2535 ),
    inference(avatar_component_clause,[],[f32755]) ).

fof(f32854,plain,
    ( spl0_2550
    | ~ spl0_786
    | ~ spl0_1494 ),
    inference(avatar_split_clause,[],[f13172,f12478,f7506,f32852]) ).

fof(f32852,plain,
    ( spl0_2550
  <=> ! [X0,X1] :
        ( c_List_Otl(X0,X1) != X0
        | c_List_Olist_ONil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2550])]) ).

fof(f7506,plain,
    ( spl0_786
  <=> ! [X0,X81,X1] : c_List_Olist_OCons(X0,X81,X1) != X81 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f12478,plain,
    ( spl0_1494
  <=> ! [X1,X3] :
        ( c_List_Olist_ONil = X3
        | c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).

fof(f13172,plain,
    ( ! [X0,X1] :
        ( c_List_Otl(X0,X1) != X0
        | c_List_Olist_ONil = X0 )
    | ~ spl0_786
    | ~ spl0_1494 ),
    inference(superposition,[],[f7507,f12479]) ).

fof(f12479,plain,
    ( ! [X3,X1] :
        ( c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3
        | c_List_Olist_ONil = X3 )
    | ~ spl0_1494 ),
    inference(avatar_component_clause,[],[f12478]) ).

fof(f7507,plain,
    ( ! [X0,X1,X81] : c_List_Olist_OCons(X0,X81,X1) != X81
    | ~ spl0_786 ),
    inference(avatar_component_clause,[],[f7506]) ).

fof(f32850,plain,
    ( spl0_2549
    | ~ spl0_1020
    | ~ spl0_1486 ),
    inference(avatar_split_clause,[],[f13113,f12445,f8536,f32848]) ).

fof(f32848,plain,
    ( spl0_2549
  <=> ! [X0,X1] :
        ( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
        | c_Divides_Oop_Advd(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2549])]) ).

fof(f8536,plain,
    ( spl0_1020
  <=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f12445,plain,
    ( spl0_1486
  <=> ! [X16,X21,X15] :
        ( c_Divides_Oop_Advd(X16,X15,tc_nat)
        | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).

fof(f13113,plain,
    ( ! [X0,X1] :
        ( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
        | c_Divides_Oop_Advd(X1,X0,tc_nat) )
    | ~ spl0_1020
    | ~ spl0_1486 ),
    inference(superposition,[],[f12446,f8537]) ).

fof(f8537,plain,
    ( ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat))
    | ~ spl0_1020 ),
    inference(avatar_component_clause,[],[f8536]) ).

fof(f12446,plain,
    ( ! [X21,X16,X15] :
        ( ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat)
        | c_Divides_Oop_Advd(X16,X15,tc_nat) )
    | ~ spl0_1486 ),
    inference(avatar_component_clause,[],[f12445]) ).

fof(f32846,plain,
    ( spl0_2548
    | ~ spl0_735
    | ~ spl0_1477 ),
    inference(avatar_split_clause,[],[f13005,f12409,f7282,f32844]) ).

fof(f7282,plain,
    ( spl0_735
  <=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f12409,plain,
    ( spl0_1477
  <=> ! [X13,X12,X1] :
        ( X12 = X13
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | ~ c_lessequals(X13,X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).

fof(f13005,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
        | c_UNIV = X0 )
    | ~ spl0_735
    | ~ spl0_1477 ),
    inference(resolution,[],[f12410,f7283]) ).

fof(f7283,plain,
    ( ! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1))
    | ~ spl0_735 ),
    inference(avatar_component_clause,[],[f7282]) ).

fof(f12410,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_lessequals(X13,X12,tc_set(X1))
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | X12 = X13 )
    | ~ spl0_1477 ),
    inference(avatar_component_clause,[],[f12409]) ).

fof(f32842,plain,
    ( spl0_2547
    | ~ spl0_671
    | ~ spl0_1475 ),
    inference(avatar_split_clause,[],[f12982,f12390,f6999,f32840]) ).

fof(f32840,plain,
    ( spl0_2547
  <=> ! [X0,X1] :
        ( c_emptyset = X0
        | c_less(c_emptyset,X0,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2547])]) ).

fof(f6999,plain,
    ( spl0_671
  <=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f12390,plain,
    ( spl0_1475
  <=> ! [X13,X12,X1] :
        ( X12 = X13
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | c_less(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).

fof(f12982,plain,
    ( ! [X0,X1] :
        ( c_emptyset = X0
        | c_less(c_emptyset,X0,tc_set(X1)) )
    | ~ spl0_671
    | ~ spl0_1475 ),
    inference(resolution,[],[f12391,f7000]) ).

fof(f7000,plain,
    ( ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1))
    | ~ spl0_671 ),
    inference(avatar_component_clause,[],[f6999]) ).

fof(f12391,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_lessequals(X12,X13,tc_set(X1))
        | X12 = X13
        | c_less(X12,X13,tc_set(X1)) )
    | ~ spl0_1475 ),
    inference(avatar_component_clause,[],[f12390]) ).

fof(f32838,plain,
    ( spl0_2546
    | ~ spl0_735
    | ~ spl0_1475 ),
    inference(avatar_split_clause,[],[f12973,f12390,f7282,f32836]) ).

fof(f32836,plain,
    ( spl0_2546
  <=> ! [X0,X1] :
        ( c_UNIV = X0
        | c_less(X0,c_UNIV,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2546])]) ).

fof(f12973,plain,
    ( ! [X0,X1] :
        ( c_UNIV = X0
        | c_less(X0,c_UNIV,tc_set(X1)) )
    | ~ spl0_735
    | ~ spl0_1475 ),
    inference(resolution,[],[f12391,f7283]) ).

fof(f32834,plain,
    ( spl0_2545
    | ~ spl0_787
    | ~ spl0_870
    | ~ spl0_1590 ),
    inference(avatar_split_clause,[],[f12924,f12901,f7856,f7510,f32832]) ).

fof(f32832,plain,
    ( spl0_2545
  <=> ! [X0] :
        ( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
        | c_0 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2545])]) ).

fof(f7510,plain,
    ( spl0_787
  <=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f7856,plain,
    ( spl0_870
  <=> ! [X43] :
        ( c_0 = X43
        | ~ c_lessequals(X43,c_0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f12901,plain,
    ( spl0_1590
  <=> ! [X59,X43] :
        ( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
        | c_lessequals(X43,X59,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).

fof(f12924,plain,
    ( ! [X0] :
        ( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
        | c_0 = X0 )
    | ~ spl0_787
    | ~ spl0_870
    | ~ spl0_1590 ),
    inference(forward_demodulation,[],[f12911,f7511]) ).

fof(f7511,plain,
    ( ! [X3] : c_plus(X3,c_0,tc_nat) = X3
    | ~ spl0_787 ),
    inference(avatar_component_clause,[],[f7510]) ).

fof(f12911,plain,
    ( ! [X0] :
        ( c_List_Olist_ONil = c_List_Oupt(X0,c_plus(c_1,c_0,tc_nat))
        | c_0 = X0 )
    | ~ spl0_870
    | ~ spl0_1590 ),
    inference(resolution,[],[f12902,f7857]) ).

fof(f7857,plain,
    ( ! [X43] :
        ( ~ c_lessequals(X43,c_0,tc_nat)
        | c_0 = X43 )
    | ~ spl0_870 ),
    inference(avatar_component_clause,[],[f7856]) ).

fof(f12902,plain,
    ( ! [X59,X43] :
        ( c_lessequals(X43,X59,tc_nat)
        | c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) )
    | ~ spl0_1590 ),
    inference(avatar_component_clause,[],[f12901]) ).

fof(f32830,plain,
    ( spl0_2544
    | ~ spl0_787
    | ~ spl0_997
    | ~ spl0_1587 ),
    inference(avatar_split_clause,[],[f12884,f12878,f8441,f7510,f32827]) ).

fof(f32827,plain,
    ( spl0_2544
  <=> c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2544])]) ).

fof(f8441,plain,
    ( spl0_997
  <=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).

fof(f12878,plain,
    ( spl0_1587
  <=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).

fof(f12884,plain,
    ( c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
    | ~ spl0_787
    | ~ spl0_997
    | ~ spl0_1587 ),
    inference(forward_demodulation,[],[f12881,f8443]) ).

fof(f8443,plain,
    ( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
    | ~ spl0_997 ),
    inference(avatar_component_clause,[],[f8441]) ).

fof(f12881,plain,
    ( c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
    | ~ spl0_787
    | ~ spl0_1587 ),
    inference(superposition,[],[f12879,f7511]) ).

fof(f12879,plain,
    ( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
    | ~ spl0_1587 ),
    inference(avatar_component_clause,[],[f12878]) ).

fof(f32825,plain,
    ( spl0_2543
    | ~ spl0_923
    | ~ spl0_1587 ),
    inference(avatar_split_clause,[],[f12883,f12878,f8140,f32823]) ).

fof(f32823,plain,
    ( spl0_2543
  <=> ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2543])]) ).

fof(f8140,plain,
    ( spl0_923
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f12883,plain,
    ( ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_923
    | ~ spl0_1587 ),
    inference(superposition,[],[f8141,f12879]) ).

fof(f8141,plain,
    ( ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
    | ~ spl0_923 ),
    inference(avatar_component_clause,[],[f8140]) ).

fof(f32821,plain,
    ( spl0_2542
    | ~ spl0_892
    | ~ spl0_1424 ),
    inference(avatar_split_clause,[],[f11987,f11167,f7944,f32819]) ).

fof(f32819,plain,
    ( spl0_2542
  <=> ! [X0,X1] :
        ( c_emptyset != X0
        | c_lessequals(X0,c_emptyset,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2542])]) ).

fof(f7944,plain,
    ( spl0_892
  <=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).

fof(f11167,plain,
    ( spl0_1424
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | c_emptyset != c_minus(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).

fof(f11987,plain,
    ( ! [X0,X1] :
        ( c_emptyset != X0
        | c_lessequals(X0,c_emptyset,tc_set(X1)) )
    | ~ spl0_892
    | ~ spl0_1424 ),
    inference(superposition,[],[f11168,f7945]) ).

fof(f7945,plain,
    ( ! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3
    | ~ spl0_892 ),
    inference(avatar_component_clause,[],[f7944]) ).

fof(f11168,plain,
    ( ! [X1,X12,X13] :
        ( c_emptyset != c_minus(X12,X13,tc_set(X1))
        | c_lessequals(X12,X13,tc_set(X1)) )
    | ~ spl0_1424 ),
    inference(avatar_component_clause,[],[f11167]) ).

fof(f32817,plain,
    ( spl0_2541
    | ~ spl0_751
    | ~ spl0_1416 ),
    inference(avatar_split_clause,[],[f11959,f11135,f7365,f32815]) ).

fof(f32815,plain,
    ( spl0_2541
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2541])]) ).

fof(f11135,plain,
    ( spl0_1416
  <=> ! [X16,X1,X26] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_lessequals(X26,X16,X1)
        | c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).

fof(f11959,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
    | ~ spl0_751
    | ~ spl0_1416 ),
    inference(duplicate_literal_removal,[],[f11926]) ).

fof(f11926,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_751
    | ~ spl0_1416 ),
    inference(resolution,[],[f11136,f7366]) ).

fof(f11136,plain,
    ( ! [X1,X26,X16] :
        ( ~ c_lessequals(X26,X16,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) )
    | ~ spl0_1416 ),
    inference(avatar_component_clause,[],[f11135]) ).

fof(f32805,plain,
    ( spl0_2540
    | ~ spl0_76
    | ~ spl0_118
    | ~ spl0_1416 ),
    inference(avatar_split_clause,[],[f11932,f11135,f4010,f3809,f32803]) ).

fof(f32803,plain,
    ( spl0_2540
  <=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2540])]) ).

fof(f3809,plain,
    ( spl0_76
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f4010,plain,
    ( spl0_118
  <=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f11932,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) )
    | ~ spl0_118
    | ~ spl0_1416 ),
    inference(resolution,[],[f11136,f4011]) ).

fof(f4011,plain,
    ( ! [X21] : c_lessequals(c_0,X21,tc_nat)
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f4010]) ).

fof(f32801,plain,
    ( spl0_2539
    | ~ spl0_751
    | ~ spl0_1407 ),
    inference(avatar_split_clause,[],[f11904,f11086,f7365,f32799]) ).

fof(f32799,plain,
    ( spl0_2539
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2539])]) ).

fof(f11086,plain,
    ( spl0_1407
  <=> ! [X21,X1,X15] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_lessequals(X21,X15,X1)
        | c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).

fof(f11904,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
    | ~ spl0_751
    | ~ spl0_1407 ),
    inference(duplicate_literal_removal,[],[f11871]) ).

fof(f11871,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_751
    | ~ spl0_1407 ),
    inference(resolution,[],[f11087,f7366]) ).

fof(f11087,plain,
    ( ! [X21,X1,X15] :
        ( ~ c_lessequals(X21,X15,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) )
    | ~ spl0_1407 ),
    inference(avatar_component_clause,[],[f11086]) ).

fof(f32783,plain,
    ( spl0_2538
    | ~ spl0_76
    | ~ spl0_118
    | ~ spl0_1407 ),
    inference(avatar_split_clause,[],[f11877,f11086,f4010,f3809,f32781]) ).

fof(f32781,plain,
    ( spl0_2538
  <=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2538])]) ).

fof(f11877,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) )
    | ~ spl0_118
    | ~ spl0_1407 ),
    inference(resolution,[],[f11087,f4011]) ).

fof(f32775,plain,
    ( spl0_2537
    | ~ spl0_28
    | ~ spl0_666
    | ~ spl0_1406 ),
    inference(avatar_split_clause,[],[f11852,f11082,f6214,f3569,f32772]) ).

fof(f32772,plain,
    ( spl0_2537
  <=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2537])]) ).

fof(f6214,plain,
    ( spl0_666
  <=> c_less(c_0,c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f11082,plain,
    ( spl0_1406
  <=> ! [X21,X1,X15] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_less(X21,X15,X1)
        | c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).

fof(f11852,plain,
    ( ~ class_Orderings_Oorder(tc_IntDef_Oint)
    | c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint)
    | ~ spl0_666
    | ~ spl0_1406 ),
    inference(resolution,[],[f11083,f6216]) ).

fof(f6216,plain,
    ( c_less(c_0,c_1,tc_IntDef_Oint)
    | ~ spl0_666 ),
    inference(avatar_component_clause,[],[f6214]) ).

fof(f11083,plain,
    ( ! [X21,X1,X15] :
        ( ~ c_less(X21,X15,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) )
    | ~ spl0_1406 ),
    inference(avatar_component_clause,[],[f11082]) ).

fof(f32765,plain,
    ( spl0_2536
    | ~ spl0_76
    | ~ spl0_652
    | ~ spl0_1406 ),
    inference(avatar_split_clause,[],[f11851,f11082,f6149,f3809,f32762]) ).

fof(f32762,plain,
    ( spl0_2536
  <=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2536])]) ).

fof(f6149,plain,
    ( spl0_652
  <=> c_less(c_0,c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f11851,plain,
    ( ~ class_Orderings_Oorder(tc_nat)
    | c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat)
    | ~ spl0_652
    | ~ spl0_1406 ),
    inference(resolution,[],[f11083,f6151]) ).

fof(f6151,plain,
    ( c_less(c_0,c_1,tc_nat)
    | ~ spl0_652 ),
    inference(avatar_component_clause,[],[f6149]) ).

fof(f32758,plain,
    ( spl0_2535
    | ~ spl0_1452
    | ~ spl0_2478 ),
    inference(avatar_split_clause,[],[f31942,f31925,f11298,f32755]) ).

fof(f11298,plain,
    ( spl0_1452
  <=> ! [X86,X87,X88] :
        ( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).

fof(f31925,plain,
    ( spl0_2478
  <=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).

fof(f31942,plain,
    ( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_1452
    | ~ spl0_2478 ),
    inference(resolution,[],[f31927,f11299]) ).

fof(f11299,plain,
    ( ! [X88,X86,X87] :
        ( ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg)
        | c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) )
    | ~ spl0_1452 ),
    inference(avatar_component_clause,[],[f11298]) ).

fof(f31927,plain,
    ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_2478 ),
    inference(avatar_component_clause,[],[f31925]) ).

fof(f32753,plain,
    ( spl0_2533
    | ~ spl0_2534
    | ~ spl0_794
    | ~ spl0_1320 ),
    inference(avatar_split_clause,[],[f10735,f10343,f7538,f32750,f32747]) ).

fof(f32747,plain,
    ( spl0_2533
  <=> ! [X0] : c_lessequals(c_1,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2533])]) ).

fof(f32750,plain,
    ( spl0_2534
  <=> c_lessequals(c_1,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2534])]) ).

fof(f7538,plain,
    ( spl0_794
  <=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).

fof(f10343,plain,
    ( spl0_1320
  <=> ! [X21,X15] :
        ( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
        | c_lessequals(c_1,X15,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).

fof(f10735,plain,
    ( ! [X0] :
        ( ~ c_lessequals(c_1,c_0,tc_nat)
        | c_lessequals(c_1,X0,tc_nat) )
    | ~ spl0_794
    | ~ spl0_1320 ),
    inference(superposition,[],[f10344,f7539]) ).

fof(f7539,plain,
    ( ! [X15] : c_0 = c_times(X15,c_0,tc_nat)
    | ~ spl0_794 ),
    inference(avatar_component_clause,[],[f7538]) ).

fof(f10344,plain,
    ( ! [X21,X15] :
        ( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
        | c_lessequals(c_1,X15,tc_nat) )
    | ~ spl0_1320 ),
    inference(avatar_component_clause,[],[f10343]) ).

fof(f32737,plain,
    ( spl0_2532
    | ~ spl0_45
    | ~ spl0_688
    | ~ spl0_1291 ),
    inference(avatar_split_clause,[],[f10566,f10205,f7071,f3654,f32735]) ).

fof(f32735,plain,
    ( spl0_2532
  <=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2532])]) ).

fof(f3654,plain,
    ( spl0_45
  <=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f7071,plain,
    ( spl0_688
  <=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f10205,plain,
    ( spl0_1291
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(c_0,X0,X1)
        | c_0 = c_OrderedGroup_Onprt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).

fof(f10566,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
        | c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
    | ~ spl0_688
    | ~ spl0_1291 ),
    inference(resolution,[],[f10206,f7072]) ).

fof(f7072,plain,
    ( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
    | ~ spl0_688 ),
    inference(avatar_component_clause,[],[f7071]) ).

fof(f10206,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_0,X0,X1)
        | ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = c_OrderedGroup_Onprt(X0,X1) )
    | ~ spl0_1291 ),
    inference(avatar_component_clause,[],[f10205]) ).

fof(f32733,plain,
    ( spl0_2531
    | ~ spl0_14
    | ~ spl0_1188 ),
    inference(avatar_split_clause,[],[f9930,f9559,f3499,f32731]) ).

fof(f32731,plain,
    ( spl0_2531
  <=> ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).

fof(f9559,plain,
    ( spl0_1188
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = c_plus(X18,c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).

fof(f9930,plain,
    ( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_14
    | ~ spl0_1188 ),
    inference(resolution,[],[f9560,f3501]) ).

fof(f9560,plain,
    ( ! [X1,X18] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = c_plus(X18,c_uminus(X18,X1),X1) )
    | ~ spl0_1188 ),
    inference(avatar_component_clause,[],[f9559]) ).

fof(f32729,plain,
    ( spl0_2530
    | ~ spl0_14
    | ~ spl0_1184 ),
    inference(avatar_split_clause,[],[f9915,f9543,f3499,f32727]) ).

fof(f32727,plain,
    ( spl0_2530
  <=> ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2530])]) ).

fof(f9543,plain,
    ( spl0_1184
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_uminus(X18,X1) = c_minus(c_0,X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f9915,plain,
    ( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint)
    | ~ spl0_14
    | ~ spl0_1184 ),
    inference(resolution,[],[f9544,f3501]) ).

fof(f9544,plain,
    ( ! [X1,X18] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_uminus(X18,X1) = c_minus(c_0,X18,X1) )
    | ~ spl0_1184 ),
    inference(avatar_component_clause,[],[f9543]) ).

fof(f32725,plain,
    ( spl0_2529
    | ~ spl0_14
    | ~ spl0_1182 ),
    inference(avatar_split_clause,[],[f9911,f9535,f3499,f32723]) ).

fof(f32723,plain,
    ( spl0_2529
  <=> ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2529])]) ).

fof(f9535,plain,
    ( spl0_1182
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = c_plus(c_uminus(X18,X1),X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).

fof(f9911,plain,
    ( ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
    | ~ spl0_14
    | ~ spl0_1182 ),
    inference(resolution,[],[f9536,f3501]) ).

fof(f9536,plain,
    ( ! [X1,X18] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = c_plus(c_uminus(X18,X1),X18,X1) )
    | ~ spl0_1182 ),
    inference(avatar_component_clause,[],[f9535]) ).

fof(f32721,plain,
    ( spl0_2528
    | ~ spl0_27
    | ~ spl0_1155 ),
    inference(avatar_split_clause,[],[f9806,f9426,f3564,f32719]) ).

fof(f32719,plain,
    ( spl0_2528
  <=> ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2528])]) ).

fof(f3564,plain,
    ( spl0_27
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f9426,plain,
    ( spl0_1155
  <=> ! [X21,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f9806,plain,
    ( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint)
    | ~ spl0_27
    | ~ spl0_1155 ),
    inference(resolution,[],[f9427,f3566]) ).

fof(f3566,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f3564]) ).

fof(f9427,plain,
    ( ! [X21,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) )
    | ~ spl0_1155 ),
    inference(avatar_component_clause,[],[f9426]) ).

fof(f32717,plain,
    ( spl0_2527
    | ~ spl0_96
    | ~ spl0_1150 ),
    inference(avatar_split_clause,[],[f9792,f9406,f3909,f32715]) ).

fof(f32715,plain,
    ( spl0_2527
  <=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2527])]) ).

fof(f3909,plain,
    ( spl0_96
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f9406,plain,
    ( spl0_1150
  <=> ! [X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f9792,plain,
    ( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
    | ~ spl0_96
    | ~ spl0_1150 ),
    inference(resolution,[],[f9407,f3911]) ).

fof(f3911,plain,
    ( class_Orderings_Olinorder(tc_nat)
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f3909]) ).

fof(f9407,plain,
    ( ! [X3,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 )
    | ~ spl0_1150 ),
    inference(avatar_component_clause,[],[f9406]) ).

fof(f32713,plain,
    ( spl0_2526
    | ~ spl0_32
    | ~ spl0_1150 ),
    inference(avatar_split_clause,[],[f9791,f9406,f3589,f32711]) ).

fof(f32711,plain,
    ( spl0_2526
  <=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).

fof(f3589,plain,
    ( spl0_32
  <=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f9791,plain,
    ( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
    | ~ spl0_32
    | ~ spl0_1150 ),
    inference(resolution,[],[f9407,f3591]) ).

fof(f3591,plain,
    ( class_Orderings_Olinorder(tc_IntDef_Oint)
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f3589]) ).

fof(f32709,plain,
    ( spl0_2525
    | ~ spl0_96
    | ~ spl0_1149 ),
    inference(avatar_split_clause,[],[f9790,f9402,f3909,f32707]) ).

fof(f32707,plain,
    ( spl0_2525
  <=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).

fof(f9402,plain,
    ( spl0_1149
  <=> ! [X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f9790,plain,
    ( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
    | ~ spl0_96
    | ~ spl0_1149 ),
    inference(resolution,[],[f9403,f3911]) ).

fof(f9403,plain,
    ( ! [X3,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 )
    | ~ spl0_1149 ),
    inference(avatar_component_clause,[],[f9402]) ).

fof(f32705,plain,
    ( spl0_2524
    | ~ spl0_32
    | ~ spl0_1149 ),
    inference(avatar_split_clause,[],[f9789,f9402,f3589,f32703]) ).

fof(f32703,plain,
    ( spl0_2524
  <=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2524])]) ).

fof(f9789,plain,
    ( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
    | ~ spl0_32
    | ~ spl0_1149 ),
    inference(resolution,[],[f9403,f3591]) ).

fof(f32700,plain,
    ( spl0_2523
    | ~ spl0_646
    | ~ spl0_1225 ),
    inference(avatar_split_clause,[],[f9712,f9709,f6122,f32697]) ).

fof(f6122,plain,
    ( spl0_646
  <=> c_1 = c_IntDef_Oint(c_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f9709,plain,
    ( spl0_1225
  <=> ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).

fof(f9712,plain,
    ( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_1225 ),
    inference(superposition,[],[f9710,f6124]) ).

fof(f6124,plain,
    ( c_1 = c_IntDef_Oint(c_1)
    | ~ spl0_646 ),
    inference(avatar_component_clause,[],[f6122]) ).

fof(f9710,plain,
    ( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1225 ),
    inference(avatar_component_clause,[],[f9709]) ).

fof(f32695,plain,
    ( ~ spl0_2521
    | spl0_2522
    | ~ spl0_663
    | ~ spl0_1125 ),
    inference(avatar_split_clause,[],[f9332,f9088,f6200,f32692,f32688]) ).

fof(f32688,plain,
    ( spl0_2521
  <=> c_less(c_1,c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2521])]) ).

fof(f32692,plain,
    ( spl0_2522
  <=> c_less(c_1,c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).

fof(f6200,plain,
    ( spl0_663
  <=> c_1 = c_IntDef_Onat(c_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f9088,plain,
    ( spl0_1125
  <=> ! [X48] :
        ( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
        | ~ c_less(c_1,X48,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f9332,plain,
    ( c_less(c_1,c_1,tc_nat)
    | ~ c_less(c_1,c_1,tc_IntDef_Oint)
    | ~ spl0_663
    | ~ spl0_1125 ),
    inference(superposition,[],[f9089,f6202]) ).

fof(f6202,plain,
    ( c_1 = c_IntDef_Onat(c_1)
    | ~ spl0_663 ),
    inference(avatar_component_clause,[],[f6200]) ).

fof(f9089,plain,
    ( ! [X48] :
        ( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
        | ~ c_less(c_1,X48,tc_IntDef_Oint) )
    | ~ spl0_1125 ),
    inference(avatar_component_clause,[],[f9088]) ).

fof(f32686,plain,
    ( spl0_2520
    | ~ spl0_998
    | ~ spl0_1089 ),
    inference(avatar_split_clause,[],[f9270,f8944,f8446,f32684]) ).

fof(f32684,plain,
    ( spl0_2520
  <=> ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2520])]) ).

fof(f8446,plain,
    ( spl0_998
  <=> ! [X1,X3] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f8944,plain,
    ( spl0_1089
  <=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f9270,plain,
    ( ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0))
    | ~ spl0_998
    | ~ spl0_1089 ),
    inference(superposition,[],[f8447,f8945]) ).

fof(f8945,plain,
    ( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
    | ~ spl0_1089 ),
    inference(avatar_component_clause,[],[f8944]) ).

fof(f8447,plain,
    ( ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3
    | ~ spl0_998 ),
    inference(avatar_component_clause,[],[f8446]) ).

fof(f32682,plain,
    ( spl0_2519
    | ~ spl0_869
    | ~ spl0_1071 ),
    inference(avatar_split_clause,[],[f9241,f8872,f7852,f32680]) ).

fof(f32680,plain,
    ( spl0_2519
  <=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2519])]) ).

fof(f7852,plain,
    ( spl0_869
  <=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f8872,plain,
    ( spl0_1071
  <=> ! [X43,X59] :
        ( ~ c_lessequals(X59,X43,tc_nat)
        | c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f9241,plain,
    ( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat))
    | ~ spl0_869
    | ~ spl0_1071 ),
    inference(resolution,[],[f8873,f7853]) ).

fof(f7853,plain,
    ( ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat)
    | ~ spl0_869 ),
    inference(avatar_component_clause,[],[f7852]) ).

fof(f8873,plain,
    ( ! [X59,X43] :
        ( ~ c_lessequals(X59,X43,tc_nat)
        | c_List_Olist_ONil = c_List_Oupt(X43,X59) )
    | ~ spl0_1071 ),
    inference(avatar_component_clause,[],[f8872]) ).

fof(f32678,plain,
    ( spl0_2518
    | ~ spl0_849
    | ~ spl0_1071 ),
    inference(avatar_split_clause,[],[f9240,f8872,f7772,f32676]) ).

fof(f32676,plain,
    ( spl0_2518
  <=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).

fof(f7772,plain,
    ( spl0_849
  <=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f9240,plain,
    ( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat))
    | ~ spl0_849
    | ~ spl0_1071 ),
    inference(resolution,[],[f8873,f7773]) ).

fof(f7773,plain,
    ( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
    | ~ spl0_849 ),
    inference(avatar_component_clause,[],[f7772]) ).

fof(f32674,plain,
    ( spl0_2517
    | ~ spl0_998
    | ~ spl0_1061 ),
    inference(avatar_split_clause,[],[f9213,f8832,f8446,f32672]) ).

fof(f32672,plain,
    ( spl0_2517
  <=> ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).

fof(f8832,plain,
    ( spl0_1061
  <=> ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f9213,plain,
    ( ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
    | ~ spl0_998
    | ~ spl0_1061 ),
    inference(superposition,[],[f8447,f8833]) ).

fof(f8833,plain,
    ( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
    | ~ spl0_1061 ),
    inference(avatar_component_clause,[],[f8832]) ).

fof(f32670,plain,
    ( spl0_2516
    | ~ spl0_855
    | ~ spl0_1044 ),
    inference(avatar_split_clause,[],[f9179,f8763,f7796,f32668]) ).

fof(f32668,plain,
    ( spl0_2516
  <=> ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).

fof(f8763,plain,
    ( spl0_1044
  <=> ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f9179,plain,
    ( ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_855
    | ~ spl0_1044 ),
    inference(superposition,[],[f8764,f7797]) ).

fof(f8764,plain,
    ( ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1044 ),
    inference(avatar_component_clause,[],[f8763]) ).

fof(f32666,plain,
    ( spl0_2515
    | ~ spl0_874
    | ~ spl0_1040 ),
    inference(avatar_split_clause,[],[f9152,f8747,f7872,f32664]) ).

fof(f32664,plain,
    ( spl0_2515
  <=> ! [X0] :
        ( c_less(c_0,X0,tc_IntDef_Oint)
        | c_0 = c_IntDef_Onat(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2515])]) ).

fof(f7872,plain,
    ( spl0_874
  <=> ! [X21] :
        ( c_0 = X21
        | c_less(c_0,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).

fof(f8747,plain,
    ( spl0_1040
  <=> ! [X48] :
        ( c_less(c_0,X48,tc_IntDef_Oint)
        | ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f9152,plain,
    ( ! [X0] :
        ( c_less(c_0,X0,tc_IntDef_Oint)
        | c_0 = c_IntDef_Onat(X0) )
    | ~ spl0_874
    | ~ spl0_1040 ),
    inference(resolution,[],[f8748,f7873]) ).

fof(f7873,plain,
    ( ! [X21] :
        ( c_less(c_0,X21,tc_nat)
        | c_0 = X21 )
    | ~ spl0_874 ),
    inference(avatar_component_clause,[],[f7872]) ).

fof(f8748,plain,
    ( ! [X48] :
        ( ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat)
        | c_less(c_0,X48,tc_IntDef_Oint) )
    | ~ spl0_1040 ),
    inference(avatar_component_clause,[],[f8747]) ).

fof(f32661,plain,
    ( spl0_2514
    | ~ spl0_739
    | ~ spl0_1002 ),
    inference(avatar_split_clause,[],[f8661,f8463,f7300,f32659]) ).

fof(f32659,plain,
    ( spl0_2514
  <=> ! [X0,X1] :
        ( c_Message_OinvKey(X1) != X0
        | c_Message_OinvKey(X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2514])]) ).

fof(f7300,plain,
    ( spl0_739
  <=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f8661,plain,
    ( ! [X0,X1] :
        ( c_Message_OinvKey(X1) != X0
        | c_Message_OinvKey(X0) = X1 )
    | ~ spl0_739
    | ~ spl0_1002 ),
    inference(superposition,[],[f8464,f7301]) ).

fof(f7301,plain,
    ( ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3
    | ~ spl0_739 ),
    inference(avatar_component_clause,[],[f7300]) ).

fof(f32649,plain,
    ( spl0_2513
    | ~ spl0_45
    | ~ spl0_942
    | ~ spl0_976 ),
    inference(avatar_split_clause,[],[f8626,f8356,f8219,f3654,f32647]) ).

fof(f32647,plain,
    ( spl0_2513
  <=> ! [X0] : c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2513])]) ).

fof(f8219,plain,
    ( spl0_942
  <=> ! [X48] :
        ( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
        | c_0 = c_IntDef_Onat(X48) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f8356,plain,
    ( spl0_976
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f8626,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
        | c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) )
    | ~ spl0_942
    | ~ spl0_976 ),
    inference(resolution,[],[f8357,f8220]) ).

fof(f8220,plain,
    ( ! [X48] :
        ( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
        | c_0 = c_IntDef_Onat(X48) )
    | ~ spl0_942 ),
    inference(avatar_component_clause,[],[f8219]) ).

fof(f8357,plain,
    ( ! [X18,X1] :
        ( c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1)
        | ~ class_OrderedGroup_Olordered__ab__group(X1) )
    | ~ spl0_976 ),
    inference(avatar_component_clause,[],[f8356]) ).

fof(f32645,plain,
    ( spl0_2512
    | ~ spl0_864
    | ~ spl0_950 ),
    inference(avatar_split_clause,[],[f8574,f8252,f7832,f32643]) ).

fof(f32643,plain,
    ( spl0_2512
  <=> ! [X0,X1] :
        ( c_List_Olist_ONil != X0
        | c_List_Olist_ONil = c_List_Orev(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).

fof(f7832,plain,
    ( spl0_864
  <=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f8252,plain,
    ( spl0_950
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f8574,plain,
    ( ! [X0,X1] :
        ( c_List_Olist_ONil != X0
        | c_List_Olist_ONil = c_List_Orev(X0,X1) )
    | ~ spl0_864
    | ~ spl0_950 ),
    inference(superposition,[],[f8253,f7833]) ).

fof(f7833,plain,
    ( ! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3
    | ~ spl0_864 ),
    inference(avatar_component_clause,[],[f7832]) ).

fof(f8253,plain,
    ( ! [X1,X23] :
        ( c_List_Olist_ONil != c_List_Orev(X23,X1)
        | c_List_Olist_ONil = X23 )
    | ~ spl0_950 ),
    inference(avatar_component_clause,[],[f8252]) ).

fof(f32635,plain,
    ( spl0_2511
    | ~ spl0_4
    | ~ spl0_750
    | ~ spl0_2461 ),
    inference(avatar_split_clause,[],[f31605,f31569,f7360,f3449,f32633]) ).

fof(f32633,plain,
    ( spl0_2511
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | c_Message_Omsg_ONonce(v_NB) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).

fof(f31569,plain,
    ( spl0_2461
  <=> ! [X86,X113,X120,X12,X91,X117,X112,X107,X111,X102,X13,X123] :
        ( X113 = X120
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).

fof(f31605,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | c_Message_Omsg_ONonce(v_NB) = X3 )
    | ~ spl0_750
    | ~ spl0_2461 ),
    inference(resolution,[],[f31570,f7362]) ).

fof(f31570,plain,
    ( ! [X113,X111,X120,X91,X117,X86,X107,X102,X12,X13,X123,X112] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | X113 = X120 )
    | ~ spl0_2461 ),
    inference(avatar_component_clause,[],[f31569]) ).

fof(f32625,plain,
    ( spl0_2510
    | ~ spl0_4
    | ~ spl0_750
    | ~ spl0_2460 ),
    inference(avatar_split_clause,[],[f31594,f31565,f7360,f3449,f32623]) ).

fof(f32623,plain,
    ( spl0_2510
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | c_Message_Omsg_ONonce(v_NAa) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2510])]) ).

fof(f31565,plain,
    ( spl0_2460
  <=> ! [X86,X113,X120,X12,X91,X117,X112,X107,X111,X102,X13,X123] :
        ( X112 = X123
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2460])]) ).

fof(f31594,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | c_Message_Omsg_ONonce(v_NAa) = X2 )
    | ~ spl0_750
    | ~ spl0_2460 ),
    inference(resolution,[],[f31566,f7362]) ).

fof(f31566,plain,
    ( ! [X113,X111,X120,X91,X117,X86,X107,X102,X12,X13,X123,X112] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | X112 = X123 )
    | ~ spl0_2460 ),
    inference(avatar_component_clause,[],[f31565]) ).

fof(f32615,plain,
    ( spl0_2509
    | ~ spl0_4
    | ~ spl0_750
    | ~ spl0_2459 ),
    inference(avatar_split_clause,[],[f31583,f31561,f7360,f3449,f32613]) ).

fof(f32613,plain,
    ( spl0_2509
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_Ba = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).

fof(f31561,plain,
    ( spl0_2459
  <=> ! [X86,X113,X120,X12,X91,X117,X112,X107,X111,X102,X13,X123] :
        ( X13 = X117
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2459])]) ).

fof(f31583,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_Ba = X1 )
    | ~ spl0_750
    | ~ spl0_2459 ),
    inference(resolution,[],[f31562,f7362]) ).

fof(f31562,plain,
    ( ! [X113,X111,X120,X91,X117,X86,X107,X102,X12,X13,X123,X112] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | X13 = X117 )
    | ~ spl0_2459 ),
    inference(avatar_component_clause,[],[f31561]) ).

fof(f32611,plain,
    ( spl0_2508
    | ~ spl0_1444
    | ~ spl0_2503 ),
    inference(avatar_split_clause,[],[f32455,f32417,f11266,f32608]) ).

fof(f32608,plain,
    ( spl0_2508
  <=> c_in(v_X,c_Event_Oused(v_evso),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).

fof(f32455,plain,
    ( c_in(v_X,c_Event_Oused(v_evso),tc_Message_Omsg)
    | ~ spl0_1444
    | ~ spl0_2503 ),
    inference(resolution,[],[f32419,f11267]) ).

fof(f32600,plain,
    ( spl0_2507
    | ~ spl0_4
    | ~ spl0_750
    | ~ spl0_2458 ),
    inference(avatar_split_clause,[],[f31572,f31557,f7360,f3449,f32598]) ).

fof(f32598,plain,
    ( spl0_2507
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_Aa = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).

fof(f31557,plain,
    ( spl0_2458
  <=> ! [X120,X86,X113,X111,X12,X91,X117,X112,X107,X102,X13,X123] :
        ( X12 = X111
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2458])]) ).

fof(f31572,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | v_Aa = X0 )
    | ~ spl0_750
    | ~ spl0_2458 ),
    inference(resolution,[],[f31558,f7362]) ).

fof(f31558,plain,
    ( ! [X113,X111,X120,X91,X117,X86,X107,X102,X12,X13,X123,X112] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | X12 = X111 )
    | ~ spl0_2458 ),
    inference(avatar_component_clause,[],[f31557]) ).

fof(f32538,plain,
    ( spl0_2506
    | ~ spl0_114
    | ~ spl0_2044 ),
    inference(avatar_split_clause,[],[f22527,f22374,f3994,f32536]) ).

fof(f32536,plain,
    ( spl0_2506
  <=> ! [X0] : c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).

fof(f3994,plain,
    ( spl0_114
  <=> ! [X24] : ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X24))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f22374,plain,
    ( spl0_2044
  <=> ! [X41,X0,X23] :
        ( c_in(X0,c_List_Oset(X23,X41),X41)
        | c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).

fof(f22527,plain,
    ( ! [X0] : c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ spl0_114
    | ~ spl0_2044 ),
    inference(resolution,[],[f22375,f3995]) ).

fof(f3995,plain,
    ( ! [X24] : ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X24))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f3994]) ).

fof(f22375,plain,
    ( ! [X41,X0,X23] :
        ( c_in(X0,c_List_Oset(X23,X41),X41)
        | c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) )
    | ~ spl0_2044 ),
    inference(avatar_component_clause,[],[f22374]) ).

fof(f32429,plain,
    ( spl0_2505
    | ~ spl0_120
    | ~ spl0_1890 ),
    inference(avatar_split_clause,[],[f19847,f19166,f4018,f32427]) ).

fof(f32427,plain,
    ( spl0_2505
  <=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).

fof(f4018,plain,
    ( spl0_120
  <=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f19166,plain,
    ( spl0_1890
  <=> ! [X5,X18,X27,X2,X1] :
        ( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
        | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).

fof(f19847,plain,
    ( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
    | ~ spl0_120
    | ~ spl0_1890 ),
    inference(resolution,[],[f19167,f4019]) ).

fof(f4019,plain,
    ( ! [X0,X1] : c_in(X0,c_UNIV,X1)
    | ~ spl0_120 ),
    inference(avatar_component_clause,[],[f4018]) ).

fof(f19167,plain,
    ( ! [X2,X18,X1,X27,X5] :
        ( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
        | c_in(X27,c_Relation_ORange(X5,X1,X2),X2) )
    | ~ spl0_1890 ),
    inference(avatar_component_clause,[],[f19166]) ).

fof(f32425,plain,
    ( spl0_2504
    | ~ spl0_120
    | ~ spl0_1887 ),
    inference(avatar_split_clause,[],[f19787,f19154,f4018,f32423]) ).

fof(f32423,plain,
    ( spl0_2504
  <=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2504])]) ).

fof(f19154,plain,
    ( spl0_1887
  <=> ! [X18,X5,X27,X2,X1] :
        ( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
        | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).

fof(f19787,plain,
    ( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
    | ~ spl0_120
    | ~ spl0_1887 ),
    inference(resolution,[],[f19155,f4019]) ).

fof(f19155,plain,
    ( ! [X2,X18,X1,X27,X5] :
        ( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
        | c_in(X18,c_Relation_ODomain(X5,X1,X2),X1) )
    | ~ spl0_1887 ),
    inference(avatar_component_clause,[],[f19154]) ).

fof(f32420,plain,
    ( spl0_2503
    | ~ spl0_1214
    | ~ spl0_2495 ),
    inference(avatar_split_clause,[],[f32143,f32079,f9663,f32417]) ).

fof(f32079,plain,
    ( spl0_2495
  <=> c_in(v_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2495])]) ).

fof(f32143,plain,
    ( c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_1214
    | ~ spl0_2495 ),
    inference(resolution,[],[f32081,f9664]) ).

fof(f32081,plain,
    ( c_in(v_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_2495 ),
    inference(avatar_component_clause,[],[f32079]) ).

fof(f32110,plain,
    ( spl0_2502
    | ~ spl0_652
    | ~ spl0_789
    | ~ spl0_1621 ),
    inference(avatar_split_clause,[],[f14870,f14323,f7518,f6149,f32107]) ).

fof(f32107,plain,
    ( spl0_2502
  <=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2502])]) ).

fof(f7518,plain,
    ( spl0_789
  <=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f14323,plain,
    ( spl0_1621
  <=> ! [X59,X43] :
        ( ~ c_less(X43,X59,tc_nat)
        | c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).

fof(f14870,plain,
    ( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
    | ~ spl0_652
    | ~ spl0_789
    | ~ spl0_1621 ),
    inference(forward_demodulation,[],[f14852,f7519]) ).

fof(f7519,plain,
    ( ! [X15] : c_0 = c_minus(X15,X15,tc_nat)
    | ~ spl0_789 ),
    inference(avatar_component_clause,[],[f7518]) ).

fof(f14852,plain,
    ( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
    | ~ spl0_652
    | ~ spl0_1621 ),
    inference(resolution,[],[f14324,f6151]) ).

fof(f14324,plain,
    ( ! [X59,X43] :
        ( ~ c_less(X43,X59,tc_nat)
        | c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) )
    | ~ spl0_1621 ),
    inference(avatar_component_clause,[],[f14323]) ).

fof(f32105,plain,
    ( spl0_2500
    | spl0_2501
    | ~ spl0_672
    | ~ spl0_1614 ),
    inference(avatar_split_clause,[],[f14757,f14295,f7003,f32103,f32100]) ).

fof(f32100,plain,
    ( spl0_2500
  <=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).

fof(f14757,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,tc_IntDef_Oint)
        | ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
    | ~ spl0_672
    | ~ spl0_1614 ),
    inference(resolution,[],[f14296,f7004]) ).

fof(f32098,plain,
    ( spl0_2499
    | ~ spl0_849
    | ~ spl0_1595 ),
    inference(avatar_split_clause,[],[f14243,f12948,f7772,f32096]) ).

fof(f32096,plain,
    ( spl0_2499
  <=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).

fof(f12948,plain,
    ( spl0_1595
  <=> ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).

fof(f14243,plain,
    ( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
    | ~ spl0_849
    | ~ spl0_1595 ),
    inference(superposition,[],[f7773,f12949]) ).

fof(f12949,plain,
    ( ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3
    | ~ spl0_1595 ),
    inference(avatar_component_clause,[],[f12948]) ).

fof(f32094,plain,
    ( spl0_2498
    | ~ spl0_1243
    | ~ spl0_1536 ),
    inference(avatar_split_clause,[],[f13743,f12666,f10010,f32092]) ).

fof(f32092,plain,
    ( spl0_2498
  <=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).

fof(f10010,plain,
    ( spl0_1243
  <=> ! [X2,X27,X1,X18] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).

fof(f13743,plain,
    ( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
    | ~ spl0_1243
    | ~ spl0_1536 ),
    inference(superposition,[],[f10011,f12667]) ).

fof(f10011,plain,
    ( ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2))
    | ~ spl0_1243 ),
    inference(avatar_component_clause,[],[f10010]) ).

fof(f32090,plain,
    ( spl0_2497
    | ~ spl0_796
    | ~ spl0_820
    | ~ spl0_1318 ),
    inference(avatar_split_clause,[],[f10731,f10335,f7643,f7546,f32088]) ).

fof(f32088,plain,
    ( spl0_2497
  <=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2497])]) ).

fof(f7546,plain,
    ( spl0_796
  <=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f7643,plain,
    ( spl0_820
  <=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f10335,plain,
    ( spl0_1318
  <=> ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).

fof(f10731,plain,
    ( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
    | ~ spl0_796
    | ~ spl0_820
    | ~ spl0_1318 ),
    inference(forward_demodulation,[],[f10720,f7547]) ).

fof(f7547,plain,
    ( ! [X3] : c_plus(c_0,X3,tc_nat) = X3
    | ~ spl0_796 ),
    inference(avatar_component_clause,[],[f7546]) ).

fof(f10720,plain,
    ( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
    | ~ spl0_820
    | ~ spl0_1318 ),
    inference(superposition,[],[f10336,f7644]) ).

fof(f7644,plain,
    ( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg)
    | ~ spl0_820 ),
    inference(avatar_component_clause,[],[f7643]) ).

fof(f10336,plain,
    ( ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat)
    | ~ spl0_1318 ),
    inference(avatar_component_clause,[],[f10335]) ).

fof(f32086,plain,
    ( spl0_2496
    | ~ spl0_796
    | ~ spl0_821
    | ~ spl0_1318 ),
    inference(avatar_split_clause,[],[f10730,f10335,f7647,f7546,f32084]) ).

fof(f32084,plain,
    ( spl0_2496
  <=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2496])]) ).

fof(f7647,plain,
    ( spl0_821
  <=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f10730,plain,
    ( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
    | ~ spl0_796
    | ~ spl0_821
    | ~ spl0_1318 ),
    inference(forward_demodulation,[],[f10719,f7547]) ).

fof(f10719,plain,
    ( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
    | ~ spl0_821
    | ~ spl0_1318 ),
    inference(superposition,[],[f10336,f7648]) ).

fof(f7648,plain,
    ( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg)
    | ~ spl0_821 ),
    inference(avatar_component_clause,[],[f7647]) ).

fof(f32082,plain,
    ( spl0_2495
    | ~ spl0_1451
    | ~ spl0_2483 ),
    inference(avatar_split_clause,[],[f31989,f31984,f11294,f32079]) ).

fof(f11294,plain,
    ( spl0_1451
  <=> ! [X87,X86,X88] :
        ( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).

fof(f31984,plain,
    ( spl0_2483
  <=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).

fof(f31989,plain,
    ( c_in(v_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_1451
    | ~ spl0_2483 ),
    inference(resolution,[],[f31986,f11295]) ).

fof(f11295,plain,
    ( ! [X88,X86,X87] :
        ( ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg)
        | c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg) )
    | ~ spl0_1451 ),
    inference(avatar_component_clause,[],[f11294]) ).

fof(f31986,plain,
    ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_2483 ),
    inference(avatar_component_clause,[],[f31984]) ).

fof(f32077,plain,
    ( spl0_2494
    | ~ spl0_796
    | ~ spl0_822
    | ~ spl0_1318 ),
    inference(avatar_split_clause,[],[f10729,f10335,f7651,f7546,f32075]) ).

fof(f32075,plain,
    ( spl0_2494
  <=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).

fof(f7651,plain,
    ( spl0_822
  <=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f10729,plain,
    ( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
    | ~ spl0_796
    | ~ spl0_822
    | ~ spl0_1318 ),
    inference(forward_demodulation,[],[f10718,f7547]) ).

fof(f10718,plain,
    ( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
    | ~ spl0_822
    | ~ spl0_1318 ),
    inference(superposition,[],[f10336,f7652]) ).

fof(f7652,plain,
    ( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg)
    | ~ spl0_822 ),
    inference(avatar_component_clause,[],[f7651]) ).

fof(f32073,plain,
    ( spl0_2493
    | ~ spl0_796
    | ~ spl0_819
    | ~ spl0_1318 ),
    inference(avatar_split_clause,[],[f10727,f10335,f7639,f7546,f32071]) ).

fof(f32071,plain,
    ( spl0_2493
  <=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2493])]) ).

fof(f7639,plain,
    ( spl0_819
  <=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f10727,plain,
    ( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
    | ~ spl0_796
    | ~ spl0_819
    | ~ spl0_1318 ),
    inference(forward_demodulation,[],[f10716,f7547]) ).

fof(f10716,plain,
    ( ! [X0] : c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) = c_plus(c_0,c_1,tc_nat)
    | ~ spl0_819
    | ~ spl0_1318 ),
    inference(superposition,[],[f10336,f7640]) ).

fof(f7640,plain,
    ( ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg)
    | ~ spl0_819 ),
    inference(avatar_component_clause,[],[f7639]) ).

fof(f32069,plain,
    ( spl0_2492
    | ~ spl0_873
    | ~ spl0_1318 ),
    inference(avatar_split_clause,[],[f10725,f10335,f7868,f32067]) ).

fof(f32067,plain,
    ( spl0_2492
  <=> ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2492])]) ).

fof(f10725,plain,
    ( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat)
    | ~ spl0_873
    | ~ spl0_1318 ),
    inference(superposition,[],[f7869,f10336]) ).

fof(f32065,plain,
    ( spl0_2491
    | ~ spl0_647
    | ~ spl0_1129
    | ~ spl0_1317 ),
    inference(avatar_split_clause,[],[f10715,f10331,f9201,f6127,f32063]) ).

fof(f32063,plain,
    ( spl0_2491
  <=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2491])]) ).

fof(f6127,plain,
    ( spl0_647
  <=> c_0 = c_IntDef_Oint(c_0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f9201,plain,
    ( spl0_1129
  <=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f10331,plain,
    ( spl0_1317
  <=> ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).

fof(f10715,plain,
    ( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_1129
    | ~ spl0_1317 ),
    inference(forward_demodulation,[],[f10712,f9202]) ).

fof(f9202,plain,
    ( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
    | ~ spl0_1129 ),
    inference(avatar_component_clause,[],[f9201]) ).

fof(f10712,plain,
    ( ! [X0] : c_less(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_1317 ),
    inference(superposition,[],[f10332,f6129]) ).

fof(f6129,plain,
    ( c_0 = c_IntDef_Oint(c_0)
    | ~ spl0_647 ),
    inference(avatar_component_clause,[],[f6127]) ).

fof(f10332,plain,
    ( ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
    | ~ spl0_1317 ),
    inference(avatar_component_clause,[],[f10331]) ).

fof(f32061,plain,
    ( spl0_2489
    | ~ spl0_2490
    | ~ spl0_118
    | ~ spl0_1289 ),
    inference(avatar_split_clause,[],[f10537,f10197,f4010,f32058,f32055]) ).

fof(f32055,plain,
    ( spl0_2489
  <=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).

fof(f32058,plain,
    ( spl0_2490
  <=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).

fof(f10197,plain,
    ( spl0_1289
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | ~ c_lessequals(c_0,X3,X1)
        | c_HOL_Oabs(X3,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).

fof(f10537,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
        | c_HOL_Oabs(X0,tc_nat) = X0 )
    | ~ spl0_118
    | ~ spl0_1289 ),
    inference(resolution,[],[f10198,f4011]) ).

fof(f10198,plain,
    ( ! [X3,X1] :
        ( ~ c_lessequals(c_0,X3,X1)
        | ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_HOL_Oabs(X3,X1) = X3 )
    | ~ spl0_1289 ),
    inference(avatar_component_clause,[],[f10197]) ).

fof(f32053,plain,
    ( spl0_2488
    | ~ spl0_717
    | ~ spl0_743
    | ~ spl0_911
    | ~ spl0_1283 ),
    inference(avatar_split_clause,[],[f10520,f10172,f8021,f7318,f7205,f32050]) ).

fof(f32050,plain,
    ( spl0_2488
  <=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2488])]) ).

fof(f7205,plain,
    ( spl0_717
  <=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f7318,plain,
    ( spl0_743
  <=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f8021,plain,
    ( spl0_911
  <=> 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_911])]) ).

fof(f10172,plain,
    ( spl0_1283
  <=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).

fof(f10520,plain,
    ( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
    | ~ spl0_717
    | ~ spl0_743
    | ~ spl0_911
    | ~ spl0_1283 ),
    inference(forward_demodulation,[],[f10519,f7207]) ).

fof(f7207,plain,
    ( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
    | ~ spl0_717 ),
    inference(avatar_component_clause,[],[f7205]) ).

fof(f10519,plain,
    ( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
    | ~ spl0_743
    | ~ spl0_911
    | ~ spl0_1283 ),
    inference(forward_demodulation,[],[f10515,f8023]) ).

fof(f8023,plain,
    ( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
    | ~ spl0_911 ),
    inference(avatar_component_clause,[],[f8021]) ).

fof(f10515,plain,
    ( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),c_Numeral_OPls)
    | ~ spl0_743
    | ~ spl0_1283 ),
    inference(superposition,[],[f10173,f7320]) ).

fof(f7320,plain,
    ( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
    | ~ spl0_743 ),
    inference(avatar_component_clause,[],[f7318]) ).

fof(f10173,plain,
    ( ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0)
    | ~ spl0_1283 ),
    inference(avatar_component_clause,[],[f10172]) ).

fof(f32048,plain,
    ( spl0_2487
    | ~ spl0_652
    | ~ spl0_1264 ),
    inference(avatar_split_clause,[],[f10435,f10095,f6149,f32045]) ).

fof(f32045,plain,
    ( spl0_2487
  <=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2487])]) ).

fof(f10095,plain,
    ( spl0_1264
  <=> ! [X59,X3] :
        ( ~ c_less(X3,X59,tc_nat)
        | c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).

fof(f10435,plain,
    ( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
    | ~ spl0_652
    | ~ spl0_1264 ),
    inference(resolution,[],[f10096,f6151]) ).

fof(f10096,plain,
    ( ! [X3,X59] :
        ( ~ c_less(X3,X59,tc_nat)
        | c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 )
    | ~ spl0_1264 ),
    inference(avatar_component_clause,[],[f10095]) ).

fof(f32035,plain,
    ( spl0_2486
    | ~ spl0_750
    | ~ spl0_1799 ),
    inference(avatar_split_clause,[],[f18183,f17104,f7360,f32032]) ).

fof(f32032,plain,
    ( spl0_2486
  <=> c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).

fof(f17104,plain,
    ( spl0_1799
  <=> ! [X41,X0,X23] :
        ( ~ c_in(X0,c_List_Oset(X23,X41),X41)
        | c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).

fof(f18183,plain,
    ( c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ spl0_750
    | ~ spl0_1799 ),
    inference(resolution,[],[f17105,f7362]) ).

fof(f17105,plain,
    ( ! [X41,X0,X23] :
        ( ~ c_in(X0,c_List_Oset(X23,X41),X41)
        | c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) )
    | ~ spl0_1799 ),
    inference(avatar_component_clause,[],[f17104]) ).

fof(f32000,plain,
    ( ~ spl0_4
    | spl0_2485
    | ~ spl0_750
    | ~ spl0_2443 ),
    inference(avatar_split_clause,[],[f31242,f31235,f7360,f31997,f3449]) ).

fof(f31235,plain,
    ( spl0_2443
  <=> ! [X102,X113,X13,X12,X112,X16,X86] :
        ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(X112,X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(X16,c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2443])]) ).

fof(f31242,plain,
    ( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_750
    | ~ spl0_2443 ),
    inference(resolution,[],[f31236,f7362]) ).

fof(f31236,plain,
    ( ! [X113,X86,X16,X12,X102,X13,X112] :
        ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(X16,c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(X112,X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
    | ~ spl0_2443 ),
    inference(avatar_component_clause,[],[f31235]) ).

fof(f31995,plain,
    ( spl0_2484
    | ~ spl0_114
    | ~ spl0_2010 ),
    inference(avatar_split_clause,[],[f21781,f20913,f3994,f31993]) ).

fof(f31993,plain,
    ( spl0_2484
  <=> ! [X0,X1] : c_minus(c_List_Oset(v_evso,tc_Event_Oevent),X0,tc_set(tc_Event_Oevent)) = c_minus(c_List_Oset(v_evso,tc_Event_Oevent),c_insert(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X1))),X0,tc_Event_Oevent),tc_set(tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2484])]) ).

fof(f20913,plain,
    ( spl0_2010
  <=> ! [X13,X0,X12,X1] :
        ( c_in(X0,X12,X1)
        | c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).

fof(f21781,plain,
    ( ! [X0,X1] : c_minus(c_List_Oset(v_evso,tc_Event_Oevent),X0,tc_set(tc_Event_Oevent)) = c_minus(c_List_Oset(v_evso,tc_Event_Oevent),c_insert(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X1))),X0,tc_Event_Oevent),tc_set(tc_Event_Oevent))
    | ~ spl0_114
    | ~ spl0_2010 ),
    inference(resolution,[],[f20914,f3995]) ).

fof(f20914,plain,
    ( ! [X0,X1,X12,X13] :
        ( c_in(X0,X12,X1)
        | c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) )
    | ~ spl0_2010 ),
    inference(avatar_component_clause,[],[f20913]) ).

fof(f31987,plain,
    ( spl0_2483
    | ~ spl0_750
    | ~ spl0_1842 ),
    inference(avatar_split_clause,[],[f18974,f17330,f7360,f31984]) ).

fof(f17330,plain,
    ( spl0_1842
  <=> ! [X102,X86,X12,X13] :
        ( c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).

fof(f18974,plain,
    ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_750
    | ~ spl0_1842 ),
    inference(resolution,[],[f17331,f7362]) ).

fof(f17331,plain,
    ( ! [X86,X12,X102,X13] :
        ( ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) )
    | ~ spl0_1842 ),
    inference(avatar_component_clause,[],[f17330]) ).

fof(f31954,plain,
    ( spl0_2482
    | spl0_5
    | ~ spl0_2010 ),
    inference(avatar_split_clause,[],[f21845,f20913,f3454,f31952]) ).

fof(f31952,plain,
    ( spl0_2482
  <=> ! [X0] : c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),c_insert(c_Message_Omsg_ONonce(v_NB),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2482])]) ).

fof(f21845,plain,
    ( ! [X0] : c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),c_insert(c_Message_Omsg_ONonce(v_NB),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg))
    | spl0_5
    | ~ spl0_2010 ),
    inference(resolution,[],[f20914,f3456]) ).

fof(f3456,plain,
    ( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | spl0_5 ),
    inference(avatar_component_clause,[],[f3454]) ).

fof(f31941,plain,
    ( spl0_2480
    | ~ spl0_2481
    | ~ spl0_814
    | ~ spl0_2469 ),
    inference(avatar_split_clause,[],[f31840,f31716,f7619,f31938,f31934]) ).

fof(f31934,plain,
    ( spl0_2480
  <=> c_Yahalom_Oyahalom = c_insert(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2480])]) ).

fof(f31938,plain,
    ( spl0_2481
  <=> c_emptyset = c_Yahalom_Oyahalom ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2481])]) ).

fof(f7619,plain,
    ( spl0_814
  <=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f31716,plain,
    ( spl0_2469
  <=> ! [X0] :
        ( c_emptyset != c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_emptyset = c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2469])]) ).

fof(f31840,plain,
    ( c_emptyset != c_Yahalom_Oyahalom
    | c_Yahalom_Oyahalom = c_insert(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_814
    | ~ spl0_2469 ),
    inference(inner_rewriting,[],[f31835]) ).

fof(f31835,plain,
    ( c_emptyset != c_Yahalom_Oyahalom
    | c_emptyset = c_insert(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_814
    | ~ spl0_2469 ),
    inference(superposition,[],[f31717,f7620]) ).

fof(f7620,plain,
    ( ! [X3,X1] : c_union(X3,X3,X1) = X3
    | ~ spl0_814 ),
    inference(avatar_component_clause,[],[f7619]) ).

fof(f31717,plain,
    ( ! [X0] :
        ( c_emptyset != c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_emptyset = c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)) )
    | ~ spl0_2469 ),
    inference(avatar_component_clause,[],[f31716]) ).

fof(f31932,plain,
    ( spl0_2479
    | ~ spl0_114
    | ~ spl0_1994 ),
    inference(avatar_split_clause,[],[f21457,f20849,f3994,f31930]) ).

fof(f31930,plain,
    ( spl0_2479
  <=> ! [X0,X1] : c_List_Olist__inter(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),X1,tc_Event_Oevent),v_evso,tc_Event_Oevent) = c_List_Olist__inter(X1,v_evso,tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2479])]) ).

fof(f20849,plain,
    ( spl0_1994
  <=> ! [X41,X60,X18,X65] :
        ( c_in(X18,c_List_Oset(X65,X41),X41)
        | c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).

fof(f21457,plain,
    ( ! [X0,X1] : c_List_Olist__inter(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),X1,tc_Event_Oevent),v_evso,tc_Event_Oevent) = c_List_Olist__inter(X1,v_evso,tc_Event_Oevent)
    | ~ spl0_114
    | ~ spl0_1994 ),
    inference(resolution,[],[f20850,f3995]) ).

fof(f20850,plain,
    ( ! [X65,X41,X18,X60] :
        ( c_in(X18,c_List_Oset(X65,X41),X41)
        | c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) )
    | ~ spl0_1994 ),
    inference(avatar_component_clause,[],[f20849]) ).

fof(f31928,plain,
    ( spl0_2478
    | ~ spl0_749
    | ~ spl0_1842 ),
    inference(avatar_split_clause,[],[f18973,f17330,f7355,f31925]) ).

fof(f18973,plain,
    ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
    | ~ spl0_749
    | ~ spl0_1842 ),
    inference(resolution,[],[f17331,f7357]) ).

fof(f31914,plain,
    spl0_2477,
    inference(avatar_split_clause,[],[f6,f31912]) ).

fof(f31912,plain,
    ( spl0_2477
  <=> ! [X5,X10,X9,X7,X8,X6,X2,X1] :
        ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2477])]) ).

fof(f6,axiom,
    ! [X2,X10,X1,X8,X6,X9,X7,X5] :
      ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).

fof(f31891,plain,
    spl0_2476,
    inference(avatar_split_clause,[],[f10,f31889]) ).

fof(f31889,plain,
    ( spl0_2476
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2476])]) ).

fof(f10,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).

fof(f31849,plain,
    spl0_2475,
    inference(avatar_split_clause,[],[f9,f31847]) ).

fof(f31847,plain,
    ( spl0_2475
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
        | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2475])]) ).

fof(f9,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
      | c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).

fof(f31845,plain,
    spl0_2474,
    inference(avatar_split_clause,[],[f8,f31843]) ).

fof(f31843,plain,
    ( spl0_2474
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
        | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2474])]) ).

fof(f8,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
      | c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).

fof(f31814,plain,
    spl0_2473,
    inference(avatar_split_clause,[],[f7,f31812]) ).

fof(f31812,plain,
    ( spl0_2473
  <=> ! [X5,X11,X6,X2,X1] :
        ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
        | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2473])]) ).

fof(f7,axiom,
    ! [X2,X11,X1,X6,X5] :
      ( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
      | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).

fof(f31798,plain,
    spl0_2472,
    inference(avatar_split_clause,[],[f2959,f31796]) ).

fof(f31796,plain,
    ( spl0_2472
  <=> ! [X102,X113,X13,X12,X91,X112] :
        ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | c_in(X13,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(X112,c_Message_Omsg_OMPair(X113,c_Message_Omsg_OKey(X91)))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OKey(X91))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).

fof(f2959,axiom,
    ! [X113,X91,X12,X102,X13,X112] :
      ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | c_in(X13,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(X112,c_Message_Omsg_OMPair(X113,c_Message_Omsg_OKey(X91)))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OKey(X91))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__not__see__encrypted__key_0) ).

fof(f31777,plain,
    spl0_2471,
    inference(avatar_split_clause,[],[f3,f31775]) ).

fof(f31775,plain,
    ( spl0_2471
  <=> ! [X5,X4,X6,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2471])]) ).

fof(f3,axiom,
    ! [X2,X1,X6,X4,X5] :
      ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).

fof(f31722,plain,
    spl0_2470,
    inference(avatar_split_clause,[],[f2962,f31720]) ).

fof(f2962,axiom,
    ! [X121,X86,X114,X102,X122,X12,X13,X112] :
      ( X114 = X122
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_Public_OshrK(v_sko__2VY(X121)) = X121
      | ~ c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X121),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X121),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X122))))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Osingle__Nonce__secrecy_1) ).

fof(f31718,plain,
    ( spl0_2469
    | ~ spl0_1090
    | ~ spl0_2451 ),
    inference(avatar_split_clause,[],[f31629,f31359,f8948,f31716]) ).

fof(f8948,plain,
    ( spl0_1090
  <=> ! [X13,X12,X1] :
        ( c_emptyset = X12
        | c_emptyset != c_union(X12,X13,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f31359,plain,
    ( spl0_2451
  <=> ! [X0] : c_union(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2451])]) ).

fof(f31629,plain,
    ( ! [X0] :
        ( c_emptyset != c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_emptyset = c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)) )
    | ~ spl0_1090
    | ~ spl0_2451 ),
    inference(superposition,[],[f8949,f31360]) ).

fof(f31360,plain,
    ( ! [X0] : c_union(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_2451 ),
    inference(avatar_component_clause,[],[f31359]) ).

fof(f8949,plain,
    ( ! [X1,X12,X13] :
        ( c_emptyset != c_union(X12,X13,X1)
        | c_emptyset = X12 )
    | ~ spl0_1090 ),
    inference(avatar_component_clause,[],[f8948]) ).

fof(f31714,plain,
    spl0_2468,
    inference(avatar_split_clause,[],[f2961,f31712]) ).

fof(f2961,axiom,
    ! [X121,X86,X114,X102,X122,X12,X13,X112] :
      ( X114 = X122
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_Public_OshrK(v_sko__2VY(X121)) = X121
      | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X121),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X121),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X122))))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Osingle__Nonce__secrecy_0) ).

fof(f31710,plain,
    spl0_2467,
    inference(avatar_split_clause,[],[f2941,f31708]) ).

fof(f31708,plain,
    ( spl0_2467
  <=> ! [X102,X113,X13,X12,X91,X112] :
        ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OKey(X91))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2467])]) ).

fof(f2941,axiom,
    ! [X113,X91,X12,X102,X13,X112] :
      ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OKey(X91))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OA__trusts__YM3_0) ).

fof(f31655,plain,
    spl0_2466,
    inference(avatar_split_clause,[],[f2958,f31653]) ).

fof(f2958,axiom,
    ! [X113,X111,X118,X119,X116,X117,X86,X107,X22,X102,X32,X13,X12] :
      ( X13 = X117
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_2) ).

fof(f31651,plain,
    spl0_2465,
    inference(avatar_split_clause,[],[f2957,f31649]) ).

fof(f2957,axiom,
    ! [X113,X111,X118,X119,X116,X117,X86,X107,X22,X12,X102,X32,X13] :
      ( X12 = X111
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_1) ).

fof(f31647,plain,
    spl0_2464,
    inference(avatar_split_clause,[],[f2956,f31645]) ).

fof(f2956,axiom,
    ! [X113,X111,X118,X119,X116,X117,X86,X107,X22,X102,X32,X13,X12] :
      ( X118 = X119
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(X113,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OGets(X116,c_Message_Omsg_OMPair(X107,c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X118),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(X32,X22,c_Message_Omsg_OMPair(X86,c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X119),X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_0) ).

fof(f31623,plain,
    spl0_2463,
    inference(avatar_split_clause,[],[f12,f31621]) ).

fof(f31621,plain,
    ( spl0_2463
  <=> ! [X5,X7,X8,X6,X2,X1] :
        ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2463])]) ).

fof(f12,axiom,
    ! [X2,X1,X8,X6,X7,X5] :
      ( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).

fof(f31619,plain,
    spl0_2462,
    inference(avatar_split_clause,[],[f11,f31617]) ).

fof(f31617,plain,
    ( spl0_2462
  <=> ! [X6,X9,X10,X5,X2,X1] :
        ( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2462])]) ).

fof(f11,axiom,
    ! [X2,X10,X1,X6,X9,X5] :
      ( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).

fof(f31571,plain,
    spl0_2461,
    inference(avatar_split_clause,[],[f2966,f31569]) ).

fof(f2966,axiom,
    ! [X113,X120,X111,X91,X117,X86,X107,X102,X12,X13,X112,X123] :
      ( X113 = X120
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_3) ).

fof(f31567,plain,
    spl0_2460,
    inference(avatar_split_clause,[],[f2965,f31565]) ).

fof(f2965,axiom,
    ! [X113,X111,X120,X91,X117,X86,X107,X102,X12,X112,X123,X13] :
      ( X112 = X123
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_2) ).

fof(f31563,plain,
    spl0_2459,
    inference(avatar_split_clause,[],[f2964,f31561]) ).

fof(f2964,axiom,
    ! [X113,X111,X120,X91,X117,X86,X107,X102,X12,X13,X112,X123] :
      ( X13 = X117
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_1) ).

fof(f31559,plain,
    spl0_2458,
    inference(avatar_split_clause,[],[f2963,f31557]) ).

fof(f2963,axiom,
    ! [X113,X111,X120,X91,X117,X86,X107,X12,X102,X13,X112,X123] :
      ( X12 = X111
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys__dest_0) ).

fof(f31555,plain,
    ( spl0_2457
    | ~ spl0_1552
    | ~ spl0_2439 ),
    inference(avatar_split_clause,[],[f31282,f31161,f12730,f31553]) ).

fof(f31553,plain,
    ( spl0_2457
  <=> ! [X0] : c_union(c_Yahalom_Oyahalom,c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),tc_List_Olist(tc_Event_Oevent)) = c_union(c_Yahalom_Oyahalom,X0,tc_List_Olist(tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2457])]) ).

fof(f12730,plain,
    ( spl0_1552
  <=> ! [X13,X12,X1] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).

fof(f31161,plain,
    ( spl0_2439
  <=> ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2439])]) ).

fof(f31282,plain,
    ( ! [X0] : c_union(c_Yahalom_Oyahalom,c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),tc_List_Olist(tc_Event_Oevent)) = c_union(c_Yahalom_Oyahalom,X0,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_1552
    | ~ spl0_2439 ),
    inference(forward_demodulation,[],[f31268,f12731]) ).

fof(f12731,plain,
    ( ! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1)
    | ~ spl0_1552 ),
    inference(avatar_component_clause,[],[f12730]) ).

fof(f31268,plain,
    ( ! [X0] : c_union(c_Yahalom_Oyahalom,c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),tc_List_Olist(tc_Event_Oevent)) = c_union(c_Yahalom_Oyahalom,c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))),tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_1552
    | ~ spl0_2439 ),
    inference(superposition,[],[f12731,f31162]) ).

fof(f31162,plain,
    ( ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent)))
    | ~ spl0_2439 ),
    inference(avatar_component_clause,[],[f31161]) ).

fof(f31511,plain,
    ( spl0_2456
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1814
    | ~ spl0_1815
    | ~ spl0_2455 ),
    inference(avatar_split_clause,[],[f31507,f31502,f17169,f17165,f14540,f10172,f8896,f7554,f3714,f31509]) ).

fof(f31509,plain,
    ( spl0_2456
  <=> ! [X11,X47] :
        ( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2456])]) ).

fof(f3714,plain,
    ( spl0_57
  <=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f7554,plain,
    ( spl0_798
  <=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f8896,plain,
    ( spl0_1077
  <=> ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f14540,plain,
    ( spl0_1675
  <=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).

fof(f17165,plain,
    ( spl0_1814
  <=> ! [X11,X1,X47] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).

fof(f17169,plain,
    ( spl0_1815
  <=> ! [X11,X1,X47] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).

fof(f31502,plain,
    ( spl0_2455
  <=> ! [X11,X47] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2455])]) ).

fof(f31507,plain,
    ( ! [X11,X47] :
        ( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1814
    | ~ spl0_1815
    | ~ spl0_2455 ),
    inference(forward_demodulation,[],[f31506,f18372]) ).

fof(f18372,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_57
    | ~ spl0_1814 ),
    inference(resolution,[],[f17166,f3716]) ).

fof(f3716,plain,
    ( class_Numeral_Onumber__ring(tc_IntDef_Oint)
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f3714]) ).

fof(f17166,plain,
    ( ! [X11,X1,X47] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) )
    | ~ spl0_1814 ),
    inference(avatar_component_clause,[],[f17165]) ).

fof(f31506,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1815
    | ~ spl0_2455 ),
    inference(forward_demodulation,[],[f31505,f15147]) ).

fof(f15147,plain,
    ( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675 ),
    inference(forward_demodulation,[],[f15146,f7556]) ).

fof(f7556,plain,
    ( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
    | ~ spl0_798 ),
    inference(avatar_component_clause,[],[f7554]) ).

fof(f15146,plain,
    ( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X0)
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675 ),
    inference(forward_demodulation,[],[f15145,f8897]) ).

fof(f8897,plain,
    ( ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0)
    | ~ spl0_1077 ),
    inference(avatar_component_clause,[],[f8896]) ).

fof(f15145,plain,
    ( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X0)
    | ~ spl0_1283
    | ~ spl0_1675 ),
    inference(superposition,[],[f10173,f14541]) ).

fof(f14541,plain,
    ( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
    | ~ spl0_1675 ),
    inference(avatar_component_clause,[],[f14540]) ).

fof(f31505,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1815
    | ~ spl0_2455 ),
    inference(forward_demodulation,[],[f31503,f18373]) ).

fof(f18373,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_57
    | ~ spl0_1815 ),
    inference(resolution,[],[f17170,f3716]) ).

fof(f17170,plain,
    ( ! [X11,X1,X47] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) )
    | ~ spl0_1815 ),
    inference(avatar_component_clause,[],[f17169]) ).

fof(f31503,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_2455 ),
    inference(avatar_component_clause,[],[f31502]) ).

fof(f31504,plain,
    spl0_2455,
    inference(avatar_split_clause,[],[f3410,f31502]) ).

fof(f3410,plain,
    ! [X11,X47] :
      ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3409,f2156]) ).

fof(f2156,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(f3409,plain,
    ! [X11,X47] :
      ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3408,f2154]) ).

fof(f2154,axiom,
    ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).

fof(f3408,plain,
    ! [X11,X47] :
      ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1452,f2156]) ).

fof(f1452,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).

fof(f31373,plain,
    spl0_2454,
    inference(avatar_split_clause,[],[f1620,f31371]) ).

fof(f31371,plain,
    ( spl0_2454
  <=> ! [X5,X18,X3,X0,X27,X1] :
        ( c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
        | c_in(c_Pair(X0,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2454])]) ).

fof(f1620,axiom,
    ! [X3,X0,X18,X1,X27,X5] :
      ( c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
      | c_in(c_Pair(X0,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).

fof(f31369,plain,
    spl0_2453,
    inference(avatar_split_clause,[],[f1501,f31367]) ).

fof(f31367,plain,
    ( spl0_2453
  <=> ! [X3,X23,X0,X5,X25,X1] :
        ( c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
        | c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2453])]) ).

fof(f1501,axiom,
    ! [X3,X0,X1,X5,X25,X23] :
      ( c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
      | c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).

fof(f31365,plain,
    spl0_2452,
    inference(avatar_split_clause,[],[f5,f31363]) ).

fof(f31363,plain,
    ( spl0_2452
  <=> ! [X5,X4,X6,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2452])]) ).

fof(f5,axiom,
    ! [X2,X1,X6,X4,X5] :
      ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).

fof(f31361,plain,
    ( spl0_2451
    | ~ spl0_1551
    | ~ spl0_2439 ),
    inference(avatar_split_clause,[],[f31281,f31161,f12726,f31359]) ).

fof(f12726,plain,
    ( spl0_1551
  <=> ! [X13,X12,X1] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).

fof(f31281,plain,
    ( ! [X0] : c_union(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = c_union(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_1551
    | ~ spl0_2439 ),
    inference(forward_demodulation,[],[f31267,f12727]) ).

fof(f12727,plain,
    ( ! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1)
    | ~ spl0_1551 ),
    inference(avatar_component_clause,[],[f12726]) ).

fof(f31267,plain,
    ( ! [X0] : c_union(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = c_union(c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))),c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_1551
    | ~ spl0_2439 ),
    inference(superposition,[],[f12727,f31162]) ).

fof(f31357,plain,
    spl0_2450,
    inference(avatar_split_clause,[],[f4,f31355]) ).

fof(f31355,plain,
    ( spl0_2450
  <=> ! [X5,X4,X6,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
        | c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2450])]) ).

fof(f4,axiom,
    ! [X2,X1,X6,X4,X5] :
      ( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
      | c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).

fof(f31317,plain,
    spl0_2449,
    inference(avatar_split_clause,[],[f1503,f31315]) ).

fof(f31315,plain,
    ( spl0_2449
  <=> ! [X3,X23,X0,X5,X25,X1] :
        ( c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
        | c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2449])]) ).

fof(f1503,axiom,
    ! [X3,X0,X1,X5,X25,X23] :
      ( c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
      | c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).

fof(f31313,plain,
    spl0_2448,
    inference(avatar_split_clause,[],[f1369,f31311]) ).

fof(f31311,plain,
    ( spl0_2448
  <=> ! [X0,X3] :
        ( ~ c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
        | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2448])]) ).

fof(f1369,axiom,
    ! [X3,X0] :
      ( ~ c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).

fof(f31309,plain,
    spl0_2447,
    inference(avatar_split_clause,[],[f1368,f31307]) ).

fof(f31307,plain,
    ( spl0_2447
  <=> ! [X0,X3] :
        ( c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
        | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2447])]) ).

fof(f1368,axiom,
    ! [X3,X0] :
      ( c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
      | c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).

fof(f31293,plain,
    ( spl0_2446
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1815
    | ~ spl0_2445 ),
    inference(avatar_split_clause,[],[f31289,f31285,f17169,f14540,f10172,f8896,f7554,f3714,f31291]) ).

fof(f31291,plain,
    ( spl0_2446
  <=> ! [X11,X47] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2446])]) ).

fof(f31285,plain,
    ( spl0_2445
  <=> ! [X11,X47] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2445])]) ).

fof(f31289,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1815
    | ~ spl0_2445 ),
    inference(forward_demodulation,[],[f31288,f15147]) ).

fof(f31288,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1815
    | ~ spl0_2445 ),
    inference(forward_demodulation,[],[f31286,f18373]) ).

fof(f31286,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_2445 ),
    inference(avatar_component_clause,[],[f31285]) ).

fof(f31287,plain,
    spl0_2445,
    inference(avatar_split_clause,[],[f3404,f31285]) ).

fof(f3404,plain,
    ! [X11,X47] :
      ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3403,f2156]) ).

fof(f3403,plain,
    ! [X11,X47] :
      ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3402,f2154]) ).

fof(f3402,plain,
    ! [X11,X47] :
      ( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1461,f2156]) ).

fof(f1461,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).

fof(f31241,plain,
    spl0_2444,
    inference(avatar_split_clause,[],[f2960,f31239]) ).

fof(f31239,plain,
    ( spl0_2444
  <=> ! [X102,X13,X117,X12,X114,X112,X120,X111] :
        ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X114)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X114),X120))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2444])]) ).

fof(f2960,axiom,
    ! [X111,X120,X117,X114,X102,X12,X13,X112] :
      ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(c_Message_Omsg_ONonce(X114),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(X112,c_Message_Omsg_ONonce(X114)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X111),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X114),X120))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ono__nonce__YM1__YM2_0) ).

fof(f31237,plain,
    spl0_2443,
    inference(avatar_split_clause,[],[f2955,f31235]) ).

fof(f2955,axiom,
    ! [X113,X86,X16,X102,X12,X13,X112] :
      ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OMPair(X112,X113))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(X16,c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).

fof(f31198,plain,
    spl0_2442,
    inference(avatar_split_clause,[],[f1791,f31196]) ).

fof(f31196,plain,
    ( spl0_2442
  <=> ! [X52,X53,X23,X25,X2,X1] :
        ( c_Nat_Osize(X25,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X2))
        | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X52,tc_List_Olist(X2))
        | c_List_Ozip(c_append(X23,X25,X1),c_append(X52,X53,X2),X1,X2) = c_append(c_List_Ozip(X23,X52,X1,X2),c_List_Ozip(X25,X53,X1,X2),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2442])]) ).

fof(f1791,axiom,
    ! [X2,X1,X52,X53,X25,X23] :
      ( c_Nat_Osize(X25,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X2))
      | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X52,tc_List_Olist(X2))
      | c_List_Ozip(c_append(X23,X25,X1),c_append(X52,X53,X2),X1,X2) = c_append(c_List_Ozip(X23,X52,X1,X2),c_List_Ozip(X25,X53,X1,X2),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).

fof(f31173,plain,
    ( spl0_2441
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1815
    | ~ spl0_2440 ),
    inference(avatar_split_clause,[],[f31169,f31165,f17169,f14540,f10172,f8896,f7554,f3714,f31171]) ).

fof(f31171,plain,
    ( spl0_2441
  <=> ! [X11] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2441])]) ).

fof(f31165,plain,
    ( spl0_2440
  <=> ! [X11] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2440])]) ).

fof(f31169,plain,
    ( ! [X11] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1815
    | ~ spl0_2440 ),
    inference(forward_demodulation,[],[f31168,f15147]) ).

fof(f31168,plain,
    ( ! [X11] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1815
    | ~ spl0_2440 ),
    inference(forward_demodulation,[],[f31166,f18373]) ).

fof(f31166,plain,
    ( ! [X11] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_2440 ),
    inference(avatar_component_clause,[],[f31165]) ).

fof(f31167,plain,
    spl0_2440,
    inference(avatar_split_clause,[],[f3407,f31165]) ).

fof(f3407,plain,
    ! [X11] :
      ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3406,f2156]) ).

fof(f3406,plain,
    ! [X11] :
      ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3405,f2154]) ).

fof(f3405,plain,
    ! [X11] :
      ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1450,f2156]) ).

fof(f1450,axiom,
    ! [X11] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).

fof(f31163,plain,
    ( spl0_2439
    | ~ spl0_4
    | ~ spl0_2012 ),
    inference(avatar_split_clause,[],[f22003,f20921,f3449,f31161]) ).

fof(f22003,plain,
    ( ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evso,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent)))
    | ~ spl0_4
    | ~ spl0_2012 ),
    inference(resolution,[],[f20922,f3451]) ).

fof(f3451,plain,
    ( c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f3449]) ).

fof(f31159,plain,
    spl0_2438,
    inference(avatar_split_clause,[],[f2948,f31157]) ).

fof(f31157,plain,
    ( spl0_2438
  <=> ! [X102,X12,X114,X91,X22,X86] :
        ( c_Yahalom_OKeyWithNonce(X91,X114,X102)
        | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(X22,X12,X86),X102,tc_Event_Oevent))
        | c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_sko__2VZ(X12,X91,X114,X86)),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(v_sko__2Va(X12,X91,X114,X86),c_Message_Omsg_ONonce(X114))))),v_sko__2Vb(X12,X91,X114,X86)) = X86 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2438])]) ).

fof(f2948,axiom,
    ! [X91,X86,X114,X22,X102,X12] :
      ( c_Yahalom_OKeyWithNonce(X91,X114,X102)
      | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(X22,X12,X86),X102,tc_Event_Oevent))
      | c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_sko__2VZ(X12,X91,X114,X86)),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(v_sko__2Va(X12,X91,X114,X86),c_Message_Omsg_ONonce(X114))))),v_sko__2Vb(X12,X91,X114,X86)) = X86 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_1) ).

fof(f31120,plain,
    ( spl0_2437
    | ~ spl0_57
    | ~ spl0_1814
    | ~ spl0_1850
    | ~ spl0_2436 ),
    inference(avatar_split_clause,[],[f31116,f31111,f17549,f17165,f3714,f31118]) ).

fof(f31118,plain,
    ( spl0_2437
  <=> ! [X11,X47] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2437])]) ).

fof(f31111,plain,
    ( spl0_2436
  <=> ! [X11,X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2436])]) ).

fof(f31116,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1814
    | ~ spl0_1850
    | ~ spl0_2436 ),
    inference(forward_demodulation,[],[f31115,f17551]) ).

fof(f31115,plain,
    ( ! [X11,X47] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1814
    | ~ spl0_2436 ),
    inference(forward_demodulation,[],[f31114,f18372]) ).

fof(f31114,plain,
    ( ! [X11,X47] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1814
    | ~ spl0_2436 ),
    inference(forward_demodulation,[],[f31112,f18372]) ).

fof(f31112,plain,
    ( ! [X11,X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2436 ),
    inference(avatar_component_clause,[],[f31111]) ).

fof(f31113,plain,
    spl0_2436,
    inference(avatar_split_clause,[],[f1451,f31111]) ).

fof(f1451,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).

fof(f31078,plain,
    spl0_2435,
    inference(avatar_split_clause,[],[f1504,f31076]) ).

fof(f31076,plain,
    ( spl0_2435
  <=> ! [X3,X23,X0,X5,X25,X1] :
        ( c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
        | ~ c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
        | c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2435])]) ).

fof(f1504,axiom,
    ! [X3,X0,X1,X5,X25,X23] :
      ( c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
      | ~ c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
      | c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).

fof(f31051,plain,
    ( spl0_2434
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1815
    | ~ spl0_2433 ),
    inference(avatar_split_clause,[],[f31045,f31041,f17169,f14540,f10172,f8896,f7554,f3714,f31049]) ).

fof(f31049,plain,
    ( spl0_2434
  <=> ! [X11] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2434])]) ).

fof(f31041,plain,
    ( spl0_2433
  <=> ! [X11] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2433])]) ).

fof(f31045,plain,
    ( ! [X11] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_798
    | ~ spl0_1077
    | ~ spl0_1283
    | ~ spl0_1675
    | ~ spl0_1815
    | ~ spl0_2433 ),
    inference(forward_demodulation,[],[f31044,f15147]) ).

fof(f31044,plain,
    ( ! [X11] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1815
    | ~ spl0_2433 ),
    inference(forward_demodulation,[],[f31042,f18373]) ).

fof(f31042,plain,
    ( ! [X11] :
        ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_2433 ),
    inference(avatar_component_clause,[],[f31041]) ).

fof(f31043,plain,
    spl0_2433,
    inference(avatar_split_clause,[],[f3401,f31041]) ).

fof(f3401,plain,
    ! [X11] :
      ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3400,f2156]) ).

fof(f3400,plain,
    ! [X11] :
      ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3399,f2154]) ).

fof(f3399,plain,
    ! [X11] :
      ( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
      | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1459,f2156]) ).

fof(f1459,axiom,
    ! [X11] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).

fof(f31039,plain,
    spl0_2432,
    inference(avatar_split_clause,[],[f54,f31037]) ).

fof(f31037,plain,
    ( spl0_2432
  <=> ! [X3,X23,X5,X25,X1] :
        ( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2432])]) ).

fof(f54,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).

fof(f31035,plain,
    spl0_2431,
    inference(avatar_split_clause,[],[f51,f31033]) ).

fof(f31033,plain,
    ( spl0_2431
  <=> ! [X3,X23,X5,X25,X1] :
        ( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2431])]) ).

fof(f51,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).

fof(f31015,plain,
    ( spl0_2430
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2425 ),
    inference(avatar_split_clause,[],[f30919,f30916,f12670,f9587,f31013]) ).

fof(f31013,plain,
    ( spl0_2430
  <=> ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2430])]) ).

fof(f9587,plain,
    ( spl0_1195
  <=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).

fof(f30916,plain,
    ( spl0_2425
  <=> ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2425])]) ).

fof(f30919,plain,
    ( ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2425 ),
    inference(forward_demodulation,[],[f30917,f13748]) ).

fof(f13748,plain,
    ( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
    | ~ spl0_1195
    | ~ spl0_1537 ),
    inference(superposition,[],[f9588,f12671]) ).

fof(f9588,plain,
    ( ! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3
    | ~ spl0_1195 ),
    inference(avatar_component_clause,[],[f9587]) ).

fof(f30917,plain,
    ( ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_2425 ),
    inference(avatar_component_clause,[],[f30916]) ).

fof(f31011,plain,
    ( spl0_2429
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2424 ),
    inference(avatar_split_clause,[],[f30914,f30911,f12670,f9583,f31009]) ).

fof(f31009,plain,
    ( spl0_2429
  <=> ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2429])]) ).

fof(f9583,plain,
    ( spl0_1194
  <=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).

fof(f30911,plain,
    ( spl0_2424
  <=> ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2424])]) ).

fof(f30914,plain,
    ( ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2424 ),
    inference(forward_demodulation,[],[f30912,f13749]) ).

fof(f13749,plain,
    ( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
    | ~ spl0_1194
    | ~ spl0_1537 ),
    inference(superposition,[],[f9584,f12671]) ).

fof(f9584,plain,
    ( ! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3
    | ~ spl0_1194 ),
    inference(avatar_component_clause,[],[f9583]) ).

fof(f30912,plain,
    ( ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_2424 ),
    inference(avatar_component_clause,[],[f30911]) ).

fof(f31007,plain,
    ( spl0_2428
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2423 ),
    inference(avatar_split_clause,[],[f30909,f30906,f12670,f9587,f31005]) ).

fof(f31005,plain,
    ( spl0_2428
  <=> ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2428])]) ).

fof(f30906,plain,
    ( spl0_2423
  <=> ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2423])]) ).

fof(f30909,plain,
    ( ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2423 ),
    inference(forward_demodulation,[],[f30907,f13748]) ).

fof(f30907,plain,
    ( ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_2423 ),
    inference(avatar_component_clause,[],[f30906]) ).

fof(f31003,plain,
    ( ~ spl0_2427
    | ~ spl0_787
    | ~ spl0_2395 ),
    inference(avatar_split_clause,[],[f30893,f30556,f7510,f31000]) ).

fof(f31000,plain,
    ( spl0_2427
  <=> c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2427])]) ).

fof(f30556,plain,
    ( spl0_2395
  <=> ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2395])]) ).

fof(f30893,plain,
    ( ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_787
    | ~ spl0_2395 ),
    inference(superposition,[],[f30557,f7511]) ).

fof(f30557,plain,
    ( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2395 ),
    inference(avatar_component_clause,[],[f30556]) ).

fof(f30998,plain,
    ( spl0_2426
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2422 ),
    inference(avatar_split_clause,[],[f30904,f30901,f12670,f9583,f30996]) ).

fof(f30996,plain,
    ( spl0_2426
  <=> ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2426])]) ).

fof(f30901,plain,
    ( spl0_2422
  <=> ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2422])]) ).

fof(f30904,plain,
    ( ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2422 ),
    inference(forward_demodulation,[],[f30902,f13749]) ).

fof(f30902,plain,
    ( ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_2422 ),
    inference(avatar_component_clause,[],[f30901]) ).

fof(f30918,plain,
    spl0_2425,
    inference(avatar_split_clause,[],[f3398,f30916]) ).

fof(f3398,plain,
    ! [X11,X47] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1446,f1456]) ).

fof(f1456,axiom,
    ! [X49,X5] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).

fof(f1446,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__number__of_0) ).

fof(f30913,plain,
    spl0_2424,
    inference(avatar_split_clause,[],[f3397,f30911]) ).

fof(f3397,plain,
    ! [X11,X47] :
      ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1436,f1456]) ).

fof(f1436,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__number__of_0) ).

fof(f30908,plain,
    spl0_2423,
    inference(avatar_split_clause,[],[f3396,f30906]) ).

fof(f3396,plain,
    ! [X11,X47] :
      ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1443,f1456]) ).

fof(f1443,axiom,
    ! [X11,X47] :
      ( ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__neg__number__of_0) ).

fof(f30903,plain,
    spl0_2422,
    inference(avatar_split_clause,[],[f3395,f30901]) ).

fof(f3395,plain,
    ! [X11,X47] :
      ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
      | ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1433,f1456]) ).

fof(f1433,axiom,
    ! [X11,X47] :
      ( ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__neg__number__of_0) ).

fof(f30899,plain,
    spl0_2421,
    inference(avatar_split_clause,[],[f1622,f30897]) ).

fof(f30897,plain,
    ( spl0_2421
  <=> ! [X62,X3,X0,X5,X1] :
        ( ~ c_in(c_Pair(X62,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_in(c_Pair(c_List_Olist_OCons(X0,X62,X1),c_List_Olist_OCons(X0,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2421])]) ).

fof(f1622,axiom,
    ! [X3,X0,X1,X62,X5] :
      ( ~ c_in(c_Pair(X62,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | c_in(c_Pair(c_List_Olist_OCons(X0,X62,X1),c_List_Olist_OCons(X0,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).

fof(f30891,plain,
    spl0_2420,
    inference(avatar_split_clause,[],[f1505,f30889]) ).

fof(f30889,plain,
    ( spl0_2420
  <=> ! [X23,X0,X5,X25,X1] :
        ( ~ c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
        | c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X0,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2420])]) ).

fof(f1505,axiom,
    ! [X0,X1,X5,X25,X23] :
      ( ~ c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
      | c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X0,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).

fof(f30887,plain,
    spl0_2419,
    inference(avatar_split_clause,[],[f1188,f30885]) ).

fof(f30885,plain,
    ( spl0_2419
  <=> ! [X5,X6,X2,X1] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2419])]) ).

fof(f1188,axiom,
    ! [X2,X1,X6,X5] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).

fof(f30883,plain,
    spl0_2418,
    inference(avatar_split_clause,[],[f1187,f30881]) ).

fof(f30881,plain,
    ( spl0_2418
  <=> ! [X5,X6,X2,X1] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2418])]) ).

fof(f1187,axiom,
    ! [X2,X1,X6,X5] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).

fof(f30855,plain,
    ( spl0_2417
    | ~ spl0_1850
    | ~ spl0_2415 ),
    inference(avatar_split_clause,[],[f30847,f30844,f17549,f30853]) ).

fof(f30853,plain,
    ( spl0_2417
  <=> ! [X11] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2417])]) ).

fof(f30844,plain,
    ( spl0_2415
  <=> ! [X11] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2415])]) ).

fof(f30847,plain,
    ( ! [X11] :
        ( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1850
    | ~ spl0_2415 ),
    inference(forward_demodulation,[],[f30845,f17551]) ).

fof(f30845,plain,
    ( ! [X11] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2415 ),
    inference(avatar_component_clause,[],[f30844]) ).

fof(f30851,plain,
    spl0_2416,
    inference(avatar_split_clause,[],[f1705,f30849]) ).

fof(f30849,plain,
    ( spl0_2416
  <=> ! [X43,X23,X25,X2,X1] :
        ( ~ c_less(X43,c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat)
        | ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
        | c_List_Onth(c_List_Ozip(X23,X25,X1,X2),X43,tc_prod(X1,X2)) = c_Pair(c_List_Onth(X23,X43,X1),c_List_Onth(X25,X43,X2),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2416])]) ).

fof(f1705,axiom,
    ! [X2,X1,X25,X23,X43] :
      ( ~ c_less(X43,c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat)
      | ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
      | c_List_Onth(c_List_Ozip(X23,X25,X1,X2),X43,tc_prod(X1,X2)) = c_Pair(c_List_Onth(X23,X43,X1),c_List_Onth(X25,X43,X2),X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).

fof(f30846,plain,
    spl0_2415,
    inference(avatar_split_clause,[],[f1449,f30844]) ).

fof(f1449,axiom,
    ! [X11] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).

fof(f30697,plain,
    spl0_2414,
    inference(avatar_split_clause,[],[f1619,f30695]) ).

fof(f30695,plain,
    ( spl0_2414
  <=> ! [X18,X3,X0,X5,X27,X1] :
        ( X18 = X27
        | c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2414])]) ).

fof(f1619,axiom,
    ! [X3,X0,X18,X1,X27,X5] :
      ( X18 = X27
      | c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).

fof(f30693,plain,
    spl0_2413,
    inference(avatar_split_clause,[],[f1500,f30691]) ).

fof(f30691,plain,
    ( spl0_2413
  <=> ! [X3,X23,X0,X5,X25,X1] :
        ( X0 = X3
        | c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2413])]) ).

fof(f1500,axiom,
    ! [X3,X0,X1,X5,X25,X23] :
      ( X0 = X3
      | c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).

fof(f30689,plain,
    spl0_2412,
    inference(avatar_split_clause,[],[f1383,f30687]) ).

fof(f30687,plain,
    ( spl0_2412
  <=> ! [X47,X0,X14,X3] :
        ( c_plus(X0,X47,tc_nat) != c_plus(X14,X3,tc_nat)
        | c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2412])]) ).

fof(f1383,axiom,
    ! [X3,X0,X47,X14] :
      ( c_plus(X0,X47,tc_nat) != c_plus(X14,X3,tc_nat)
      | c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).

fof(f30685,plain,
    spl0_2411,
    inference(avatar_split_clause,[],[f1382,f30683]) ).

fof(f30683,plain,
    ( spl0_2411
  <=> ! [X47,X0,X14,X3] :
        ( c_plus(X0,X47,tc_nat) = c_plus(X14,X3,tc_nat)
        | ~ c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2411])]) ).

fof(f1382,axiom,
    ! [X3,X0,X47,X14] :
      ( c_plus(X0,X47,tc_nat) = c_plus(X14,X3,tc_nat)
      | ~ c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).

fof(f30681,plain,
    spl0_2410,
    inference(avatar_split_clause,[],[f85,f30679]) ).

fof(f30679,plain,
    ( spl0_2410
  <=> ! [X31,X4,X18,X6,X5,X27,X2,X1] :
        ( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
        | ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
        | c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2410])]) ).

fof(f85,axiom,
    ! [X2,X31,X18,X1,X6,X27,X4,X5] :
      ( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
      | ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
      | c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).

fof(f30677,plain,
    ( ~ spl0_2409
    | ~ spl0_787
    | ~ spl0_2390 ),
    inference(avatar_split_clause,[],[f30615,f30344,f7510,f30674]) ).

fof(f30674,plain,
    ( spl0_2409
  <=> c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2409])]) ).

fof(f30344,plain,
    ( spl0_2390
  <=> ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2390])]) ).

fof(f30615,plain,
    ( ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_1,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_787
    | ~ spl0_2390 ),
    inference(superposition,[],[f30345,f7511]) ).

fof(f30345,plain,
    ( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2390 ),
    inference(avatar_component_clause,[],[f30344]) ).

fof(f30672,plain,
    spl0_2408,
    inference(avatar_split_clause,[],[f53,f30670]) ).

fof(f30670,plain,
    ( spl0_2408
  <=> ! [X5,X3,X23,X25,X1] :
        ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
        | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2408])]) ).

fof(f53,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
      | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).

fof(f30668,plain,
    spl0_2407,
    inference(avatar_split_clause,[],[f50,f30666]) ).

fof(f30666,plain,
    ( spl0_2407
  <=> ! [X5,X3,X23,X25,X1] :
        ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
        | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2407])]) ).

fof(f50,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
      | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).

fof(f30629,plain,
    ( spl0_2406
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2401 ),
    inference(avatar_split_clause,[],[f30586,f30583,f12670,f9587,f30627]) ).

fof(f30627,plain,
    ( spl0_2406
  <=> ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2406])]) ).

fof(f30583,plain,
    ( spl0_2401
  <=> ! [X11,X47] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2401])]) ).

fof(f30586,plain,
    ( ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2401 ),
    inference(forward_demodulation,[],[f30584,f13748]) ).

fof(f30584,plain,
    ( ! [X11,X47] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2401 ),
    inference(avatar_component_clause,[],[f30583]) ).

fof(f30625,plain,
    ( spl0_2405
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2400 ),
    inference(avatar_split_clause,[],[f30581,f30578,f12670,f9587,f30623]) ).

fof(f30623,plain,
    ( spl0_2405
  <=> ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2405])]) ).

fof(f30578,plain,
    ( spl0_2400
  <=> ! [X11,X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2400])]) ).

fof(f30581,plain,
    ( ! [X11,X47] :
        ( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2400 ),
    inference(forward_demodulation,[],[f30579,f13748]) ).

fof(f30579,plain,
    ( ! [X11,X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2400 ),
    inference(avatar_component_clause,[],[f30578]) ).

fof(f30621,plain,
    ( spl0_2404
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2399 ),
    inference(avatar_split_clause,[],[f30576,f30573,f12670,f9583,f30619]) ).

fof(f30619,plain,
    ( spl0_2404
  <=> ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2404])]) ).

fof(f30573,plain,
    ( spl0_2399
  <=> ! [X11,X47] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2399])]) ).

fof(f30576,plain,
    ( ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2399 ),
    inference(forward_demodulation,[],[f30574,f13749]) ).

fof(f30574,plain,
    ( ! [X11,X47] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2399 ),
    inference(avatar_component_clause,[],[f30573]) ).

fof(f30613,plain,
    ( spl0_2403
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2398 ),
    inference(avatar_split_clause,[],[f30571,f30568,f12670,f9583,f30611]) ).

fof(f30611,plain,
    ( spl0_2403
  <=> ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2403])]) ).

fof(f30568,plain,
    ( spl0_2398
  <=> ! [X11,X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2398])]) ).

fof(f30571,plain,
    ( ! [X11,X47] :
        ( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2398 ),
    inference(forward_demodulation,[],[f30569,f13749]) ).

fof(f30569,plain,
    ( ! [X11,X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
        | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2398 ),
    inference(avatar_component_clause,[],[f30568]) ).

fof(f30590,plain,
    spl0_2402,
    inference(avatar_split_clause,[],[f1502,f30588]) ).

fof(f30588,plain,
    ( spl0_2402
  <=> ! [X5,X23,X0,X3,X25,X1] :
        ( X0 = X3
        | c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2402])]) ).

fof(f1502,axiom,
    ! [X3,X0,X1,X5,X25,X23] :
      ( X0 = X3
      | c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).

fof(f30585,plain,
    spl0_2401,
    inference(avatar_split_clause,[],[f1448,f30583]) ).

fof(f1448,axiom,
    ! [X11,X47] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__number__of_0) ).

fof(f30580,plain,
    spl0_2400,
    inference(avatar_split_clause,[],[f1444,f30578]) ).

fof(f1444,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__pos__number__of_0) ).

fof(f30575,plain,
    spl0_2399,
    inference(avatar_split_clause,[],[f1438,f30573]) ).

fof(f1438,axiom,
    ! [X11,X47] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__number__of_0) ).

fof(f30570,plain,
    spl0_2398,
    inference(avatar_split_clause,[],[f1434,f30568]) ).

fof(f1434,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__pos__number__of_0) ).

fof(f30566,plain,
    spl0_2397,
    inference(avatar_split_clause,[],[f55,f30564]) ).

fof(f30564,plain,
    ( spl0_2397
  <=> ! [X3,X23,X5,X25,X1] :
        ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
        | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2397])]) ).

fof(f55,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
      | ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).

fof(f30562,plain,
    spl0_2396,
    inference(avatar_split_clause,[],[f52,f30560]) ).

fof(f30560,plain,
    ( spl0_2396
  <=> ! [X3,X23,X5,X25,X1] :
        ( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
        | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2396])]) ).

fof(f52,axiom,
    ! [X3,X1,X5,X25,X23] :
      ( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
      | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).

fof(f30558,plain,
    ( spl0_2395
    | ~ spl0_1854
    | ~ spl0_2360 ),
    inference(avatar_split_clause,[],[f29626,f29361,f17663,f30556]) ).

fof(f17663,plain,
    ( spl0_1854
  <=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).

fof(f29361,plain,
    ( spl0_2360
  <=> ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2360])]) ).

fof(f29626,plain,
    ( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1854
    | ~ spl0_2360 ),
    inference(superposition,[],[f29362,f17664]) ).

fof(f17664,plain,
    ( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
    | ~ spl0_1854 ),
    inference(avatar_component_clause,[],[f17663]) ).

fof(f29362,plain,
    ( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2360 ),
    inference(avatar_component_clause,[],[f29361]) ).

fof(f30420,plain,
    spl0_2394,
    inference(avatar_split_clause,[],[f1470,f30418]) ).

fof(f30418,plain,
    ( spl0_2394
  <=> ! [X11,X27,X47] :
        ( c_Numeral_Obit_OB0 = X27
        | c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).

fof(f1470,axiom,
    ! [X11,X47,X27] :
      ( c_Numeral_Obit_OB0 = X27
      | c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).

fof(f30416,plain,
    spl0_2393,
    inference(avatar_split_clause,[],[f83,f30414]) ).

fof(f30414,plain,
    ( spl0_2393
  <=> ! [X5,X31,X30,X6,X2,X1] :
        ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
        | c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2393])]) ).

fof(f83,axiom,
    ! [X31,X2,X1,X6,X5,X30] :
      ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
      | c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).

fof(f30412,plain,
    spl0_2392,
    inference(avatar_split_clause,[],[f82,f30410]) ).

fof(f30410,plain,
    ( spl0_2392
  <=> ! [X5,X31,X30,X6,X2,X1] :
        ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
        | c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2392])]) ).

fof(f82,axiom,
    ! [X31,X2,X1,X6,X5,X30] :
      ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
      | c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).

fof(f30408,plain,
    spl0_2391,
    inference(avatar_split_clause,[],[f20,f30406]) ).

fof(f30406,plain,
    ( spl0_2391
  <=> ! [X13,X14,X12,X2,X1] :
        ( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2391])]) ).

fof(f20,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).

fof(f30346,plain,
    ( spl0_2390
    | ~ spl0_1854
    | ~ spl0_2257 ),
    inference(avatar_split_clause,[],[f27056,f26839,f17663,f30344]) ).

fof(f26839,plain,
    ( spl0_2257
  <=> ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2257])]) ).

fof(f27056,plain,
    ( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Oreplicate(c_plus(c_1,X0,tc_nat),c_Event_Obad,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1854
    | ~ spl0_2257 ),
    inference(superposition,[],[f26840,f17664]) ).

fof(f26840,plain,
    ( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2257 ),
    inference(avatar_component_clause,[],[f26839]) ).

fof(f30272,plain,
    spl0_2389,
    inference(avatar_split_clause,[],[f3302,f30270]) ).

fof(f30270,plain,
    ( spl0_2389
  <=> ! [X15,X47] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2389])]) ).

fof(f3302,plain,
    ! [X47,X15] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3301,f2156]) ).

fof(f3301,plain,
    ! [X47,X15] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3300,f3045]) ).

fof(f3045,plain,
    ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
    inference(definition_unfolding,[],[f2101,f2544,f2544]) ).

fof(f2544,axiom,
    ! [X14] : c_Suc(X14) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).

fof(f2101,axiom,
    ! [X21,X15] : c_Suc(c_plus(X15,X21,tc_nat)) = c_plus(c_Suc(X15),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).

fof(f3300,plain,
    ! [X47,X15] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3100,f3264]) ).

fof(f3264,plain,
    ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3263,f2156]) ).

fof(f3263,plain,
    ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3262,f2154]) ).

fof(f3262,plain,
    ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3066,f2156]) ).

fof(f3066,plain,
    ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1882,f2544,f2544]) ).

fof(f1882,axiom,
    ! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).

fof(f3100,plain,
    ! [X47,X15] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1880,f2544,f2544,f2544]) ).

fof(f1880,axiom,
    ! [X47,X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).

fof(f30252,plain,
    ( spl0_2388
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2387 ),
    inference(avatar_split_clause,[],[f30248,f30244,f21025,f11334,f10936,f7067,f6122,f30250]) ).

fof(f30250,plain,
    ( spl0_2388
  <=> ! [X15,X47] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X15,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2388])]) ).

fof(f7067,plain,
    ( spl0_687
  <=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f10936,plain,
    ( spl0_1373
  <=> ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).

fof(f11334,plain,
    ( spl0_1461
  <=> ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).

fof(f21025,plain,
    ( spl0_2031
  <=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).

fof(f30244,plain,
    ( spl0_2387
  <=> ! [X15,X47] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2387])]) ).

fof(f30248,plain,
    ( ! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X15,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2387 ),
    inference(forward_demodulation,[],[f30247,f21026]) ).

fof(f21026,plain,
    ( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_2031 ),
    inference(avatar_component_clause,[],[f21025]) ).

fof(f30247,plain,
    ( ! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2387 ),
    inference(forward_demodulation,[],[f30245,f12301]) ).

fof(f12301,plain,
    ( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461 ),
    inference(forward_demodulation,[],[f12300,f7068]) ).

fof(f7068,plain,
    ( ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3
    | ~ spl0_687 ),
    inference(avatar_component_clause,[],[f7067]) ).

fof(f12300,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_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461 ),
    inference(forward_demodulation,[],[f12262,f11635]) ).

fof(f11635,plain,
    ( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
    | ~ spl0_646
    | ~ spl0_1373 ),
    inference(superposition,[],[f10937,f6124]) ).

fof(f10937,plain,
    ( ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
    | ~ spl0_1373 ),
    inference(avatar_component_clause,[],[f10936]) ).

fof(f12262,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_687
    | ~ spl0_1461 ),
    inference(superposition,[],[f7068,f11335]) ).

fof(f11335,plain,
    ( ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat))
    | ~ spl0_1461 ),
    inference(avatar_component_clause,[],[f11334]) ).

fof(f30245,plain,
    ( ! [X47,X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
    | ~ spl0_2387 ),
    inference(avatar_component_clause,[],[f30244]) ).

fof(f30246,plain,
    spl0_2387,
    inference(avatar_split_clause,[],[f3299,f30244]) ).

fof(f3299,plain,
    ! [X47,X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3298,f2156]) ).

fof(f3298,plain,
    ! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3297,f3045]) ).

fof(f3297,plain,
    ! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3099,f3264]) ).

fof(f3099,plain,
    ! [X47,X15] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1879,f2544,f2544,f2544]) ).

fof(f1879,axiom,
    ! [X47,X15] : c_div(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).

fof(f30242,plain,
    spl0_2386,
    inference(avatar_split_clause,[],[f3183,f30240]) ).

fof(f30240,plain,
    ( spl0_2386
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
        | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2386])]) ).

fof(f3183,plain,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
    inference(definition_unfolding,[],[f2724,f2716]) ).

fof(f2716,axiom,
    ! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).

fof(f2724,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).

fof(f30238,plain,
    spl0_2385,
    inference(avatar_split_clause,[],[f3182,f30236]) ).

fof(f30236,plain,
    ( spl0_2385
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2385])]) ).

fof(f3182,plain,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
    inference(definition_unfolding,[],[f2721,f2716]) ).

fof(f2721,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).

fof(f30220,plain,
    spl0_2384,
    inference(avatar_split_clause,[],[f1621,f30218]) ).

fof(f30218,plain,
    ( spl0_2384
  <=> ! [X5,X18,X3,X0,X27,X1] :
        ( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
        | c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2384])]) ).

fof(f1621,axiom,
    ! [X3,X0,X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
      | c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).

fof(f30216,plain,
    spl0_2383,
    inference(avatar_split_clause,[],[f1460,f30214]) ).

fof(f30214,plain,
    ( spl0_2383
  <=> ! [X11,X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2383])]) ).

fof(f1460,axiom,
    ! [X11,X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).

fof(f30212,plain,
    spl0_2382,
    inference(avatar_split_clause,[],[f19,f30210]) ).

fof(f30210,plain,
    ( spl0_2382
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
        | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2382])]) ).

fof(f19,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
      | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).

fof(f30208,plain,
    spl0_2381,
    inference(avatar_split_clause,[],[f18,f30206]) ).

fof(f30206,plain,
    ( spl0_2381
  <=> ! [X14,X13,X12,X2,X1] :
        ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
        | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2381])]) ).

fof(f18,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
      | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).

fof(f30103,plain,
    spl0_2380,
    inference(avatar_split_clause,[],[f3227,f30101]) ).

fof(f30101,plain,
    ( spl0_2380
  <=> ! [X87,X86,X88] :
        ( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2380])]) ).

fof(f3227,plain,
    ! [X88,X86,X87] :
      ( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
    inference(definition_unfolding,[],[f2821,f2812]) ).

fof(f2812,axiom,
    ! [X0,X86] : c_Message_OHPair(X86,X0) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X0)),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_2) ).

fof(f2821,axiom,
    ! [X88,X86,X87] :
      ( ~ c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
      | c_in(c_Message_OHPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_2) ).

fof(f30099,plain,
    spl0_2379,
    inference(avatar_split_clause,[],[f3152,f30097]) ).

fof(f30097,plain,
    ( spl0_2379
  <=> ! [X47,X0,X23,X1] :
        ( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
        | c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2379])]) ).

fof(f3152,plain,
    ! [X0,X47,X1,X23] :
      ( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
      | c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),tc_nat),X1),X1) ),
    inference(definition_unfolding,[],[f1768,f1766,f1766]) ).

fof(f1766,axiom,
    ! [X21,X1,X26] : c_List_Osublist(X26,c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Otake(X21,X26,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).

fof(f1768,axiom,
    ! [X0,X47,X1,X23] :
      ( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
      | c_List_Otake(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).

fof(f30095,plain,
    spl0_2378,
    inference(avatar_split_clause,[],[f17,f30093]) ).

fof(f30093,plain,
    ( spl0_2378
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
        | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
        | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2378])]) ).

fof(f17,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
      | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
      | ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).

fof(f30091,plain,
    ( spl0_2377
    | ~ spl0_811
    | ~ spl0_2170
    | ~ spl0_2337 ),
    inference(avatar_split_clause,[],[f28782,f28716,f23995,f7607,f30088]) ).

fof(f30088,plain,
    ( spl0_2377
  <=> c_UNIV = c_union(c_uminus(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2377])]) ).

fof(f7607,plain,
    ( spl0_811
  <=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f23995,plain,
    ( spl0_2170
  <=> ! [X13,X12,X1] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).

fof(f28716,plain,
    ( spl0_2337
  <=> c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2337])]) ).

fof(f28782,plain,
    ( c_UNIV = c_union(c_uminus(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_811
    | ~ spl0_2170
    | ~ spl0_2337 ),
    inference(forward_demodulation,[],[f28771,f7608]) ).

fof(f7608,plain,
    ( ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1))
    | ~ spl0_811 ),
    inference(avatar_component_clause,[],[f7607]) ).

fof(f28771,plain,
    ( c_uminus(c_emptyset,tc_set(tc_Message_Oagent)) = c_union(c_uminus(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_2170
    | ~ spl0_2337 ),
    inference(superposition,[],[f23996,f28718]) ).

fof(f28718,plain,
    ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_2337 ),
    inference(avatar_component_clause,[],[f28716]) ).

fof(f23996,plain,
    ( ! [X1,X12,X13] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1))
    | ~ spl0_2170 ),
    inference(avatar_component_clause,[],[f23995]) ).

fof(f29800,plain,
    spl0_2376,
    inference(avatar_split_clause,[],[f3096,f29798]) ).

fof(f29798,plain,
    ( spl0_2376
  <=> ! [X21,X23,X25,X1] : c_List_Osublist(c_append(X23,X25,X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_append(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Osublist(X25,c_SetInterval_OlessThan(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),tc_nat),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2376])]) ).

fof(f3096,plain,
    ! [X21,X1,X25,X23] : c_List_Osublist(c_append(X23,X25,X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_append(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Osublist(X25,c_SetInterval_OlessThan(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),tc_nat),X1),X1),
    inference(definition_unfolding,[],[f1771,f1766,f1766,f1766]) ).

fof(f1771,axiom,
    ! [X21,X1,X25,X23] : c_List_Otake(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Otake(X21,X23,X1),c_List_Otake(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).

fof(f29796,plain,
    spl0_2375,
    inference(avatar_split_clause,[],[f1998,f29794]) ).

fof(f29794,plain,
    ( spl0_2375
  <=> ! [X2,X27,X18,X47] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2375])]) ).

fof(f1998,axiom,
    ! [X2,X47,X18,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).

fof(f29792,plain,
    spl0_2374,
    inference(avatar_split_clause,[],[f1992,f29790]) ).

fof(f29790,plain,
    ( spl0_2374
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2374])]) ).

fof(f1992,axiom,
    ! [X2,X47,X18,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).

fof(f29774,plain,
    spl0_2373,
    inference(avatar_split_clause,[],[f1986,f29772]) ).

fof(f29772,plain,
    ( spl0_2373
  <=> ! [X2,X27,X18,X47] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2373])]) ).

fof(f1986,axiom,
    ! [X2,X47,X18,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).

fof(f29770,plain,
    spl0_2372,
    inference(avatar_split_clause,[],[f1980,f29768]) ).

fof(f29768,plain,
    ( spl0_2372
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2372])]) ).

fof(f1980,axiom,
    ! [X2,X47,X18,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).

fof(f29766,plain,
    spl0_2371,
    inference(avatar_split_clause,[],[f115,f29764]) ).

fof(f29764,plain,
    ( spl0_2371
  <=> ! [X13,X14,X12,X2,X1] :
        ( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
        | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
        | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2371])]) ).

fof(f115,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
      | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
      | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).

fof(f29762,plain,
    spl0_2370,
    inference(avatar_split_clause,[],[f84,f29760]) ).

fof(f29760,plain,
    ( spl0_2370
  <=> ! [X5,X31,X30,X6,X2,X1] :
        ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
        | c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2370])]) ).

fof(f84,axiom,
    ! [X31,X2,X1,X6,X5,X30] :
      ( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
      | c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).

fof(f29682,plain,
    ( spl0_2369
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2367 ),
    inference(avatar_split_clause,[],[f29674,f29671,f21025,f7546,f7510,f29680]) ).

fof(f29680,plain,
    ( spl0_2369
  <=> ! [X18,X21,X1] :
        ( c_Nat_Opower(c_uminus(X18,X1),c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1)
        | ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2369])]) ).

fof(f29671,plain,
    ( spl0_2367
  <=> ! [X18,X21,X1] :
        ( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
        | ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2367])]) ).

fof(f29674,plain,
    ( ! [X21,X18,X1] :
        ( c_Nat_Opower(c_uminus(X18,X1),c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_plus(c_1,c_1,tc_nat),X21,tc_nat),X1)
        | ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2367 ),
    inference(forward_demodulation,[],[f29672,f21108]) ).

fof(f21108,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_787
    | ~ spl0_796
    | ~ spl0_2031 ),
    inference(forward_demodulation,[],[f21029,f7511]) ).

fof(f21029,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_796
    | ~ spl0_2031 ),
    inference(superposition,[],[f21026,f7547]) ).

fof(f29672,plain,
    ( ! [X21,X18,X1] :
        ( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
        | ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
    | ~ spl0_2367 ),
    inference(avatar_component_clause,[],[f29671]) ).

fof(f29678,plain,
    ( spl0_2368
    | ~ spl0_1750
    | ~ spl0_2320 ),
    inference(avatar_split_clause,[],[f28673,f28531,f15898,f29676]) ).

fof(f29676,plain,
    ( spl0_2368
  <=> ! [X0,X1] : ~ c_in(v_B,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2368])]) ).

fof(f15898,plain,
    ( spl0_1750
  <=> ! [X18,X13,X12,X1] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).

fof(f28531,plain,
    ( spl0_2320
  <=> ! [X0] : ~ c_in(v_B,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2320])]) ).

fof(f28673,plain,
    ( ! [X0,X1] : ~ c_in(v_B,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1750
    | ~ spl0_2320 ),
    inference(superposition,[],[f28532,f15899]) ).

fof(f15899,plain,
    ( ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1)
    | ~ spl0_1750 ),
    inference(avatar_component_clause,[],[f15898]) ).

fof(f28532,plain,
    ( ! [X0] : ~ c_in(v_B,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2320 ),
    inference(avatar_component_clause,[],[f28531]) ).

fof(f29673,plain,
    spl0_2367,
    inference(avatar_split_clause,[],[f3392,f29671]) ).

fof(f3392,plain,
    ! [X21,X18,X1] :
      ( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
      | ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(forward_demodulation,[],[f3391,f2156]) ).

fof(f3391,plain,
    ! [X21,X18,X1] :
      ( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),X1)
      | ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(forward_demodulation,[],[f3390,f2154]) ).

fof(f3390,plain,
    ! [X21,X18,X1] :
      ( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1)
      | ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(forward_demodulation,[],[f1875,f2156]) ).

fof(f1875,axiom,
    ! [X21,X1,X18] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).

fof(f29669,plain,
    spl0_2366,
    inference(avatar_split_clause,[],[f3170,f29667]) ).

fof(f29667,plain,
    ( spl0_2366
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2366])]) ).

fof(f3170,plain,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
    inference(definition_unfolding,[],[f2723,f2716]) ).

fof(f2723,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).

fof(f29665,plain,
    spl0_2365,
    inference(avatar_split_clause,[],[f3169,f29663]) ).

fof(f29663,plain,
    ( spl0_2365
  <=> ! [X3,X0,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
        | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2365])]) ).

fof(f3169,plain,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
    inference(definition_unfolding,[],[f2720,f2716]) ).

fof(f2720,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
      | ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).

fof(f29661,plain,
    spl0_2364,
    inference(avatar_split_clause,[],[f3067,f29659]) ).

fof(f29659,plain,
    ( spl0_2364
  <=> ! [X85,X1] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).

fof(f3067,plain,
    ! [X1,X85] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1,X1),
    inference(definition_unfolding,[],[f2711,f2716,f2716,f2716]) ).

fof(f2711,axiom,
    ! [X1,X85] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X85,X1),c_Transitive__Closure_Ortrancl(X85,X1),X1,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).

fof(f29657,plain,
    spl0_2363,
    inference(avatar_split_clause,[],[f16,f29655]) ).

fof(f29655,plain,
    ( spl0_2363
  <=> ! [X9,X13,X7,X12,X2,X1] :
        ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2363])]) ).

fof(f16,axiom,
    ! [X2,X1,X9,X7,X12,X13] :
      ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).

fof(f29645,plain,
    ( spl0_2362
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2359 ),
    inference(avatar_split_clause,[],[f28915,f28912,f12670,f9587,f29643]) ).

fof(f29643,plain,
    ( spl0_2362
  <=> ! [X11] :
        ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2362])]) ).

fof(f28912,plain,
    ( spl0_2359
  <=> ! [X11] :
        ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2359])]) ).

fof(f28915,plain,
    ( ! [X11] :
        ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2359 ),
    inference(forward_demodulation,[],[f28913,f13748]) ).

fof(f28913,plain,
    ( ! [X11] :
        ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_2359 ),
    inference(avatar_component_clause,[],[f28912]) ).

fof(f29641,plain,
    ( spl0_2361
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2358 ),
    inference(avatar_split_clause,[],[f28910,f28907,f12670,f9583,f29639]) ).

fof(f29639,plain,
    ( spl0_2361
  <=> ! [X11] :
        ( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2361])]) ).

fof(f28907,plain,
    ( spl0_2358
  <=> ! [X11] :
        ( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2358])]) ).

fof(f28910,plain,
    ( ! [X11] :
        ( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2358 ),
    inference(forward_demodulation,[],[f28908,f13749]) ).

fof(f28908,plain,
    ( ! [X11] :
        ( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
    | ~ spl0_2358 ),
    inference(avatar_component_clause,[],[f28907]) ).

fof(f29363,plain,
    ( spl0_2360
    | ~ spl0_1501
    | ~ spl0_2320 ),
    inference(avatar_split_clause,[],[f28670,f28531,f12512,f29361]) ).

fof(f28670,plain,
    ( ! [X0] : ~ c_in(v_B,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1501
    | ~ spl0_2320 ),
    inference(superposition,[],[f28532,f12513]) ).

fof(f28914,plain,
    spl0_2359,
    inference(avatar_split_clause,[],[f3349,f28912]) ).

fof(f3349,plain,
    ! [X11] :
      ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1445,f1456]) ).

fof(f1445,axiom,
    ! [X11] :
      ( ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).

fof(f28909,plain,
    spl0_2358,
    inference(avatar_split_clause,[],[f3348,f28907]) ).

fof(f3348,plain,
    ! [X11] :
      ( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f1435,f1456]) ).

fof(f1435,axiom,
    ! [X11] :
      ( ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).

fof(f28896,plain,
    ( spl0_2357
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2356 ),
    inference(avatar_split_clause,[],[f28892,f28888,f21025,f11334,f10936,f7546,f7510,f7067,f6122,f28894]) ).

fof(f28894,plain,
    ( spl0_2357
  <=> ! [X15] : c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2357])]) ).

fof(f28888,plain,
    ( spl0_2356
  <=> ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2356])]) ).

fof(f28892,plain,
    ( ! [X15] : c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2356 ),
    inference(forward_demodulation,[],[f28891,f12301]) ).

fof(f28891,plain,
    ( ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2356 ),
    inference(forward_demodulation,[],[f28889,f21108]) ).

fof(f28889,plain,
    ( ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
    | ~ spl0_2356 ),
    inference(avatar_component_clause,[],[f28888]) ).

fof(f28890,plain,
    spl0_2356,
    inference(avatar_split_clause,[],[f3296,f28888]) ).

fof(f3296,plain,
    ! [X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3295,f3264]) ).

fof(f3295,plain,
    ! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3294,f2156]) ).

fof(f3294,plain,
    ! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3293,f2154]) ).

fof(f3293,plain,
    ! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3098,f2156]) ).

fof(f3098,plain,
    ! [X15] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1884,f2544,f2544,f2544]) ).

fof(f1884,axiom,
    ! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).

fof(f28841,plain,
    ( spl0_2355
    | ~ spl0_2159
    | ~ spl0_2313 ),
    inference(avatar_split_clause,[],[f28428,f28144,f23898,f28839]) ).

fof(f28839,plain,
    ( spl0_2355
  <=> ! [X0] : ~ c_in(c_Pair(X0,v_B,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2355])]) ).

fof(f23898,plain,
    ( spl0_2159
  <=> ! [X5,X18,X27,X2,X1] :
        ( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
        | c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).

fof(f28144,plain,
    ( spl0_2313
  <=> ! [X0] : ~ c_in(v_B,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2313])]) ).

fof(f28428,plain,
    ( ! [X0] : ~ c_in(c_Pair(X0,v_B,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent))
    | ~ spl0_2159
    | ~ spl0_2313 ),
    inference(resolution,[],[f28145,f23899]) ).

fof(f23899,plain,
    ( ! [X2,X18,X1,X27,X5] :
        ( c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1)
        | ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1)) )
    | ~ spl0_2159 ),
    inference(avatar_component_clause,[],[f23898]) ).

fof(f28145,plain,
    ( ! [X0] : ~ c_in(v_B,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2313 ),
    inference(avatar_component_clause,[],[f28144]) ).

fof(f28837,plain,
    ( spl0_2354
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2353 ),
    inference(avatar_split_clause,[],[f28833,f28829,f21025,f11334,f10936,f7067,f6122,f28835]) ).

fof(f28835,plain,
    ( spl0_2354
  <=> ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2354])]) ).

fof(f28829,plain,
    ( spl0_2353
  <=> ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2353])]) ).

fof(f28833,plain,
    ( ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2353 ),
    inference(forward_demodulation,[],[f28832,f21026]) ).

fof(f28832,plain,
    ( ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_1,c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2353 ),
    inference(forward_demodulation,[],[f28830,f12301]) ).

fof(f28830,plain,
    ( ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat)
    | ~ spl0_2353 ),
    inference(avatar_component_clause,[],[f28829]) ).

fof(f28831,plain,
    spl0_2353,
    inference(avatar_split_clause,[],[f3286,f28829]) ).

fof(f3286,plain,
    ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3285,f2156]) ).

fof(f3285,plain,
    ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3284,f3045]) ).

fof(f3284,plain,
    ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3091,f3264]) ).

fof(f3091,plain,
    ! [X21,X15] : c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1977,f2544,f2544,f2544]) ).

fof(f1977,axiom,
    ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).

fof(f28815,plain,
    ( spl0_2352
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2351 ),
    inference(avatar_split_clause,[],[f28811,f28807,f21025,f11334,f10936,f7067,f6122,f28813]) ).

fof(f28813,plain,
    ( spl0_2352
  <=> ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2352])]) ).

fof(f28807,plain,
    ( spl0_2351
  <=> ! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2351])]) ).

fof(f28811,plain,
    ( ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_1,c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2351 ),
    inference(forward_demodulation,[],[f28810,f21026]) ).

fof(f28810,plain,
    ( ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_1,c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2351 ),
    inference(forward_demodulation,[],[f28808,f12301]) ).

fof(f28808,plain,
    ( ! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat)
    | ~ spl0_2351 ),
    inference(avatar_component_clause,[],[f28807]) ).

fof(f28809,plain,
    spl0_2351,
    inference(avatar_split_clause,[],[f3283,f28807]) ).

fof(f3283,plain,
    ! [X21,X15] : c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3282,f2156]) ).

fof(f3282,plain,
    ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3281,f3045]) ).

fof(f3281,plain,
    ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3090,f3264]) ).

fof(f3090,plain,
    ! [X21,X15] : c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) = c_div(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1885,f2544,f2544,f2544]) ).

fof(f1885,axiom,
    ! [X21,X15] : c_div(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).

fof(f28801,plain,
    ( spl0_2350
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2349 ),
    inference(avatar_split_clause,[],[f28797,f28793,f21025,f11334,f10936,f7067,f6122,f28799]) ).

fof(f28799,plain,
    ( spl0_2350
  <=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2350])]) ).

fof(f28793,plain,
    ( spl0_2349
  <=> ! [X9,X16,X2,X1] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2349])]) ).

fof(f28797,plain,
    ( ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2349 ),
    inference(forward_demodulation,[],[f28796,f12301]) ).

fof(f28796,plain,
    ( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2)
    | ~ spl0_2031
    | ~ spl0_2349 ),
    inference(forward_demodulation,[],[f28794,f21026]) ).

fof(f28794,plain,
    ( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2)
    | ~ spl0_2349 ),
    inference(avatar_component_clause,[],[f28793]) ).

fof(f28795,plain,
    spl0_2349,
    inference(avatar_split_clause,[],[f3280,f28793]) ).

fof(f3280,plain,
    ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
    inference(forward_demodulation,[],[f3089,f3264]) ).

fof(f3089,plain,
    ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1205,f2544,f2544,f2544]) ).

fof(f1205,axiom,
    ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).

fof(f28787,plain,
    ( spl0_2348
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2347 ),
    inference(avatar_split_clause,[],[f28761,f28757,f21025,f11334,f10936,f7067,f6122,f28785]) ).

fof(f28785,plain,
    ( spl0_2348
  <=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2348])]) ).

fof(f28757,plain,
    ( spl0_2347
  <=> ! [X9,X16,X2,X1] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2347])]) ).

fof(f28761,plain,
    ( ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),X9,X1,X2),X1,X2)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2031
    | ~ spl0_2347 ),
    inference(forward_demodulation,[],[f28760,f12301]) ).

fof(f28760,plain,
    ( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X16,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2)
    | ~ spl0_2031
    | ~ spl0_2347 ),
    inference(forward_demodulation,[],[f28758,f21026]) ).

fof(f28758,plain,
    ( ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2)
    | ~ spl0_2347 ),
    inference(avatar_component_clause,[],[f28757]) ).

fof(f28759,plain,
    spl0_2347,
    inference(avatar_split_clause,[],[f3279,f28757]) ).

fof(f3279,plain,
    ! [X2,X1,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(X16,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
    inference(forward_demodulation,[],[f3088,f3264]) ).

fof(f3088,plain,
    ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),X9,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1204,f2544,f2544,f2544]) ).

fof(f1204,axiom,
    ! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).

fof(f28755,plain,
    spl0_2346,
    inference(avatar_split_clause,[],[f2951,f28753]) ).

fof(f28753,plain,
    ( spl0_2346
  <=> ! [X102,X0,X13,X12,X113,X112,X86] :
        ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(X0)),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2346])]) ).

fof(f2951,axiom,
    ! [X113,X0,X86,X102,X12,X13,X112] :
      ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(X0)),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__not__shrK_0) ).

fof(f28751,plain,
    spl0_2345,
    inference(avatar_split_clause,[],[f2003,f28749]) ).

fof(f28749,plain,
    ( spl0_2345
  <=> ! [X4,X47,X27,X2] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_Ring__and__Field_Osemiring(X2)
        | c_times(c_Numeral_Onumber__of(X47,X2),c_plus(X27,X4,X2),X2) = c_plus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2345])]) ).

fof(f2003,axiom,
    ! [X2,X47,X27,X4] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_Ring__and__Field_Osemiring(X2)
      | c_times(c_Numeral_Onumber__of(X47,X2),c_plus(X27,X4,X2),X2) = c_plus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).

fof(f28747,plain,
    spl0_2344,
    inference(avatar_split_clause,[],[f2002,f28745]) ).

fof(f28745,plain,
    ( spl0_2344
  <=> ! [X4,X47,X27,X2] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_Ring__and__Field_Oring(X2)
        | c_times(c_Numeral_Onumber__of(X47,X2),c_minus(X27,X4,X2),X2) = c_minus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2344])]) ).

fof(f2002,axiom,
    ! [X2,X47,X27,X4] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_Ring__and__Field_Oring(X2)
      | c_times(c_Numeral_Onumber__of(X47,X2),c_minus(X27,X4,X2),X2) = c_minus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).

fof(f28743,plain,
    spl0_2343,
    inference(avatar_split_clause,[],[f2000,f28741]) ).

fof(f28741,plain,
    ( spl0_2343
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_less(X18,X27,X2)
        | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2343])]) ).

fof(f2000,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_less(X18,X27,X2)
      | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).

fof(f28739,plain,
    spl0_2342,
    inference(avatar_split_clause,[],[f1999,f28737]) ).

fof(f28737,plain,
    ( spl0_2342
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_less(X27,X18,X2)
        | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2342])]) ).

fof(f1999,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_less(X27,X18,X2)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).

fof(f28735,plain,
    spl0_2341,
    inference(avatar_split_clause,[],[f1997,f28733]) ).

fof(f28733,plain,
    ( spl0_2341
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_less(X27,X18,X2)
        | ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2341])]) ).

fof(f1997,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_less(X27,X18,X2)
      | ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).

fof(f28731,plain,
    spl0_2340,
    inference(avatar_split_clause,[],[f1996,f28729]) ).

fof(f28729,plain,
    ( spl0_2340
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_less(X18,X27,X2)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2340])]) ).

fof(f1996,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_less(X18,X27,X2)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).

fof(f28727,plain,
    spl0_2339,
    inference(avatar_split_clause,[],[f1994,f28725]) ).

fof(f28725,plain,
    ( spl0_2339
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_less(X18,X27,X2)
        | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2339])]) ).

fof(f1994,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_less(X18,X27,X2)
      | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).

fof(f28723,plain,
    spl0_2338,
    inference(avatar_split_clause,[],[f1993,f28721]) ).

fof(f28721,plain,
    ( spl0_2338
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_less(X27,X18,X2)
        | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2338])]) ).

fof(f1993,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_less(X27,X18,X2)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).

fof(f28719,plain,
    ( spl0_2337
    | ~ spl0_892
    | ~ spl0_2192 ),
    inference(avatar_split_clause,[],[f27840,f24816,f7944,f28716]) ).

fof(f24816,plain,
    ( spl0_2192
  <=> ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).

fof(f27840,plain,
    ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_892
    | ~ spl0_2192 ),
    inference(superposition,[],[f24817,f7945]) ).

fof(f24817,plain,
    ( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_2192 ),
    inference(avatar_component_clause,[],[f24816]) ).

fof(f28714,plain,
    spl0_2336,
    inference(avatar_split_clause,[],[f1991,f28712]) ).

fof(f28712,plain,
    ( spl0_2336
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_less(X27,X18,X2)
        | ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2336])]) ).

fof(f1991,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_less(X27,X18,X2)
      | ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).

fof(f28710,plain,
    spl0_2335,
    inference(avatar_split_clause,[],[f1990,f28708]) ).

fof(f28708,plain,
    ( spl0_2335
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_less(X18,X27,X2)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2335])]) ).

fof(f1990,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_less(X18,X27,X2)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).

fof(f28706,plain,
    spl0_2334,
    inference(avatar_split_clause,[],[f1988,f28704]) ).

fof(f28704,plain,
    ( spl0_2334
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_lessequals(X18,X27,X2)
        | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2334])]) ).

fof(f1988,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_lessequals(X18,X27,X2)
      | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).

fof(f28702,plain,
    spl0_2333,
    inference(avatar_split_clause,[],[f1987,f28700]) ).

fof(f28700,plain,
    ( spl0_2333
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_lessequals(X27,X18,X2)
        | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2333])]) ).

fof(f1987,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_lessequals(X27,X18,X2)
      | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).

fof(f28698,plain,
    spl0_2332,
    inference(avatar_split_clause,[],[f1985,f28696]) ).

fof(f28696,plain,
    ( spl0_2332
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_lessequals(X27,X18,X2)
        | ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2332])]) ).

fof(f1985,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_lessequals(X27,X18,X2)
      | ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).

fof(f28694,plain,
    spl0_2331,
    inference(avatar_split_clause,[],[f1984,f28692]) ).

fof(f28692,plain,
    ( spl0_2331
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_lessequals(X18,X27,X2)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2331])]) ).

fof(f1984,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_lessequals(X18,X27,X2)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).

fof(f28690,plain,
    spl0_2330,
    inference(avatar_split_clause,[],[f1982,f28688]) ).

fof(f28688,plain,
    ( spl0_2330
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_lessequals(X18,X27,X2)
        | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2330])]) ).

fof(f1982,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_lessequals(X18,X27,X2)
      | c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).

fof(f28686,plain,
    spl0_2329,
    inference(avatar_split_clause,[],[f1981,f28684]) ).

fof(f28684,plain,
    ( spl0_2329
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_lessequals(X27,X18,X2)
        | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2329])]) ).

fof(f1981,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_lessequals(X27,X18,X2)
      | c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).

fof(f28682,plain,
    spl0_2328,
    inference(avatar_split_clause,[],[f1979,f28680]) ).

fof(f28680,plain,
    ( spl0_2328
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_lessequals(X27,X18,X2)
        | ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
        | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2328])]) ).

fof(f1979,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_lessequals(X27,X18,X2)
      | ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).

fof(f28678,plain,
    spl0_2327,
    inference(avatar_split_clause,[],[f1978,f28676]) ).

fof(f28676,plain,
    ( spl0_2327
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | c_lessequals(X18,X27,X2)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
        | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2327])]) ).

fof(f1978,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_lessequals(X18,X27,X2)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
      | ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).

fof(f28667,plain,
    spl0_2326,
    inference(avatar_split_clause,[],[f1948,f28665]) ).

fof(f28665,plain,
    ( spl0_2326
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_Ring__and__Field_Osemiring(X2)
        | c_times(c_plus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_plus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2326])]) ).

fof(f1948,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_Ring__and__Field_Osemiring(X2)
      | c_times(c_plus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_plus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).

fof(f28663,plain,
    spl0_2325,
    inference(avatar_split_clause,[],[f1947,f28661]) ).

fof(f28661,plain,
    ( spl0_2325
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_Ring__and__Field_Oring(X2)
        | c_times(c_minus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_minus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2325])]) ).

fof(f1947,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_Ring__and__Field_Oring(X2)
      | c_times(c_minus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_minus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).

fof(f28659,plain,
    spl0_2324,
    inference(avatar_split_clause,[],[f1862,f28657]) ).

fof(f28657,plain,
    ( spl0_2324
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2324])]) ).

fof(f1862,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).

fof(f28655,plain,
    spl0_2323,
    inference(avatar_split_clause,[],[f117,f28653]) ).

fof(f28653,plain,
    ( spl0_2323
  <=> ! [X2,X14,X13,X12,X1] :
        ( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
        | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
        | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2323])]) ).

fof(f117,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
      | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
      | c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).

fof(f28651,plain,
    spl0_2322,
    inference(avatar_split_clause,[],[f116,f28649]) ).

fof(f28649,plain,
    ( spl0_2322
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
        | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
        | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2322])]) ).

fof(f116,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
      | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
      | c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).

fof(f28647,plain,
    spl0_2321,
    inference(avatar_split_clause,[],[f13,f28645]) ).

fof(f28645,plain,
    ( spl0_2321
  <=> ! [X4,X13,X12,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2321])]) ).

fof(f13,axiom,
    ! [X2,X1,X4,X12,X13] :
      ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).

fof(f28533,plain,
    ( spl0_2320
    | ~ spl0_1955
    | ~ spl0_2313 ),
    inference(avatar_split_clause,[],[f28432,f28144,f19613,f28531]) ).

fof(f19613,plain,
    ( spl0_1955
  <=> ! [X13,X18,X1] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).

fof(f28432,plain,
    ( ! [X0] : ~ c_in(v_B,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1955
    | ~ spl0_2313 ),
    inference(superposition,[],[f28145,f19614]) ).

fof(f19614,plain,
    ( ! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1)
    | ~ spl0_1955 ),
    inference(avatar_component_clause,[],[f19613]) ).

fof(f28506,plain,
    ( spl0_2319
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2318 ),
    inference(avatar_split_clause,[],[f28502,f28499,f11334,f10936,f7067,f6122,f28504]) ).

fof(f28504,plain,
    ( spl0_2319
  <=> ! [X16,X7,X9,X2,X1] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2319])]) ).

fof(f28499,plain,
    ( spl0_2318
  <=> ! [X16,X7,X9,X2,X1] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2318])]) ).

fof(f28502,plain,
    ( ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2318 ),
    inference(forward_demodulation,[],[f28500,f12301]) ).

fof(f28500,plain,
    ( ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2)
    | ~ spl0_2318 ),
    inference(avatar_component_clause,[],[f28499]) ).

fof(f28501,plain,
    spl0_2318,
    inference(avatar_split_clause,[],[f3097,f28499]) ).

fof(f3097,plain,
    ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1208,f2544]) ).

fof(f1208,axiom,
    ! [X2,X1,X9,X16,X7] : c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).

fof(f28497,plain,
    spl0_2317,
    inference(avatar_split_clause,[],[f2331,f28495]) ).

fof(f28495,plain,
    ( spl0_2317
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_0,X0,X1)
        | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2317])]) ).

fof(f2331,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,X0,X1)
      | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).

fof(f28493,plain,
    spl0_2316,
    inference(avatar_split_clause,[],[f2321,f28491]) ).

fof(f28491,plain,
    ( spl0_2316
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(X0,c_0,X1)
        | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2316])]) ).

fof(f2321,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(X0,c_0,X1)
      | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).

fof(f28489,plain,
    spl0_2315,
    inference(avatar_split_clause,[],[f1469,f28487]) ).

fof(f28487,plain,
    ( spl0_2315
  <=> ! [X27,X11,X47] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2315])]) ).

fof(f1469,axiom,
    ! [X11,X47,X27] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_1) ).

fof(f28485,plain,
    spl0_2314,
    inference(avatar_split_clause,[],[f77,f28483]) ).

fof(f28483,plain,
    ( spl0_2314
  <=> ! [X5,X29,X2,X1] :
        ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
        | c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2314])]) ).

fof(f77,axiom,
    ! [X2,X29,X1,X5] :
      ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
      | c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).

fof(f28146,plain,
    ( spl0_2313
    | ~ spl0_1843
    | ~ spl0_2297 ),
    inference(avatar_split_clause,[],[f28096,f27997,f17349,f28144]) ).

fof(f17349,plain,
    ( spl0_1843
  <=> ! [X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).

fof(f27997,plain,
    ( spl0_2297
  <=> ! [X0] : ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2297])]) ).

fof(f28096,plain,
    ( ! [X0] : ~ c_in(v_B,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1843
    | ~ spl0_2297 ),
    inference(superposition,[],[f27998,f17350]) ).

fof(f17350,plain,
    ( ! [X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1))
    | ~ spl0_1843 ),
    inference(avatar_component_clause,[],[f17349]) ).

fof(f27998,plain,
    ( ! [X0] : ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_2297 ),
    inference(avatar_component_clause,[],[f27997]) ).

fof(f28128,plain,
    spl0_2312,
    inference(avatar_split_clause,[],[f3226,f28126]) ).

fof(f28126,plain,
    ( spl0_2312
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2312])]) ).

fof(f3226,plain,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(definition_unfolding,[],[f1840,f2129]) ).

fof(f2129,axiom,
    ! [X11] : c_Numeral_Obin__minus(X11) = c_Numeral_Obin__mult(c_Numeral_OMin,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).

fof(f1840,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).

fof(f28124,plain,
    spl0_2311,
    inference(avatar_split_clause,[],[f3225,f28122]) ).

fof(f28122,plain,
    ( spl0_2311
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
        | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2311])]) ).

fof(f3225,plain,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(definition_unfolding,[],[f1839,f2129]) ).

fof(f1839,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).

fof(f28120,plain,
    spl0_2310,
    inference(avatar_split_clause,[],[f3224,f28118]) ).

fof(f28118,plain,
    ( spl0_2310
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).

fof(f3224,plain,
    ! [X83,X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(definition_unfolding,[],[f1842,f2129]) ).

fof(f1842,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).

fof(f28116,plain,
    spl0_2309,
    inference(avatar_split_clause,[],[f3223,f28114]) ).

fof(f28114,plain,
    ( spl0_2309
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2309])]) ).

fof(f3223,plain,
    ! [X83,X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(definition_unfolding,[],[f1844,f2129]) ).

fof(f1844,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).

fof(f28112,plain,
    spl0_2308,
    inference(avatar_split_clause,[],[f3221,f28110]) ).

fof(f28110,plain,
    ( spl0_2308
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2308])]) ).

fof(f3221,plain,
    ! [X83,X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(definition_unfolding,[],[f1846,f2129]) ).

fof(f1846,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).

fof(f28108,plain,
    spl0_2307,
    inference(avatar_split_clause,[],[f2001,f28106]) ).

fof(f28106,plain,
    ( spl0_2307
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_less(X18,X27,X2)
        | ~ c_less(X27,X18,X2)
        | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2307])]) ).

fof(f2001,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_less(X18,X27,X2)
      | ~ c_less(X27,X18,X2)
      | c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).

fof(f28104,plain,
    spl0_2306,
    inference(avatar_split_clause,[],[f1995,f28102]) ).

fof(f28102,plain,
    ( spl0_2306
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_less(X18,X27,X2)
        | ~ c_less(X27,X18,X2)
        | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2306])]) ).

fof(f1995,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_less(X18,X27,X2)
      | ~ c_less(X27,X18,X2)
      | c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).

fof(f28100,plain,
    spl0_2305,
    inference(avatar_split_clause,[],[f1989,f28098]) ).

fof(f28098,plain,
    ( spl0_2305
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_lessequals(X18,X27,X2)
        | ~ c_lessequals(X27,X18,X2)
        | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2305])]) ).

fof(f1989,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_lessequals(X18,X27,X2)
      | ~ c_lessequals(X27,X18,X2)
      | c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).

fof(f28088,plain,
    spl0_2304,
    inference(avatar_split_clause,[],[f1983,f28086]) ).

fof(f28086,plain,
    ( spl0_2304
  <=> ! [X18,X47,X27,X2] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
        | ~ class_Numeral_Onumber(X2)
        | ~ c_lessequals(X18,X27,X2)
        | ~ c_lessequals(X27,X18,X2)
        | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2304])]) ).

fof(f1983,axiom,
    ! [X2,X18,X47,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
      | ~ class_Numeral_Onumber(X2)
      | ~ c_lessequals(X18,X27,X2)
      | ~ c_lessequals(X27,X18,X2)
      | c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).

fof(f28084,plain,
    spl0_2303,
    inference(avatar_split_clause,[],[f1794,f28082]) ).

fof(f28082,plain,
    ( spl0_2303
  <=> ! [X0,X23,X25,X2,X1] :
        ( c_in(X0,c_List_Oset(X23,X1),X1)
        | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
        | c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2303])]) ).

fof(f1794,axiom,
    ! [X2,X0,X1,X25,X23] :
      ( c_in(X0,c_List_Oset(X23,X1),X1)
      | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
      | c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).

fof(f28080,plain,
    spl0_2302,
    inference(avatar_split_clause,[],[f1793,f28078]) ).

fof(f28078,plain,
    ( spl0_2302
  <=> ! [X0,X23,X25,X2,X1] :
        ( ~ c_in(X0,c_List_Oset(X23,X1),X1)
        | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
        | c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2302])]) ).

fof(f1793,axiom,
    ! [X2,X0,X1,X25,X23] :
      ( ~ c_in(X0,c_List_Oset(X23,X1),X1)
      | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
      | c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).

fof(f28076,plain,
    spl0_2301,
    inference(avatar_split_clause,[],[f1789,f28074]) ).

fof(f28074,plain,
    ( spl0_2301
  <=> ! [X3,X0,X23,X25,X2,X1] : c_List_Ozip(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X2),X1,X2) = c_List_Olist_OCons(c_Pair(X0,X3,X1,X2),c_List_Ozip(X23,X25,X1,X2),tc_prod(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2301])]) ).

fof(f1789,axiom,
    ! [X2,X3,X0,X1,X25,X23] : c_List_Ozip(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X2),X1,X2) = c_List_Olist_OCons(c_Pair(X0,X3,X1,X2),c_List_Ozip(X23,X25,X1,X2),tc_prod(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).

fof(f28072,plain,
    spl0_2300,
    inference(avatar_split_clause,[],[f1616,f28070]) ).

fof(f28070,plain,
    ( spl0_2300
  <=> ! [X5,X1,X3] :
        ( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X3,X1),c_Main_Olexord__Nil__left__2(X3,X1),X1) = X3
        | ~ c_in(c_Pair(c_List_Olist_ONil,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2300])]) ).

fof(f1616,axiom,
    ! [X3,X1,X5] :
      ( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X3,X1),c_Main_Olexord__Nil__left__2(X3,X1),X1) = X3
      | ~ c_in(c_Pair(c_List_Olist_ONil,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).

fof(f28068,plain,
    spl0_2299,
    inference(avatar_split_clause,[],[f1458,f28066]) ).

fof(f28066,plain,
    ( spl0_2299
  <=> ! [X11] :
        ( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).

fof(f1458,axiom,
    ! [X11] :
      ( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).

fof(f28064,plain,
    spl0_2298,
    inference(avatar_split_clause,[],[f118,f28062]) ).

fof(f28062,plain,
    ( spl0_2298
  <=> ! [X13,X14,X12,X2,X1] :
        ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
        | c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
        | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2298])]) ).

fof(f118,axiom,
    ! [X2,X1,X14,X12,X13] :
      ( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
      | c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
      | ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).

fof(f27999,plain,
    ( spl0_2297
    | ~ spl0_1864
    | ~ spl0_2192 ),
    inference(avatar_split_clause,[],[f27856,f24816,f17761,f27997]) ).

fof(f17761,plain,
    ( spl0_1864
  <=> ! [X18,X13,X12,X1] :
        ( ~ c_in(X18,X13,X1)
        | c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).

fof(f27856,plain,
    ( ! [X0] : ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_1864
    | ~ spl0_2192 ),
    inference(trivial_inequality_removal,[],[f27854]) ).

fof(f27854,plain,
    ( ! [X0] :
        ( c_emptyset != c_emptyset
        | ~ c_in(v_B,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) )
    | ~ spl0_1864
    | ~ spl0_2192 ),
    inference(superposition,[],[f17762,f24817]) ).

fof(f17762,plain,
    ( ! [X18,X1,X12,X13] :
        ( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1)
        | ~ c_in(X18,X13,X1) )
    | ~ spl0_1864 ),
    inference(avatar_component_clause,[],[f17761]) ).

fof(f27881,plain,
    spl0_2296,
    inference(avatar_split_clause,[],[f3220,f27879]) ).

fof(f27879,plain,
    ( spl0_2296
  <=> ! [X25,X1,X23] :
        ( ~ c_List_Odistinct(X23,X1)
        | ~ c_List_Odistinct(X25,X1)
        | c_List_Odistinct(c_append(X23,X25,X1),X1)
        | c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2296])]) ).

fof(f3220,plain,
    ! [X1,X25,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | ~ c_List_Odistinct(X25,X1)
      | c_List_Odistinct(c_append(X23,X25,X1),X1)
      | c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ),
    inference(definition_unfolding,[],[f1558,f2373]) ).

fof(f2373,axiom,
    ! [X1,X12,X13] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).

fof(f1558,axiom,
    ! [X1,X25,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | ~ c_List_Odistinct(X25,X1)
      | c_List_Odistinct(c_append(X23,X25,X1),X1)
      | c_emptyset != c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).

fof(f27877,plain,
    spl0_2295,
    inference(avatar_split_clause,[],[f3199,f27875]) ).

fof(f27875,plain,
    ( spl0_2295
  <=> ! [X86,X87,X88] :
        ( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2295])]) ).

fof(f3199,plain,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    inference(definition_unfolding,[],[f2819,f2812]) ).

fof(f2819,axiom,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | ~ c_in(c_Message_OHPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_0) ).

fof(f27873,plain,
    spl0_2294,
    inference(avatar_split_clause,[],[f3190,f27871]) ).

fof(f27871,plain,
    ( spl0_2294
  <=> ! [X18,X13,X12,X1] :
        ( c_in(X18,X13,X1)
        | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
        | c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2294])]) ).

fof(f3190,plain,
    ! [X18,X1,X12,X13] :
      ( c_in(X18,X13,X1)
      | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
      | c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
    inference(definition_unfolding,[],[f2679,f2373,f2373]) ).

fof(f2679,axiom,
    ! [X18,X1,X12,X13] :
      ( c_in(X18,X13,X1)
      | c_emptyset != c_inter(X12,X13,X1)
      | c_emptyset = c_inter(c_insert(X18,X12,X1),X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).

fof(f27869,plain,
    spl0_2293,
    inference(avatar_split_clause,[],[f3188,f27867]) ).

fof(f27867,plain,
    ( spl0_2293
  <=> ! [X13,X12,X27,X1] :
        ( c_in(X27,X12,X1)
        | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
        | c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2293])]) ).

fof(f3188,plain,
    ! [X1,X27,X12,X13] :
      ( c_in(X27,X12,X1)
      | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
      | c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ),
    inference(definition_unfolding,[],[f2666,f2373,f2373]) ).

fof(f2666,axiom,
    ! [X1,X27,X12,X13] :
      ( c_in(X27,X12,X1)
      | c_emptyset != c_inter(X12,X13,X1)
      | c_emptyset = c_inter(X12,c_insert(X27,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).

fof(f27865,plain,
    spl0_2292,
    inference(avatar_split_clause,[],[f2942,f27863]) ).

fof(f27863,plain,
    ( spl0_2292
  <=> ! [X102,X86,X13] :
        ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Event_Oevent_OGets(X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(c_Event_Oevent_OSays(v_sko__wPE(X13,X86,X102),X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2292])]) ).

fof(f2942,axiom,
    ! [X86,X102,X13] :
      ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Event_Oevent_OGets(X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
      | c_in(c_Event_Oevent_OSays(v_sko__wPE(X13,X86,X102),X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__Says_0) ).

fof(f27830,plain,
    spl0_2291,
    inference(avatar_split_clause,[],[f2848,f27828]) ).

fof(f27828,plain,
    ( spl0_2291
  <=> ! [X86,X91,X88] :
        ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
        | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2291])]) ).

fof(f2848,axiom,
    ! [X91,X88,X86] :
      ( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).

fof(f27826,plain,
    spl0_2290,
    inference(avatar_split_clause,[],[f1792,f27824]) ).

fof(f27824,plain,
    ( spl0_2290
  <=> ! [X59,X43,X0,X3,X2,X1] : c_List_Ozip(c_List_Oreplicate(X43,X0,X1),c_List_Oreplicate(X59,X3,X2),X1,X2) = c_List_Oreplicate(c_Orderings_Omin(X43,X59,tc_nat),c_Pair(X0,X3,X1,X2),tc_prod(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2290])]) ).

fof(f1792,axiom,
    ! [X2,X3,X0,X59,X1,X43] : c_List_Ozip(c_List_Oreplicate(X43,X0,X1),c_List_Oreplicate(X59,X3,X2),X1,X2) = c_List_Oreplicate(c_Orderings_Omin(X43,X59,tc_nat),c_Pair(X0,X3,X1,X2),tc_prod(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).

fof(f27822,plain,
    spl0_2289,
    inference(avatar_split_clause,[],[f1698,f27820]) ).

fof(f27820,plain,
    ( spl0_2289
  <=> ! [X43,X23,X21,X1] :
        ( ~ c_lessequals(c_plus(X21,X43,tc_nat),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
        | c_List_Onth(c_List_Odrop(X21,X23,X1),X43,X1) = c_List_Onth(X23,c_plus(X21,X43,tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2289])]) ).

fof(f1698,axiom,
    ! [X21,X1,X23,X43] :
      ( ~ c_lessequals(c_plus(X21,X43,tc_nat),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
      | c_List_Onth(c_List_Odrop(X21,X23,X1),X43,X1) = c_List_Onth(X23,c_plus(X21,X43,tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).

fof(f27776,plain,
    ( spl0_2288
    | ~ spl0_57
    | ~ spl0_1588
    | ~ spl0_2284 ),
    inference(avatar_split_clause,[],[f27251,f27248,f12886,f3714,f27774]) ).

fof(f27774,plain,
    ( spl0_2288
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2288])]) ).

fof(f12886,plain,
    ( spl0_1588
  <=> ! [X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).

fof(f27248,plain,
    ( spl0_2284
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).

fof(f27251,plain,
    ( ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
    | ~ spl0_57
    | ~ spl0_1588
    | ~ spl0_2284 ),
    inference(forward_demodulation,[],[f27249,f14195]) ).

fof(f14195,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_57
    | ~ spl0_1588 ),
    inference(resolution,[],[f12887,f3716]) ).

fof(f12887,plain,
    ( ! [X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) )
    | ~ spl0_1588 ),
    inference(avatar_component_clause,[],[f12886]) ).

fof(f27249,plain,
    ( ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
    | ~ spl0_2284 ),
    inference(avatar_component_clause,[],[f27248]) ).

fof(f27335,plain,
    ( spl0_2287
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2265 ),
    inference(avatar_split_clause,[],[f27071,f27068,f12670,f9587,f27333]) ).

fof(f27333,plain,
    ( spl0_2287
  <=> ! [X11] :
        ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).

fof(f27068,plain,
    ( spl0_2265
  <=> ! [X11] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2265])]) ).

fof(f27071,plain,
    ( ! [X11] :
        ( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1195
    | ~ spl0_1537
    | ~ spl0_2265 ),
    inference(forward_demodulation,[],[f27069,f13748]) ).

fof(f27069,plain,
    ( ! [X11] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2265 ),
    inference(avatar_component_clause,[],[f27068]) ).

fof(f27331,plain,
    ( spl0_2286
    | ~ spl0_811
    | ~ spl0_2170
    | ~ spl0_2236 ),
    inference(avatar_split_clause,[],[f26120,f26060,f23995,f7607,f27328]) ).

fof(f27328,plain,
    ( spl0_2286
  <=> c_UNIV = c_union(c_uminus(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2286])]) ).

fof(f26060,plain,
    ( spl0_2236
  <=> c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2236])]) ).

fof(f26120,plain,
    ( c_UNIV = c_union(c_uminus(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_811
    | ~ spl0_2170
    | ~ spl0_2236 ),
    inference(forward_demodulation,[],[f26113,f7608]) ).

fof(f26113,plain,
    ( c_uminus(c_emptyset,tc_set(tc_Message_Oagent)) = c_union(c_uminus(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_set(tc_Message_Oagent)),c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_2170
    | ~ spl0_2236 ),
    inference(superposition,[],[f23996,f26062]) ).

fof(f26062,plain,
    ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_2236 ),
    inference(avatar_component_clause,[],[f26060]) ).

fof(f27326,plain,
    ( spl0_2285
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2264 ),
    inference(avatar_split_clause,[],[f27066,f27063,f12670,f9583,f27324]) ).

fof(f27324,plain,
    ( spl0_2285
  <=> ! [X11] :
        ( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2285])]) ).

fof(f27063,plain,
    ( spl0_2264
  <=> ! [X11] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2264])]) ).

fof(f27066,plain,
    ( ! [X11] :
        ( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1194
    | ~ spl0_1537
    | ~ spl0_2264 ),
    inference(forward_demodulation,[],[f27064,f13749]) ).

fof(f27064,plain,
    ( ! [X11] :
        ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
    | ~ spl0_2264 ),
    inference(avatar_component_clause,[],[f27063]) ).

fof(f27250,plain,
    spl0_2284,
    inference(avatar_split_clause,[],[f3197,f27248]) ).

fof(f3197,plain,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1859,f2129,f2129]) ).

fof(f1859,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).

fof(f27246,plain,
    spl0_2283,
    inference(avatar_split_clause,[],[f3106,f27244]) ).

fof(f27244,plain,
    ( spl0_2283
  <=> ! [X4,X47,X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1),X4,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2283])]) ).

fof(f3106,plain,
    ! [X11,X1,X47,X4] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1),X4,X1) ),
    inference(definition_unfolding,[],[f2107,f2129]) ).

fof(f2107,axiom,
    ! [X11,X1,X47,X4] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1),X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).

fof(f27222,plain,
    ( spl0_2282
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2281 ),
    inference(avatar_split_clause,[],[f27218,f27215,f11334,f10936,f7067,f6122,f27220]) ).

fof(f27220,plain,
    ( spl0_2282
  <=> ! [X41,X21,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_plus(c_1,X21,tc_nat),tc_set(tc_prod(X41,X41))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2282])]) ).

fof(f27215,plain,
    ( spl0_2281
  <=> ! [X41,X21,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2281])]) ).

fof(f27218,plain,
    ( ! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_plus(c_1,X21,tc_nat),tc_set(tc_prod(X41,X41)))
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2281 ),
    inference(forward_demodulation,[],[f27216,f12301]) ).

fof(f27216,plain,
    ( ! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41)))
    | ~ spl0_2281 ),
    inference(avatar_component_clause,[],[f27215]) ).

fof(f27217,plain,
    spl0_2281,
    inference(avatar_split_clause,[],[f3092,f27215]) ).

fof(f3092,plain,
    ! [X21,X41,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41))),
    inference(definition_unfolding,[],[f2391,f2544]) ).

fof(f2391,axiom,
    ! [X21,X41,X85] : c_Nat_Opower(X85,c_Suc(X21),tc_set(tc_prod(X41,X41))) = c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).

fof(f27213,plain,
    spl0_2280,
    inference(avatar_split_clause,[],[f3087,f27211]) ).

fof(f27211,plain,
    ( spl0_2280
  <=> ! [X18,X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),c_insert(X18,X13,X1),X1,X1) = c_insert(X18,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2280])]) ).

fof(f3087,plain,
    ! [X18,X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),c_insert(X18,X13,X1),X1,X1) = c_insert(X18,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1),
    inference(definition_unfolding,[],[f2686,f2373,f2373]) ).

fof(f2686,axiom,
    ! [X18,X1,X12,X13] : c_inter(c_insert(X18,X12,X1),c_insert(X18,X13,X1),X1) = c_insert(X18,c_inter(X12,X13,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).

fof(f27209,plain,
    spl0_2279,
    inference(avatar_split_clause,[],[f3080,f27207]) ).

fof(f27207,plain,
    ( spl0_2279
  <=> ! [X13,X12,X1] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X12,X1),tc_List_Olist(X1)),c_List_Olists(X13,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2279])]) ).

fof(f3080,plain,
    ! [X1,X12,X13] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X12,X1),tc_List_Olist(X1)),c_List_Olists(X13,X1),tc_List_Olist(X1),tc_List_Olist(X1)),
    inference(definition_unfolding,[],[f1637,f2373,f2373]) ).

fof(f1637,axiom,
    ! [X1,X12,X13] : c_List_Olists(c_inter(X12,X13,X1),X1) = c_inter(c_List_Olists(X12,X1),c_List_Olists(X13,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).

fof(f27205,plain,
    spl0_2278,
    inference(avatar_split_clause,[],[f3079,f27203]) ).

fof(f27203,plain,
    ( spl0_2278
  <=> ! [X13,X12,X1] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X12,X1),tc_set(X1)),c_Pow(X13,X1),tc_set(X1),tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2278])]) ).

fof(f3079,plain,
    ! [X1,X12,X13] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X12,X1),tc_set(X1)),c_Pow(X13,X1),tc_set(X1),tc_set(X1)),
    inference(definition_unfolding,[],[f2624,f2373,f2373]) ).

fof(f2624,axiom,
    ! [X1,X12,X13] : c_Pow(c_inter(X12,X13,X1),X1) = c_inter(c_Pow(X12,X1),c_Pow(X13,X1),tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).

fof(f27123,plain,
    ( spl0_2277
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2276 ),
    inference(avatar_split_clause,[],[f27119,f27115,f11334,f10936,f7067,f6122,f27121]) ).

fof(f27121,plain,
    ( spl0_2277
  <=> ! [X16,X21] : c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),c_plus(c_1,X16,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2277])]) ).

fof(f27115,plain,
    ( spl0_2276
  <=> ! [X16,X21] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).

fof(f27119,plain,
    ( ! [X21,X16] : c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),c_plus(c_1,X16,tc_nat))
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2276 ),
    inference(forward_demodulation,[],[f27118,f12301]) ).

fof(f27118,plain,
    ( ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_plus(c_1,X16,tc_nat)),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2276 ),
    inference(forward_demodulation,[],[f27116,f12301]) ).

fof(f27116,plain,
    ( ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_2276 ),
    inference(avatar_component_clause,[],[f27115]) ).

fof(f27117,plain,
    spl0_2276,
    inference(avatar_split_clause,[],[f3073,f27115]) ).

fof(f3073,plain,
    ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f1162,f2544,f2544,f2544]) ).

fof(f1162,axiom,
    ! [X21,X16] : c_Binomial_Obinomial(c_Suc(X21),c_Suc(X16)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Suc(X16)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).

fof(f27111,plain,
    spl0_2275,
    inference(avatar_split_clause,[],[f3032,f27109]) ).

fof(f27109,plain,
    ( spl0_2275
  <=> ! [X5,X1] : c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),c_Relation_OId,tc_prod(X1,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2275])]) ).

fof(f3032,plain,
    ! [X1,X5] : c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),c_Relation_OId,tc_prod(X1,X1)),X1),
    inference(definition_unfolding,[],[f2710,f2716,f2716,f2716]) ).

fof(f2710,axiom,
    ! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X5,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).

fof(f27107,plain,
    spl0_2274,
    inference(avatar_split_clause,[],[f2949,f27105]) ).

fof(f27105,plain,
    ( spl0_2274
  <=> ! [X61,X102,X115,X12,X114,X91,X24] : c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X24),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X61,c_Message_Omsg_ONonce(X114))))),X115)),X102,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).

fof(f2949,axiom,
    ! [X91,X114,X24,X12,X61,X115,X102] : c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X24),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X61,c_Message_Omsg_ONonce(X114))))),X115)),X102,tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_2) ).

fof(f27103,plain,
    ( spl0_2273
    | ~ spl0_1750
    | ~ spl0_2225 ),
    inference(avatar_split_clause,[],[f26017,f25697,f15898,f27101]) ).

fof(f27101,plain,
    ( spl0_2273
  <=> ! [X0,X1] : ~ c_in(v_A,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2273])]) ).

fof(f25697,plain,
    ( spl0_2225
  <=> ! [X0] : ~ c_in(v_A,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).

fof(f26017,plain,
    ( ! [X0,X1] : ~ c_in(v_A,c_Inter(c_union(X0,c_insert(c_Event_Obad,X1,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1750
    | ~ spl0_2225 ),
    inference(superposition,[],[f25698,f15899]) ).

fof(f25698,plain,
    ( ! [X0] : ~ c_in(v_A,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2225 ),
    inference(avatar_component_clause,[],[f25697]) ).

fof(f27099,plain,
    spl0_2272,
    inference(avatar_split_clause,[],[f2934,f27097]) ).

fof(f27097,plain,
    ( spl0_2272
  <=> ! [X86,X109,X88] :
        ( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | ~ c_in(X109,c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg)
        | c_in(X109,c_union(c_Message_Osynth(c_Message_Oanalz(X88)),c_Message_Oparts(X88),tc_Message_Omsg),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2272])]) ).

fof(f2934,axiom,
    ! [X109,X88,X86] :
      ( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | ~ c_in(X109,c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg)
      | c_in(X109,c_union(c_Message_Osynth(c_Message_Oanalz(X88)),c_Message_Oparts(X88),tc_Message_Omsg),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).

fof(f27095,plain,
    spl0_2271,
    inference(avatar_split_clause,[],[f2316,f27093]) ).

fof(f27093,plain,
    ( spl0_2271
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_Nat_Opower(c_HOL_Oabs(X0,X1),c_Numeral_Onumber__of(X11,tc_nat),X1) = c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2271])]) ).

fof(f2316,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_Nat_Opower(c_HOL_Oabs(X0,X1),c_Numeral_Onumber__of(X11,tc_nat),X1) = c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).

fof(f27091,plain,
    spl0_2270,
    inference(avatar_split_clause,[],[f1826,f27089]) ).

fof(f27089,plain,
    ( spl0_2270
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X83),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2270])]) ).

fof(f1826,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X83),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).

fof(f27087,plain,
    spl0_2269,
    inference(avatar_split_clause,[],[f1695,f27085]) ).

fof(f27085,plain,
    ( spl0_2269
  <=> ! [X0,X1,X23,X47] :
        ( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
        | c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Numeral_Onumber__of(X47,tc_nat),X1) = c_List_Onth(X23,c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).

fof(f1695,axiom,
    ! [X0,X47,X1,X23] :
      ( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
      | c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Numeral_Onumber__of(X47,tc_nat),X1) = c_List_Onth(X23,c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).

fof(f27083,plain,
    spl0_2268,
    inference(avatar_split_clause,[],[f1573,f27081]) ).

fof(f27081,plain,
    ( spl0_2268
  <=> ! [X21,X23,X25,X1] : c_List_Odrop(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Odrop(X21,X23,X1),c_List_Odrop(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2268])]) ).

fof(f1573,axiom,
    ! [X21,X1,X25,X23] : c_List_Odrop(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Odrop(X21,X23,X1),c_List_Odrop(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).

fof(f27079,plain,
    spl0_2267,
    inference(avatar_split_clause,[],[f1571,f27077]) ).

fof(f27077,plain,
    ( spl0_2267
  <=> ! [X47,X0,X23,X1] :
        ( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
        | c_List_Odrop(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).

fof(f1571,axiom,
    ! [X0,X47,X1,X23] :
      ( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
      | c_List_Odrop(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).

fof(f27075,plain,
    spl0_2266,
    inference(avatar_split_clause,[],[f1526,f27073]) ).

fof(f27073,plain,
    ( spl0_2266
  <=> ! [X23,X12,X25,X1] :
        ( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2266])]) ).

fof(f1526,axiom,
    ! [X1,X25,X12,X23] :
      ( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).

fof(f27070,plain,
    spl0_2265,
    inference(avatar_split_clause,[],[f1447,f27068]) ).

fof(f1447,axiom,
    ! [X11] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).

fof(f27065,plain,
    spl0_2264,
    inference(avatar_split_clause,[],[f1437,f27063]) ).

fof(f1437,axiom,
    ! [X11] :
      ( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).

fof(f27061,plain,
    spl0_2263,
    inference(avatar_split_clause,[],[f1381,f27059]) ).

fof(f27059,plain,
    ( spl0_2263
  <=> ! [X0,X3] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X0,X3,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2263])]) ).

fof(f1381,axiom,
    ! [X3,X0] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X0,X3,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
    file('/export/starexec/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(f27051,plain,
    spl0_2262,
    inference(avatar_split_clause,[],[f1269,f27049]) ).

fof(f27049,plain,
    ( spl0_2262
  <=> ! [X24,X0,X12,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X24,X12,X1)
        | c_less(X0,X24,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_less(X0,c_Finite__Set_OMin(X12,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2262])]) ).

fof(f1269,axiom,
    ! [X0,X1,X24,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X24,X12,X1)
      | c_less(X0,X24,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_less(X0,c_Finite__Set_OMin(X12,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).

fof(f27047,plain,
    spl0_2261,
    inference(avatar_split_clause,[],[f1266,f27045]) ).

fof(f27045,plain,
    ( spl0_2261
  <=> ! [X24,X0,X12,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X24,X12,X1)
        | c_lessequals(X0,X24,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2261])]) ).

fof(f1266,axiom,
    ! [X0,X1,X24,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X24,X12,X1)
      | c_lessequals(X0,X24,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).

fof(f27043,plain,
    spl0_2260,
    inference(avatar_split_clause,[],[f1262,f27041]) ).

fof(f27041,plain,
    ( spl0_2260
  <=> ! [X24,X0,X12,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X24,X12,X1)
        | c_less(X24,X0,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_less(c_Finite__Set_OMax(X12,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2260])]) ).

fof(f1262,axiom,
    ! [X0,X1,X24,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X24,X12,X1)
      | c_less(X24,X0,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_less(c_Finite__Set_OMax(X12,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).

fof(f27039,plain,
    spl0_2259,
    inference(avatar_split_clause,[],[f1259,f27037]) ).

fof(f27037,plain,
    ( spl0_2259
  <=> ! [X24,X0,X12,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X24,X12,X1)
        | c_lessequals(X24,X0,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2259])]) ).

fof(f1259,axiom,
    ! [X0,X1,X24,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X24,X12,X1)
      | c_lessequals(X24,X0,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).

fof(f27035,plain,
    spl0_2258,
    inference(avatar_split_clause,[],[f78,f27033]) ).

fof(f27033,plain,
    ( spl0_2258
  <=> ! [X5,X29,X2,X1] :
        ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
        | c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2258])]) ).

fof(f78,axiom,
    ! [X2,X29,X1,X5] :
      ( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
      | c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).

fof(f26841,plain,
    ( spl0_2257
    | ~ spl0_1501
    | ~ spl0_2225 ),
    inference(avatar_split_clause,[],[f26014,f25697,f12512,f26839]) ).

fof(f26014,plain,
    ( ! [X0] : ~ c_in(v_A,c_Inter(c_List_Oset(c_List_Olist_OCons(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1501
    | ~ spl0_2225 ),
    inference(superposition,[],[f25698,f12513]) ).

fof(f26231,plain,
    ( spl0_2256
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2254 ),
    inference(avatar_split_clause,[],[f26223,f26220,f21025,f7546,f7510,f26229]) ).

fof(f26229,plain,
    ( spl0_2256
  <=> ! [X2,X11] :
        ( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_plus(c_1,c_1,tc_nat),X2)
        | ~ class_Power_Orecpower(X2)
        | ~ class_Numeral_Onumber(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).

fof(f26220,plain,
    ( spl0_2254
  <=> ! [X2,X11] :
        ( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
        | ~ class_Power_Orecpower(X2)
        | ~ class_Numeral_Onumber(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2254])]) ).

fof(f26223,plain,
    ( ! [X2,X11] :
        ( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_plus(c_1,c_1,tc_nat),X2)
        | ~ class_Power_Orecpower(X2)
        | ~ class_Numeral_Onumber(X2) )
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2254 ),
    inference(forward_demodulation,[],[f26221,f21108]) ).

fof(f26221,plain,
    ( ! [X2,X11] :
        ( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
        | ~ class_Power_Orecpower(X2)
        | ~ class_Numeral_Onumber(X2) )
    | ~ spl0_2254 ),
    inference(avatar_component_clause,[],[f26220]) ).

fof(f26227,plain,
    ( spl0_2255
    | ~ spl0_2159
    | ~ spl0_2224 ),
    inference(avatar_split_clause,[],[f25564,f25296,f23898,f26225]) ).

fof(f26225,plain,
    ( spl0_2255
  <=> ! [X0] : ~ c_in(c_Pair(X0,v_A,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2255])]) ).

fof(f25296,plain,
    ( spl0_2224
  <=> ! [X0] : ~ c_in(v_A,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).

fof(f25564,plain,
    ( ! [X0] : ~ c_in(c_Pair(X0,v_A,tc_Message_Oagent,tc_Message_Oagent),c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),tc_prod(tc_Message_Oagent,tc_Message_Oagent))
    | ~ spl0_2159
    | ~ spl0_2224 ),
    inference(resolution,[],[f25297,f23899]) ).

fof(f25297,plain,
    ( ! [X0] : ~ c_in(v_A,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_2224 ),
    inference(avatar_component_clause,[],[f25296]) ).

fof(f26222,plain,
    spl0_2254,
    inference(avatar_split_clause,[],[f3389,f26220]) ).

fof(f3389,plain,
    ! [X2,X11] :
      ( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
      | ~ class_Power_Orecpower(X2)
      | ~ class_Numeral_Onumber(X2) ),
    inference(forward_demodulation,[],[f3388,f2156]) ).

fof(f3388,plain,
    ! [X2,X11] :
      ( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X2)
      | ~ class_Power_Orecpower(X2)
      | ~ class_Numeral_Onumber(X2) ),
    inference(forward_demodulation,[],[f3387,f2154]) ).

fof(f3387,plain,
    ! [X2,X11] :
      ( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X2)
      | ~ class_Power_Orecpower(X2)
      | ~ class_Numeral_Onumber(X2) ),
    inference(forward_demodulation,[],[f1874,f2156]) ).

fof(f1874,axiom,
    ! [X2,X11] :
      ( ~ class_Power_Orecpower(X2)
      | ~ class_Numeral_Onumber(X2)
      | c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).

fof(f26218,plain,
    spl0_2253,
    inference(avatar_split_clause,[],[f3326,f26216]) ).

fof(f26216,plain,
    ( spl0_2253
  <=> ! [X16,X59,X15] :
        ( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X15,c_minus(X59,X16,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X16,X59,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2253])]) ).

fof(f3326,plain,
    ! [X59,X16,X15] :
      ( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X15,c_minus(X59,X16,tc_nat),tc_nat),tc_nat)
      | ~ c_lessequals(X16,X59,tc_nat) ),
    inference(forward_demodulation,[],[f3325,f3052]) ).

fof(f3052,plain,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat),
    inference(definition_unfolding,[],[f2540,f2544]) ).

fof(f2540,axiom,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Suc(X14),X26,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).

fof(f3325,plain,
    ! [X59,X16,X15] :
      ( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),X15,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X16,X15,tc_nat),X59,tc_nat),tc_nat)
      | ~ c_lessequals(X16,X59,tc_nat) ),
    inference(forward_demodulation,[],[f3135,f3052]) ).

fof(f3135,plain,
    ! [X59,X16,X15] :
      ( ~ c_lessequals(X16,X59,tc_nat)
      | c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),X15,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat),c_plus(X16,X15,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1798,f2544,f2544]) ).

fof(f1798,axiom,
    ! [X59,X16,X15] :
      ( ~ c_lessequals(X16,X59,tc_nat)
      | c_minus(c_Suc(c_minus(X59,X16,tc_nat)),X15,tc_nat) = c_minus(c_Suc(X59),c_plus(X16,X15,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).

fof(f26214,plain,
    spl0_2252,
    inference(avatar_split_clause,[],[f3324,f26212]) ).

fof(f26212,plain,
    ( spl0_2252
  <=> ! [X16,X59,X15] :
        ( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X59,X16,tc_nat),X15,tc_nat),tc_nat)
        | ~ c_lessequals(X16,X59,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2252])]) ).

fof(f3324,plain,
    ! [X59,X16,X15] :
      ( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X59,X16,tc_nat),X15,tc_nat),tc_nat)
      | ~ c_lessequals(X16,X59,tc_nat) ),
    inference(forward_demodulation,[],[f3323,f3051]) ).

fof(f3051,plain,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2547,f2544]) ).

fof(f2547,axiom,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Suc(X26),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).

fof(f3323,plain,
    ! [X59,X16,X15] :
      ( c_minus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X59,c_plus(X15,X16,tc_nat),tc_nat),tc_nat)
      | ~ c_lessequals(X16,X59,tc_nat) ),
    inference(forward_demodulation,[],[f3134,f3051]) ).

fof(f3134,plain,
    ! [X59,X16,X15] :
      ( ~ c_lessequals(X16,X59,tc_nat)
      | c_minus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X59,X16,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X15,X16,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1797,f2544,f2544]) ).

fof(f1797,axiom,
    ! [X59,X16,X15] :
      ( ~ c_lessequals(X16,X59,tc_nat)
      | c_minus(X15,c_Suc(c_minus(X59,X16,tc_nat)),tc_nat) = c_minus(c_plus(X15,X16,tc_nat),c_Suc(X59),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).

fof(f26164,plain,
    ( spl0_2251
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2250 ),
    inference(avatar_split_clause,[],[f26160,f26157,f11334,f10936,f7067,f6122,f26162]) ).

fof(f26162,plain,
    ( spl0_2251
  <=> ! [X12,X0,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_plus(c_1,c_Finite__Set_Ocard(X12,X1),tc_nat)
        | c_in(X0,X12,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2251])]) ).

fof(f26157,plain,
    ( spl0_2250
  <=> ! [X12,X0,X1] :
        ( c_in(X0,X12,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).

fof(f26160,plain,
    ( ! [X0,X1,X12] :
        ( c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_plus(c_1,c_Finite__Set_Ocard(X12,X1),tc_nat)
        | c_in(X0,X12,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2250 ),
    inference(forward_demodulation,[],[f26158,f12301]) ).

fof(f26158,plain,
    ( ! [X0,X1,X12] :
        ( c_in(X0,X12,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) )
    | ~ spl0_2250 ),
    inference(avatar_component_clause,[],[f26157]) ).

fof(f26159,plain,
    spl0_2250,
    inference(avatar_split_clause,[],[f3187,f26157]) ).

fof(f3187,plain,
    ! [X0,X1,X12] :
      ( c_in(X0,X12,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X12,X1),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1280,f2544]) ).

fof(f1280,axiom,
    ! [X0,X1,X12] :
      ( c_in(X0,X12,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Suc(c_Finite__Set_Ocard(X12,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).

fof(f26134,plain,
    ( spl0_2249
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2248 ),
    inference(avatar_split_clause,[],[f26130,f26127,f11334,f10936,f7067,f6122,f26132]) ).

fof(f26132,plain,
    ( spl0_2249
  <=> ! [X0,X23,X21,X1] : c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) = c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_plus(c_1,X21,tc_nat),tc_nat),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).

fof(f26127,plain,
    ( spl0_2248
  <=> ! [X0,X23,X21,X1] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).

fof(f26130,plain,
    ( ! [X21,X0,X1,X23] : c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1) = c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_plus(c_1,X21,tc_nat),tc_nat),X1)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2248 ),
    inference(forward_demodulation,[],[f26128,f12301]) ).

fof(f26128,plain,
    ( ! [X21,X0,X1,X23] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1)
    | ~ spl0_2248 ),
    inference(avatar_component_clause,[],[f26127]) ).

fof(f26129,plain,
    spl0_2248,
    inference(avatar_split_clause,[],[f3082,f26127]) ).

fof(f3082,plain,
    ! [X21,X0,X1,X23] : c_List_Osublist(c_List_Olist_OCons(X0,X23,X1),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),X1) = c_List_Olist_OCons(X0,c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X1),
    inference(definition_unfolding,[],[f1769,f1766,f2544,f1766]) ).

fof(f1769,axiom,
    ! [X21,X0,X1,X23] : c_List_Otake(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(X21,X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).

fof(f26125,plain,
    spl0_2247,
    inference(avatar_split_clause,[],[f2952,f26123]) ).

fof(f26123,plain,
    ( spl0_2247
  <=> ! [X102,X91] :
        ( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Message_Omsg_OKey(X91),c_Event_Oused(X102),tc_Message_Omsg)
        | ~ c_in(X91,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102))),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2247])]) ).

fof(f2952,axiom,
    ! [X91,X102] :
      ( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(c_Message_Omsg_OKey(X91),c_Event_Oused(X102),tc_Message_Omsg)
      | ~ c_in(X91,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102))),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).

fof(f26103,plain,
    spl0_2246,
    inference(avatar_split_clause,[],[f2829,f26101]) ).

fof(f26101,plain,
    ( spl0_2246
  <=> ! [X86,X87,X88] :
        ( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).

fof(f2829,axiom,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Oanalz(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_0) ).

fof(f26099,plain,
    spl0_2245,
    inference(avatar_split_clause,[],[f2385,f26097]) ).

fof(f26097,plain,
    ( spl0_2245
  <=> ! [X18,X5,X27,X2,X1] :
        ( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
        | c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2245])]) ).

fof(f2385,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
      | c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).

fof(f26095,plain,
    spl0_2244,
    inference(avatar_split_clause,[],[f2384,f26093]) ).

fof(f26093,plain,
    ( spl0_2244
  <=> ! [X18,X5,X27,X2,X1] :
        ( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2244])]) ).

fof(f2384,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
      | ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).

fof(f26091,plain,
    spl0_2243,
    inference(avatar_split_clause,[],[f2332,f26089]) ).

fof(f26089,plain,
    ( spl0_2243
  <=> ! [X11,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
        | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).

fof(f2332,axiom,
    ! [X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).

fof(f26087,plain,
    spl0_2242,
    inference(avatar_split_clause,[],[f2322,f26085]) ).

fof(f26085,plain,
    ( spl0_2242
  <=> ! [X11,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
        | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2242])]) ).

fof(f2322,axiom,
    ! [X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
      | c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).

fof(f26083,plain,
    spl0_2241,
    inference(avatar_split_clause,[],[f1877,f26081]) ).

fof(f26081,plain,
    ( spl0_2241
  <=> ! [X11,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_nat),tc_IntDef_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).

fof(f1877,axiom,
    ! [X11,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_nat),tc_IntDef_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).

fof(f26079,plain,
    spl0_2240,
    inference(avatar_split_clause,[],[f1828,f26077]) ).

fof(f26077,plain,
    ( spl0_2240
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).

fof(f1828,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).

fof(f26075,plain,
    spl0_2239,
    inference(avatar_split_clause,[],[f1273,f26073]) ).

fof(f26073,plain,
    ( spl0_2239
  <=> ! [X2,X0,X12] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
        | c_Finite__Set_OMin(c_insert(X0,X12,X2),X2) = c_Orderings_Omin(X0,c_Finite__Set_OMin(X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).

fof(f1273,axiom,
    ! [X2,X0,X12] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
      | c_Finite__Set_OMin(c_insert(X0,X12,X2),X2) = c_Orderings_Omin(X0,c_Finite__Set_OMin(X12,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).

fof(f26071,plain,
    spl0_2238,
    inference(avatar_split_clause,[],[f1271,f26069]) ).

fof(f26069,plain,
    ( spl0_2238
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
        | ~ c_less(X0,c_Main_OMin__gr__iff__1(X12,X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2238])]) ).

fof(f1271,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
      | ~ c_less(X0,c_Main_OMin__gr__iff__1(X12,X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).

fof(f26067,plain,
    spl0_2237,
    inference(avatar_split_clause,[],[f1270,f26065]) ).

fof(f26065,plain,
    ( spl0_2237
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
        | c_in(c_Main_OMin__gr__iff__1(X12,X0,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).

fof(f1270,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
      | c_in(c_Main_OMin__gr__iff__1(X12,X0,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).

fof(f26063,plain,
    ( spl0_2236
    | ~ spl0_892
    | ~ spl0_2189 ),
    inference(avatar_split_clause,[],[f25141,f24534,f7944,f26060]) ).

fof(f24534,plain,
    ( spl0_2189
  <=> ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).

fof(f25141,plain,
    ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_892
    | ~ spl0_2189 ),
    inference(superposition,[],[f24535,f7945]) ).

fof(f24535,plain,
    ( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_2189 ),
    inference(avatar_component_clause,[],[f24534]) ).

fof(f26058,plain,
    spl0_2235,
    inference(avatar_split_clause,[],[f1268,f26056]) ).

fof(f26056,plain,
    ( spl0_2235
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
        | ~ c_lessequals(X0,c_Main_OMin__ge__iff__1(X12,X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2235])]) ).

fof(f1268,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
      | ~ c_lessequals(X0,c_Main_OMin__ge__iff__1(X12,X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).

fof(f26054,plain,
    spl0_2234,
    inference(avatar_split_clause,[],[f1267,f26052]) ).

fof(f26052,plain,
    ( spl0_2234
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
        | c_in(c_Main_OMin__ge__iff__1(X12,X0,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).

fof(f1267,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
      | c_in(c_Main_OMin__ge__iff__1(X12,X0,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).

fof(f26050,plain,
    spl0_2233,
    inference(avatar_split_clause,[],[f1264,f26048]) ).

fof(f26048,plain,
    ( spl0_2233
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
        | ~ c_less(c_Main_OMax__less__iff__1(X12,X0,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2233])]) ).

fof(f1264,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
      | ~ c_less(c_Main_OMax__less__iff__1(X12,X0,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).

fof(f26046,plain,
    spl0_2232,
    inference(avatar_split_clause,[],[f1263,f26044]) ).

fof(f26044,plain,
    ( spl0_2232
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
        | c_in(c_Main_OMax__less__iff__1(X12,X0,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2232])]) ).

fof(f1263,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
      | c_in(c_Main_OMax__less__iff__1(X12,X0,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).

fof(f26042,plain,
    spl0_2231,
    inference(avatar_split_clause,[],[f1261,f26040]) ).

fof(f26040,plain,
    ( spl0_2231
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
        | ~ c_lessequals(c_Main_OMax__le__iff__1(X12,X0,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2231])]) ).

fof(f1261,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
      | ~ c_lessequals(c_Main_OMax__le__iff__1(X12,X0,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).

fof(f26038,plain,
    spl0_2230,
    inference(avatar_split_clause,[],[f1260,f26036]) ).

fof(f26036,plain,
    ( spl0_2230
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
        | c_in(c_Main_OMax__le__iff__1(X12,X0,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2230])]) ).

fof(f1260,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
      | c_in(c_Main_OMax__le__iff__1(X12,X0,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).

fof(f26034,plain,
    spl0_2229,
    inference(avatar_split_clause,[],[f1258,f26032]) ).

fof(f26032,plain,
    ( spl0_2229
  <=> ! [X2,X0,X12] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
        | c_Finite__Set_OMax(c_insert(X0,X12,X2),X2) = c_Orderings_Omax(X0,c_Finite__Set_OMax(X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2229])]) ).

fof(f1258,axiom,
    ! [X2,X0,X12] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
      | c_Finite__Set_OMax(c_insert(X0,X12,X2),X2) = c_Orderings_Omax(X0,c_Finite__Set_OMax(X12,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).

fof(f26030,plain,
    spl0_2228,
    inference(avatar_split_clause,[],[f73,f26028]) ).

fof(f73,axiom,
    ! [X2,X1,X27,X5,X12] :
      ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
      | c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).

fof(f26026,plain,
    spl0_2227,
    inference(avatar_split_clause,[],[f15,f26024]) ).

fof(f26024,plain,
    ( spl0_2227
  <=> ! [X4,X13,X12,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2227])]) ).

fof(f15,axiom,
    ! [X2,X1,X4,X12,X13] :
      ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).

fof(f26022,plain,
    spl0_2226,
    inference(avatar_split_clause,[],[f14,f26020]) ).

fof(f26020,plain,
    ( spl0_2226
  <=> ! [X4,X13,X12,X2,X1] :
        ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2226])]) ).

fof(f14,axiom,
    ! [X2,X1,X4,X12,X13] :
      ( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).

fof(f25699,plain,
    ( spl0_2225
    | ~ spl0_1955
    | ~ spl0_2224 ),
    inference(avatar_split_clause,[],[f25568,f25296,f19613,f25697]) ).

fof(f25568,plain,
    ( ! [X0] : ~ c_in(v_A,c_Inter(c_insert(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1955
    | ~ spl0_2224 ),
    inference(superposition,[],[f25297,f19614]) ).

fof(f25298,plain,
    ( spl0_2224
    | ~ spl0_1843
    | ~ spl0_2203 ),
    inference(avatar_split_clause,[],[f25254,f25204,f17349,f25296]) ).

fof(f25204,plain,
    ( spl0_2203
  <=> ! [X0] : ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).

fof(f25254,plain,
    ( ! [X0] : ~ c_in(v_A,c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent),tc_Message_Oagent)
    | ~ spl0_1843
    | ~ spl0_2203 ),
    inference(superposition,[],[f25205,f17350]) ).

fof(f25205,plain,
    ( ! [X0] : ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_2203 ),
    inference(avatar_component_clause,[],[f25204]) ).

fof(f25294,plain,
    spl0_2223,
    inference(avatar_split_clause,[],[f3196,f25292]) ).

fof(f25292,plain,
    ( spl0_2223
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2223])]) ).

fof(f3196,plain,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(definition_unfolding,[],[f1856,f2129]) ).

fof(f1856,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).

fof(f25290,plain,
    spl0_2222,
    inference(avatar_split_clause,[],[f3195,f25288]) ).

fof(f25288,plain,
    ( spl0_2222
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2222])]) ).

fof(f3195,plain,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X83)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1857,f2129]) ).

fof(f1857,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).

fof(f25286,plain,
    spl0_2221,
    inference(avatar_split_clause,[],[f3168,f25284]) ).

fof(f25284,plain,
    ( spl0_2221
  <=> ! [X21,X43,X15] :
        ( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
        | c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) = c_List_Osublist(c_List_Oupt(X43,X21),c_SetInterval_OlessThan(X15,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2221])]) ).

fof(f3168,plain,
    ! [X21,X15,X43] :
      ( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
      | c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) = c_List_Osublist(c_List_Oupt(X43,X21),c_SetInterval_OlessThan(X15,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1777,f1766]) ).

fof(f1777,axiom,
    ! [X21,X15,X43] :
      ( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
      | c_List_Otake(X15,c_List_Oupt(X43,X21),tc_nat) = c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).

fof(f25282,plain,
    spl0_2220,
    inference(avatar_split_clause,[],[f3047,f25280]) ).

fof(f25280,plain,
    ( spl0_2220
  <=> ! [X85,X1] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),c_Relation_OId,tc_prod(X1,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2220])]) ).

fof(f3047,plain,
    ! [X1,X85] : c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),c_Relation_OId,tc_prod(X1,X1)),X1),
    inference(definition_unfolding,[],[f2712,f2716,f2716]) ).

fof(f2712,axiom,
    ! [X1,X85] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Transitive__Closure_Ortrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).

fof(f25278,plain,
    spl0_2219,
    inference(avatar_split_clause,[],[f2849,f25276]) ).

fof(f25276,plain,
    ( spl0_2219
  <=> ! [X86,X91,X88] :
        ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
        | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).

fof(f2849,axiom,
    ! [X91,X88,X86] :
      ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).

fof(f25274,plain,
    spl0_2218,
    inference(avatar_split_clause,[],[f2562,f25272]) ).

fof(f25272,plain,
    ( spl0_2218
  <=> ! [X15,X43,X21,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_lessequals(X43,X21,X1)
        | c_minus(c_SetInterval_OatLeastLessThan(X43,X15,X1),c_SetInterval_OatLeastLessThan(X43,X21,X1),tc_set(X1)) = c_SetInterval_OatLeastLessThan(X21,X15,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).

fof(f2562,axiom,
    ! [X21,X1,X15,X43] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_lessequals(X43,X21,X1)
      | c_minus(c_SetInterval_OatLeastLessThan(X43,X15,X1),c_SetInterval_OatLeastLessThan(X43,X21,X1),tc_set(X1)) = c_SetInterval_OatLeastLessThan(X21,X15,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).

fof(f25270,plain,
    spl0_2217,
    inference(avatar_split_clause,[],[f2356,f25268]) ).

fof(f25268,plain,
    ( spl0_2217
  <=> ! [X3,X0,X27,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_less(X0,X3,tc_nat)
        | ~ c_less(c_1,X27,X1)
        | c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).

fof(f2356,axiom,
    ! [X3,X0,X1,X27] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_less(X0,X3,tc_nat)
      | ~ c_less(c_1,X27,X1)
      | c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).

fof(f25266,plain,
    spl0_2216,
    inference(avatar_split_clause,[],[f2355,f25264]) ).

fof(f25264,plain,
    ( spl0_2216
  <=> ! [X3,X0,X27,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_less(c_1,X27,X1)
        | c_less(X0,X3,tc_nat)
        | ~ c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).

fof(f2355,axiom,
    ! [X3,X0,X1,X27] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_less(c_1,X27,X1)
      | c_less(X0,X3,tc_nat)
      | ~ c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).

fof(f25262,plain,
    spl0_2215,
    inference(avatar_split_clause,[],[f2351,f25260]) ).

fof(f25260,plain,
    ( spl0_2215
  <=> ! [X3,X0,X27,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_lessequals(X0,X3,tc_nat)
        | ~ c_less(c_1,X27,X1)
        | c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2215])]) ).

fof(f2351,axiom,
    ! [X3,X0,X1,X27] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_lessequals(X0,X3,tc_nat)
      | ~ c_less(c_1,X27,X1)
      | c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).

fof(f25258,plain,
    spl0_2214,
    inference(avatar_split_clause,[],[f2350,f25256]) ).

fof(f25256,plain,
    ( spl0_2214
  <=> ! [X3,X0,X27,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_less(c_1,X27,X1)
        | c_lessequals(X0,X3,tc_nat)
        | ~ c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).

fof(f2350,axiom,
    ! [X3,X0,X1,X27] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_less(c_1,X27,X1)
      | c_lessequals(X0,X3,tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).

fof(f25246,plain,
    spl0_2213,
    inference(avatar_split_clause,[],[f2336,f25244]) ).

fof(f25244,plain,
    ( spl0_2213
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_0,X0,X1)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).

fof(f2336,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_0,X0,X1)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).

fof(f25242,plain,
    spl0_2212,
    inference(avatar_split_clause,[],[f2333,f25240]) ).

fof(f25240,plain,
    ( spl0_2212
  <=> ! [X11,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_0,c_0,X1)
        | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
        | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).

fof(f2333,axiom,
    ! [X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,c_0,X1)
      | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
      | ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).

fof(f25238,plain,
    spl0_2211,
    inference(avatar_split_clause,[],[f2330,f25236]) ).

fof(f25236,plain,
    ( spl0_2211
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_0,X0,X1)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).

fof(f2330,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_0,X0,X1)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).

fof(f25234,plain,
    spl0_2210,
    inference(avatar_split_clause,[],[f2328,f25232]) ).

fof(f25232,plain,
    ( spl0_2210
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_0,X0,X1)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | ~ c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).

fof(f2328,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_0,X0,X1)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | ~ c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).

fof(f25230,plain,
    spl0_2209,
    inference(avatar_split_clause,[],[f2325,f25228]) ).

fof(f25228,plain,
    ( spl0_2209
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(X0,c_0,X1)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).

fof(f2325,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(X0,c_0,X1)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).

fof(f25226,plain,
    spl0_2208,
    inference(avatar_split_clause,[],[f2319,f25224]) ).

fof(f25224,plain,
    ( spl0_2208
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(X0,c_0,X1)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).

fof(f2319,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(X0,c_0,X1)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).

fof(f25222,plain,
    spl0_2207,
    inference(avatar_split_clause,[],[f2168,f25220]) ).

fof(f25220,plain,
    ( spl0_2207
  <=> ! [X48,X47,X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).

fof(f2168,axiom,
    ! [X48,X11,X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).

fof(f25218,plain,
    spl0_2206,
    inference(avatar_split_clause,[],[f2108,f25216]) ).

fof(f25216,plain,
    ( spl0_2206
  <=> ! [X48,X47,X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2206])]) ).

fof(f2108,axiom,
    ! [X48,X11,X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).

fof(f25214,plain,
    spl0_2205,
    inference(avatar_split_clause,[],[f1861,f25212]) ).

fof(f25212,plain,
    ( spl0_2205
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).

fof(f1861,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).

fof(f25210,plain,
    spl0_2204,
    inference(avatar_split_clause,[],[f1834,f25208]) ).

fof(f25208,plain,
    ( spl0_2204
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).

fof(f1834,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_0) ).

fof(f25206,plain,
    ( spl0_2203
    | ~ spl0_1864
    | ~ spl0_2189 ),
    inference(avatar_split_clause,[],[f25157,f24534,f17761,f25204]) ).

fof(f25157,plain,
    ( ! [X0] : ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
    | ~ spl0_1864
    | ~ spl0_2189 ),
    inference(trivial_inequality_removal,[],[f25155]) ).

fof(f25155,plain,
    ( ! [X0] :
        ( c_emptyset != c_emptyset
        | ~ c_in(v_A,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent) )
    | ~ spl0_1864
    | ~ spl0_2189 ),
    inference(superposition,[],[f17762,f24535]) ).

fof(f25202,plain,
    spl0_2202,
    inference(avatar_split_clause,[],[f1825,f25200]) ).

fof(f25200,plain,
    ( spl0_2202
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).

fof(f1825,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).

fof(f25198,plain,
    spl0_2201,
    inference(avatar_split_clause,[],[f1635,f25196]) ).

fof(f25196,plain,
    ( spl0_2201
  <=> ! [X43,X23,X0,X3,X1] :
        ( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
        | c_List_Olist__update(c_List_Olist__update(X23,X43,X0,X1),X43,X3,X1) = c_List_Olist__update(X23,X43,X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).

fof(f1635,axiom,
    ! [X3,X0,X1,X23,X43] :
      ( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
      | c_List_Olist__update(c_List_Olist__update(X23,X43,X0,X1),X43,X3,X1) = c_List_Olist__update(X23,X43,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).

fof(f25194,plain,
    spl0_2200,
    inference(avatar_split_clause,[],[f1634,f25192]) ).

fof(f25192,plain,
    ( spl0_2200
  <=> ! [X3,X0,X23,X25,X1] : c_List_Olist__update(c_append(X23,c_List_Olist_OCons(X0,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X3,X1) = c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).

fof(f1634,axiom,
    ! [X3,X0,X1,X25,X23] : c_List_Olist__update(c_append(X23,c_List_Olist_OCons(X0,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X3,X1) = c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).

fof(f25190,plain,
    spl0_2199,
    inference(avatar_split_clause,[],[f1355,f25188]) ).

fof(f25188,plain,
    ( spl0_2199
  <=> ! [X0,X3] :
        ( X0 = X3
        | c_IntDef_OAbs__Integ(X0) != c_IntDef_OAbs__Integ(X3)
        | ~ c_in(X0,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
        | ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).

fof(f1355,axiom,
    ! [X3,X0] :
      ( X0 = X3
      | c_IntDef_OAbs__Integ(X0) != c_IntDef_OAbs__Integ(X3)
      | ~ c_in(X0,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
      | ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).

fof(f25186,plain,
    spl0_2198,
    inference(avatar_split_clause,[],[f1294,f25184]) ).

fof(f25184,plain,
    ( spl0_2198
  <=> ! [X2,X12,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_emptyset = X12
        | ~ c_in(X3,X12,X2)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
        | c_Orderings_Omax(X3,c_Finite__Set_OMin(X12,X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).

fof(f1294,axiom,
    ! [X2,X3,X12] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_emptyset = X12
      | ~ c_in(X3,X12,X2)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
      | c_Orderings_Omax(X3,c_Finite__Set_OMin(X12,X2),X2) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).

fof(f25182,plain,
    spl0_2197,
    inference(avatar_split_clause,[],[f1293,f25180]) ).

fof(f25180,plain,
    ( spl0_2197
  <=> ! [X2,X12,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_emptyset = X12
        | ~ c_in(X3,X12,X2)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
        | c_Orderings_Omin(X3,c_Finite__Set_OMax(X12,X2),X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).

fof(f1293,axiom,
    ! [X2,X3,X12] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_emptyset = X12
      | ~ c_in(X3,X12,X2)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
      | c_Orderings_Omin(X3,c_Finite__Set_OMax(X12,X2),X2) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).

fof(f25178,plain,
    spl0_2196,
    inference(avatar_split_clause,[],[f1222,f25176]) ).

fof(f25176,plain,
    ( spl0_2196
  <=> ! [X21,X16,X15] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) = c_div(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).

fof(f1222,axiom,
    ! [X21,X16,X15] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) = c_div(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).

fof(f25174,plain,
    spl0_2195,
    inference(avatar_split_clause,[],[f1220,f25172]) ).

fof(f25172,plain,
    ( spl0_2195
  <=> ! [X21,X16,X15] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_div(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) = c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).

fof(f1220,axiom,
    ! [X21,X16,X15] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_div(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) = c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).

fof(f25170,plain,
    spl0_2194,
    inference(avatar_split_clause,[],[f121,f25168]) ).

fof(f25168,plain,
    ( spl0_2194
  <=> ! [X5,X18,X27,X1] :
        ( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
        | c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).

fof(f121,axiom,
    ! [X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
      | c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

fof(f25166,plain,
    spl0_2193,
    inference(avatar_split_clause,[],[f74,f25164]) ).

fof(f25164,plain,
    ( spl0_2193
  <=> ! [X5,X18,X12,X27,X2,X1] :
        ( ~ c_in(X18,X12,X1)
        | c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
        | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).

fof(f74,axiom,
    ! [X2,X18,X1,X27,X5,X12] :
      ( ~ c_in(X18,X12,X1)
      | c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
      | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).

fof(f24818,plain,
    ( spl0_2192
    | ~ spl0_1585
    | ~ spl0_2037 ),
    inference(avatar_split_clause,[],[f22415,f22217,f12869,f24816]) ).

fof(f12869,plain,
    ( spl0_1585
  <=> ! [X13,X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).

fof(f22217,plain,
    ( spl0_2037
  <=> ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).

fof(f22415,plain,
    ( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_1585
    | ~ spl0_2037 ),
    inference(superposition,[],[f12870,f22218]) ).

fof(f22218,plain,
    ( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
    | ~ spl0_2037 ),
    inference(avatar_component_clause,[],[f22217]) ).

fof(f12870,plain,
    ( ! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1)
    | ~ spl0_1585 ),
    inference(avatar_component_clause,[],[f12869]) ).

fof(f24544,plain,
    ( ~ spl0_2190
    | spl0_2191
    | ~ spl0_1290
    | ~ spl0_2036 ),
    inference(avatar_split_clause,[],[f22360,f22076,f10201,f24542,f24538]) ).

fof(f24538,plain,
    ( spl0_2190
  <=> class_OrderedGroup_Oab__group__add(tc_set(tc_Message_Oagent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).

fof(f24542,plain,
    ( spl0_2191
  <=> ! [X0] :
        ( c_0 != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
        | c_Event_Obad = c_insert(v_A,X0,tc_Message_Oagent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).

fof(f10201,plain,
    ( spl0_1290
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | X18 = X27
        | c_0 != c_minus(X18,X27,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).

fof(f22076,plain,
    ( spl0_2036
  <=> ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).

fof(f22360,plain,
    ( ! [X0] :
        ( c_0 != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
        | c_Event_Obad = c_insert(v_A,X0,tc_Message_Oagent)
        | ~ class_OrderedGroup_Oab__group__add(tc_set(tc_Message_Oagent)) )
    | ~ spl0_1290
    | ~ spl0_2036 ),
    inference(superposition,[],[f10202,f22077]) ).

fof(f22077,plain,
    ( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
    | ~ spl0_2036 ),
    inference(avatar_component_clause,[],[f22076]) ).

fof(f10202,plain,
    ( ! [X18,X1,X27] :
        ( c_0 != c_minus(X18,X27,X1)
        | X18 = X27
        | ~ class_OrderedGroup_Oab__group__add(X1) )
    | ~ spl0_1290 ),
    inference(avatar_component_clause,[],[f10201]) ).

fof(f24536,plain,
    ( spl0_2189
    | ~ spl0_1585
    | ~ spl0_2036 ),
    inference(avatar_split_clause,[],[f22350,f22076,f12869,f24534]) ).

fof(f22350,plain,
    ( ! [X0] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent),c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent,tc_Message_Oagent)
    | ~ spl0_1585
    | ~ spl0_2036 ),
    inference(superposition,[],[f12870,f22077]) ).

fof(f24368,plain,
    ( spl0_2187
    | ~ spl0_2188
    | ~ spl0_1092
    | ~ spl0_2116 ),
    inference(avatar_split_clause,[],[f23756,f23707,f8956,f24365,f24361]) ).

fof(f24361,plain,
    ( spl0_2187
  <=> c_emptyset = c_insert(v_B,c_emptyset,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).

fof(f24365,plain,
    ( spl0_2188
  <=> c_in(c_Main_Oall__not__in__conv__1(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2188])]) ).

fof(f8956,plain,
    ( spl0_1092
  <=> ! [X12,X1] :
        ( c_emptyset = X12
        | c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f23707,plain,
    ( spl0_2116
  <=> ! [X0] :
        ( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X0,c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2116])]) ).

fof(f23756,plain,
    ( ~ c_in(c_Main_Oall__not__in__conv__1(c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent)
    | c_emptyset = c_insert(v_B,c_emptyset,tc_Message_Oagent)
    | ~ spl0_1092
    | ~ spl0_2116 ),
    inference(resolution,[],[f23708,f8957]) ).

fof(f8957,plain,
    ( ! [X1,X12] :
        ( c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1)
        | c_emptyset = X12 )
    | ~ spl0_1092 ),
    inference(avatar_component_clause,[],[f8956]) ).

fof(f23708,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent)
        | ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
    | ~ spl0_2116 ),
    inference(avatar_component_clause,[],[f23707]) ).

fof(f24151,plain,
    ( spl0_2186
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2185 ),
    inference(avatar_split_clause,[],[f24147,f24143,f21025,f7546,f7510,f24149]) ).

fof(f24149,plain,
    ( spl0_2186
  <=> ! [X15] :
        ( c_1 = c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat)
        | ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).

fof(f24143,plain,
    ( spl0_2185
  <=> ! [X15] :
        ( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
        | c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).

fof(f24147,plain,
    ( ! [X15] :
        ( c_1 = c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat)
        | ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2185 ),
    inference(forward_demodulation,[],[f24146,f21108]) ).

fof(f24146,plain,
    ( ! [X15] :
        ( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
        | c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
    | ~ spl0_787
    | ~ spl0_796
    | ~ spl0_2031
    | ~ spl0_2185 ),
    inference(forward_demodulation,[],[f24144,f21108]) ).

fof(f24144,plain,
    ( ! [X15] :
        ( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
        | c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
    | ~ spl0_2185 ),
    inference(avatar_component_clause,[],[f24143]) ).

fof(f24145,plain,
    spl0_2185,
    inference(avatar_split_clause,[],[f3375,f24143]) ).

fof(f3375,plain,
    ! [X15] :
      ( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
      | c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f3374,f2156]) ).

fof(f3374,plain,
    ! [X15] :
      ( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),tc_nat)
      | c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f3373,f2154]) ).

fof(f3373,plain,
    ! [X15] :
      ( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
      | c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f3372,f2156]) ).

fof(f3372,plain,
    ! [X15] :
      ( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
      | ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f3371,f2156]) ).

fof(f3371,plain,
    ! [X15] :
      ( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat)
      | ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f3370,f2154]) ).

fof(f3370,plain,
    ! [X15] :
      ( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat)
      | ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f1975,f2156]) ).

fof(f1975,axiom,
    ! [X15] :
      ( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)
      | ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_0) ).

fof(f24118,plain,
    ( spl0_2184
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2183 ),
    inference(avatar_split_clause,[],[f24114,f24111,f11334,f10936,f7067,f6122,f24116]) ).

fof(f24116,plain,
    ( spl0_2184
  <=> ! [X16,X21,X15] : c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).

fof(f24111,plain,
    ( spl0_2183
  <=> ! [X16,X21,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).

fof(f24114,plain,
    ( ! [X21,X16,X15] : c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_plus(c_1,X16,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2183 ),
    inference(forward_demodulation,[],[f24112,f12301]) ).

fof(f24112,plain,
    ( ! [X21,X16,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat)
    | ~ spl0_2183 ),
    inference(avatar_component_clause,[],[f24111]) ).

fof(f24113,plain,
    spl0_2183,
    inference(avatar_split_clause,[],[f3276,f24111]) ).

fof(f3276,plain,
    ! [X21,X16,X15] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3275,f2037]) ).

fof(f2037,axiom,
    ! [X59,X16,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).

fof(f3275,plain,
    ! [X21,X16,X15] : c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X21,X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3083,f3052]) ).

fof(f3083,plain,
    ! [X21,X16,X15] : c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2018,f2544,f2544]) ).

fof(f2018,axiom,
    ! [X21,X16,X15] : c_minus(c_minus(c_Suc(X15),X21,tc_nat),c_Suc(X16),tc_nat) = c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).

fof(f24109,plain,
    spl0_2182,
    inference(avatar_split_clause,[],[f3219,f24107]) ).

fof(f24107,plain,
    ( spl0_2182
  <=> ! [X0,X1,X3] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
        | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).

fof(f3219,plain,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(definition_unfolding,[],[f2140,f2129]) ).

fof(f2140,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).

fof(f24105,plain,
    spl0_2181,
    inference(avatar_split_clause,[],[f3218,f24103]) ).

fof(f24103,plain,
    ( spl0_2181
  <=> ! [X0,X1,X3] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).

fof(f3218,plain,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f2148,f2129]) ).

fof(f2148,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).

fof(f24101,plain,
    spl0_2180,
    inference(avatar_split_clause,[],[f3217,f24099]) ).

fof(f24099,plain,
    ( spl0_2180
  <=> ! [X0,X1,X3] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
        | c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).

fof(f3217,plain,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(definition_unfolding,[],[f2149,f2129]) ).

fof(f2149,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).

fof(f24097,plain,
    spl0_2179,
    inference(avatar_split_clause,[],[f3216,f24095]) ).

fof(f24095,plain,
    ( spl0_2179
  <=> ! [X0,X1,X3] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
        | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).

fof(f3216,plain,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(definition_unfolding,[],[f2139,f2129]) ).

fof(f2139,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).

fof(f24093,plain,
    spl0_2178,
    inference(avatar_split_clause,[],[f3194,f24091]) ).

fof(f24091,plain,
    ( spl0_2178
  <=> ! [X13,X12,X32,X1] :
        ( ~ c_lessequals(X32,X13,tc_set(X1))
        | ~ c_lessequals(X32,X12,tc_set(X1))
        | c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).

fof(f3194,plain,
    ! [X1,X12,X32,X13] :
      ( ~ c_lessequals(X32,X13,tc_set(X1))
      | ~ c_lessequals(X32,X12,tc_set(X1))
      | c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
    inference(definition_unfolding,[],[f2611,f2373]) ).

fof(f2611,axiom,
    ! [X1,X12,X32,X13] :
      ( ~ c_lessequals(X32,X13,tc_set(X1))
      | ~ c_lessequals(X32,X12,tc_set(X1))
      | c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).

fof(f24089,plain,
    ( spl0_2176
    | ~ spl0_2177
    | ~ spl0_1092
    | ~ spl0_2100 ),
    inference(avatar_split_clause,[],[f23420,f23210,f8956,f24086,f24082]) ).

fof(f24082,plain,
    ( spl0_2176
  <=> c_emptyset = c_insert(v_A,c_emptyset,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).

fof(f24086,plain,
    ( spl0_2177
  <=> c_in(c_Main_Oall__not__in__conv__1(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).

fof(f23210,plain,
    ( spl0_2100
  <=> ! [X0] :
        ( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X0,c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).

fof(f23420,plain,
    ( ~ c_in(c_Main_Oall__not__in__conv__1(c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent)
    | c_emptyset = c_insert(v_A,c_emptyset,tc_Message_Oagent)
    | ~ spl0_1092
    | ~ spl0_2100 ),
    inference(resolution,[],[f23211,f8957]) ).

fof(f23211,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent)
        | ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
    | ~ spl0_2100 ),
    inference(avatar_component_clause,[],[f23210]) ).

fof(f24080,plain,
    spl0_2175,
    inference(avatar_split_clause,[],[f3163,f24078]) ).

fof(f24078,plain,
    ( spl0_2175
  <=> ! [X13,X12,X1,X18] :
        ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
        | c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).

fof(f3163,plain,
    ! [X1,X18,X12,X13] :
      ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
      | c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
    inference(definition_unfolding,[],[f2681,f2373,f2373]) ).

fof(f2681,axiom,
    ! [X1,X18,X12,X13] :
      ( c_emptyset = c_inter(X12,X13,X1)
      | c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).

fof(f24076,plain,
    spl0_2174,
    inference(avatar_split_clause,[],[f3161,f24074]) ).

fof(f24074,plain,
    ( spl0_2174
  <=> ! [X13,X12,X27,X1] :
        ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
        | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).

fof(f3161,plain,
    ! [X1,X27,X12,X13] :
      ( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
      | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ),
    inference(definition_unfolding,[],[f2665,f2373,f2373]) ).

fof(f2665,axiom,
    ! [X1,X27,X12,X13] :
      ( c_emptyset = c_inter(X12,X13,X1)
      | c_emptyset != c_inter(X12,c_insert(X27,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).

fof(f24011,plain,
    ( spl0_2173
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1854
    | ~ spl0_2172 ),
    inference(avatar_split_clause,[],[f24007,f24003,f17663,f11334,f10936,f7510,f7490,f7067,f6122,f24009]) ).

fof(f24009,plain,
    ( spl0_2173
  <=> ! [X59,X43] :
        ( c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat)
        | ~ c_lessequals(X43,X59,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).

fof(f7490,plain,
    ( spl0_782
  <=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f24003,plain,
    ( spl0_2172
  <=> ! [X59,X43] :
        ( ~ c_lessequals(X43,X59,tc_nat)
        | c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).

fof(f24007,plain,
    ( ! [X59,X43] :
        ( c_List_Oupt(X43,c_plus(c_1,X59,tc_nat)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat)
        | ~ c_lessequals(X43,X59,tc_nat) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1854
    | ~ spl0_2172 ),
    inference(forward_demodulation,[],[f24006,f17696]) ).

fof(f17696,plain,
    ( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854 ),
    inference(forward_demodulation,[],[f17666,f7511]) ).

fof(f17666,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_782
    | ~ spl0_1854 ),
    inference(superposition,[],[f17664,f7491]) ).

fof(f7491,plain,
    ( ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41)
    | ~ spl0_782 ),
    inference(avatar_component_clause,[],[f7490]) ).

fof(f24006,plain,
    ( ! [X59,X43] :
        ( c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
        | ~ c_lessequals(X43,X59,tc_nat) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2172 ),
    inference(forward_demodulation,[],[f24004,f12301]) ).

fof(f24004,plain,
    ( ! [X59,X43] :
        ( ~ c_lessequals(X43,X59,tc_nat)
        | c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
    | ~ spl0_2172 ),
    inference(avatar_component_clause,[],[f24003]) ).

fof(f24005,plain,
    spl0_2172,
    inference(avatar_split_clause,[],[f3133,f24003]) ).

fof(f3133,plain,
    ! [X59,X43] :
      ( ~ c_lessequals(X43,X59,tc_nat)
      | c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
    inference(definition_unfolding,[],[f1782,f2544]) ).

fof(f1782,axiom,
    ! [X59,X43] :
      ( ~ c_lessequals(X43,X59,tc_nat)
      | c_List_Oupt(X43,c_Suc(X59)) = c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).

fof(f24001,plain,
    spl0_2171,
    inference(avatar_split_clause,[],[f3086,f23999]) ).

fof(f23999,plain,
    ( spl0_2171
  <=> ! [X13,X12,X1] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),c_uminus(X13,tc_set(X1)),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2171])]) ).

fof(f3086,plain,
    ! [X1,X12,X13] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),c_uminus(X13,tc_set(X1)),X1,X1),
    inference(definition_unfolding,[],[f2577,f2373]) ).

fof(f2577,axiom,
    ! [X1,X12,X13] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_inter(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).

fof(f23997,plain,
    spl0_2170,
    inference(avatar_split_clause,[],[f3085,f23995]) ).

fof(f3085,plain,
    ! [X1,X12,X13] : c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)),
    inference(definition_unfolding,[],[f2575,f2373]) ).

fof(f2575,axiom,
    ! [X1,X12,X13] : c_uminus(c_inter(X12,X13,X1),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).

fof(f23993,plain,
    spl0_2169,
    inference(avatar_split_clause,[],[f3078,f23991]) ).

fof(f23991,plain,
    ( spl0_2169
  <=> ! [X15,X23,X21,X1] : c_List_Osublist(c_List_Osublist(X23,c_SetInterval_OlessThan(X15,tc_nat),X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Osublist(X23,c_SetInterval_OlessThan(c_Orderings_Omin(X21,X15,tc_nat),tc_nat),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).

fof(f3078,plain,
    ! [X21,X1,X15,X23] : c_List_Osublist(c_List_Osublist(X23,c_SetInterval_OlessThan(X15,tc_nat),X1),c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Osublist(X23,c_SetInterval_OlessThan(c_Orderings_Omin(X21,X15,tc_nat),tc_nat),X1),
    inference(definition_unfolding,[],[f1776,f1766,f1766,f1766]) ).

fof(f1776,axiom,
    ! [X21,X1,X15,X23] : c_List_Otake(X21,c_List_Otake(X15,X23,X1),X1) = c_List_Otake(c_Orderings_Omin(X21,X15,tc_nat),X23,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).

fof(f23970,plain,
    ( spl0_2168
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2167 ),
    inference(avatar_split_clause,[],[f23954,f23949,f11334,f10936,f7067,f6122,f23968]) ).

fof(f23968,plain,
    ( spl0_2168
  <=> ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).

fof(f23949,plain,
    ( spl0_2167
  <=> ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).

fof(f23954,plain,
    ( ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2167 ),
    inference(forward_demodulation,[],[f23953,f12301]) ).

fof(f23953,plain,
    ( ! [X21,X15] : c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2167 ),
    inference(forward_demodulation,[],[f23952,f12301]) ).

fof(f23952,plain,
    ( ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X15,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2167 ),
    inference(forward_demodulation,[],[f23950,f12301]) ).

fof(f23950,plain,
    ( ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat)
    | ~ spl0_2167 ),
    inference(avatar_component_clause,[],[f23949]) ).

fof(f23951,plain,
    spl0_2167,
    inference(avatar_split_clause,[],[f3054,f23949]) ).

fof(f3054,plain,
    ! [X21,X15] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X15,X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2055,f2544,f2544,f2544]) ).

fof(f2055,axiom,
    ! [X21,X15] : c_Orderings_Omin(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omin(X15,X21,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).

fof(f23931,plain,
    ( spl0_2166
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2165 ),
    inference(avatar_split_clause,[],[f23927,f23922,f11334,f10936,f7067,f6122,f23929]) ).

fof(f23929,plain,
    ( spl0_2166
  <=> ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).

fof(f23922,plain,
    ( spl0_2165
  <=> ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).

fof(f23927,plain,
    ( ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2165 ),
    inference(forward_demodulation,[],[f23926,f12301]) ).

fof(f23926,plain,
    ( ! [X21,X15] : c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2165 ),
    inference(forward_demodulation,[],[f23925,f12301]) ).

fof(f23925,plain,
    ( ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X15,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2165 ),
    inference(forward_demodulation,[],[f23923,f12301]) ).

fof(f23923,plain,
    ( ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat)
    | ~ spl0_2165 ),
    inference(avatar_component_clause,[],[f23922]) ).

fof(f23924,plain,
    spl0_2165,
    inference(avatar_split_clause,[],[f3053,f23922]) ).

fof(f3053,plain,
    ! [X21,X15] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X15,X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2052,f2544,f2544,f2544]) ).

fof(f2052,axiom,
    ! [X21,X15] : c_Orderings_Omax(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omax(X15,X21,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).

fof(f23920,plain,
    spl0_2164,
    inference(avatar_split_clause,[],[f2877,f23918]) ).

fof(f23918,plain,
    ( spl0_2164
  <=> ! [X87,X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).

fof(f2877,axiom,
    ! [X88,X86,X87] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).

fof(f23916,plain,
    spl0_2163,
    inference(avatar_split_clause,[],[f2859,f23914]) ).

fof(f23914,plain,
    ( spl0_2163
  <=> ! [X87,X86,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).

fof(f2859,axiom,
    ! [X88,X86,X87] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).

fof(f23912,plain,
    spl0_2162,
    inference(avatar_split_clause,[],[f2566,f23910]) ).

fof(f23910,plain,
    ( spl0_2162
  <=> ! [X15,X59,X43,X21,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_lessequals(X15,X43,X1)
        | ~ c_lessequals(X59,X21,X1)
        | c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).

fof(f2566,axiom,
    ! [X21,X59,X1,X15,X43] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_lessequals(X15,X43,X1)
      | ~ c_lessequals(X59,X21,X1)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).

fof(f23908,plain,
    spl0_2161,
    inference(avatar_split_clause,[],[f2564,f23906]) ).

fof(f23906,plain,
    ( spl0_2161
  <=> ! [X15,X59,X43,X21,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_lessequals(X59,X43,X1)
        | c_lessequals(X59,X21,X1)
        | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).

fof(f2564,axiom,
    ! [X21,X59,X1,X15,X43] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_lessequals(X59,X43,X1)
      | c_lessequals(X59,X21,X1)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).

fof(f23904,plain,
    spl0_2160,
    inference(avatar_split_clause,[],[f2563,f23902]) ).

fof(f23902,plain,
    ( spl0_2160
  <=> ! [X59,X43,X21,X15,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_lessequals(X59,X43,X1)
        | c_lessequals(X15,X43,X1)
        | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).

fof(f2563,axiom,
    ! [X21,X59,X1,X15,X43] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_lessequals(X59,X43,X1)
      | c_lessequals(X15,X43,X1)
      | ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).

fof(f23900,plain,
    spl0_2159,
    inference(avatar_split_clause,[],[f2376,f23898]) ).

fof(f2376,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
      | c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).

fof(f23884,plain,
    spl0_2158,
    inference(avatar_split_clause,[],[f2375,f23882]) ).

fof(f23882,plain,
    ( spl0_2158
  <=> ! [X5,X18,X27,X2,X1] :
        ( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
        | ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).

fof(f2375,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
      | ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).

fof(f23880,plain,
    spl0_2157,
    inference(avatar_split_clause,[],[f2335,f23878]) ).

fof(f23878,plain,
    ( spl0_2157
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = X0
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2157])]) ).

fof(f2335,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = X0
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).

fof(f23876,plain,
    spl0_2156,
    inference(avatar_split_clause,[],[f2318,f23874]) ).

fof(f23874,plain,
    ( spl0_2156
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = X0
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).

fof(f2318,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = X0
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).

fof(f23872,plain,
    spl0_2155,
    inference(avatar_split_clause,[],[f2174,f23870]) ).

fof(f23870,plain,
    ( spl0_2155
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).

fof(f2174,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).

fof(f23868,plain,
    spl0_2154,
    inference(avatar_split_clause,[],[f2121,f23866]) ).

fof(f23866,plain,
    ( spl0_2154
  <=> ! [X0,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
        | c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) = c_uminus(c_Numeral_Onumber__of(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).

fof(f2121,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) = c_uminus(c_Numeral_Onumber__of(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).

fof(f23864,plain,
    spl0_2153,
    inference(avatar_split_clause,[],[f1810,f23862]) ).

fof(f23862,plain,
    ( spl0_2153
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_lessequals(X21,X15,tc_nat)
        | c_NatArith_Oof__nat(c_minus(X15,X21,tc_nat),X1) = c_minus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).

fof(f1810,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | ~ c_lessequals(X21,X15,tc_nat)
      | c_NatArith_Oof__nat(c_minus(X15,X21,tc_nat),X1) = c_minus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).

fof(f23860,plain,
    spl0_2152,
    inference(avatar_split_clause,[],[f1672,f23858]) ).

fof(f23858,plain,
    ( spl0_2152
  <=> ! [X45,X3,X70,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).

fof(f1672,axiom,
    ! [X72,X70,X3,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).

fof(f23856,plain,
    spl0_2151,
    inference(avatar_split_clause,[],[f1671,f23854]) ).

fof(f23854,plain,
    ( spl0_2151
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).

fof(f1671,axiom,
    ! [X3,X70,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).

fof(f23852,plain,
    spl0_2150,
    inference(avatar_split_clause,[],[f1670,f23850]) ).

fof(f23850,plain,
    ( spl0_2150
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).

fof(f1670,axiom,
    ! [X3,X70,X72,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).

fof(f23848,plain,
    spl0_2149,
    inference(avatar_split_clause,[],[f1669,f23846]) ).

fof(f23846,plain,
    ( spl0_2149
  <=> ! [X45,X3,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).

fof(f1669,axiom,
    ! [X3,X72,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).

fof(f23844,plain,
    ( spl0_2148
    | ~ spl0_1834
    | ~ spl0_2074 ),
    inference(avatar_split_clause,[],[f23653,f23001,f17298,f23842]) ).

fof(f23842,plain,
    ( spl0_2148
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_insert(v_B,X1,tc_Message_Oagent),tc_Message_Oagent)
        | c_in(X0,X1,tc_Message_Oagent)
        | ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).

fof(f17298,plain,
    ( spl0_1834
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X12,X1)
        | c_in(X4,X13,X1)
        | c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).

fof(f23001,plain,
    ( spl0_2074
  <=> ! [X0,X1] :
        ( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
        | ~ c_in(X1,c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).

fof(f23653,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_insert(v_B,X1,tc_Message_Oagent),tc_Message_Oagent)
        | c_in(X0,X1,tc_Message_Oagent)
        | ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
    | ~ spl0_1834
    | ~ spl0_2074 ),
    inference(resolution,[],[f23002,f17299]) ).

fof(f17299,plain,
    ( ! [X1,X4,X12,X13] :
        ( c_in(X4,c_minus(X12,X13,tc_set(X1)),X1)
        | c_in(X4,X13,X1)
        | ~ c_in(X4,X12,X1) )
    | ~ spl0_1834 ),
    inference(avatar_component_clause,[],[f17298]) ).

fof(f23002,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
        | ~ c_in(X1,c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent) )
    | ~ spl0_2074 ),
    inference(avatar_component_clause,[],[f23001]) ).

fof(f23840,plain,
    spl0_2147,
    inference(avatar_split_clause,[],[f1668,f23838]) ).

fof(f23838,plain,
    ( spl0_2147
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).

fof(f1668,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X79,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).

fof(f23836,plain,
    spl0_2146,
    inference(avatar_split_clause,[],[f1667,f23834]) ).

fof(f23834,plain,
    ( spl0_2146
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).

fof(f1667,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).

fof(f23832,plain,
    spl0_2145,
    inference(avatar_split_clause,[],[f1666,f23830]) ).

fof(f23830,plain,
    ( spl0_2145
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).

fof(f1666,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).

fof(f23828,plain,
    spl0_2144,
    inference(avatar_split_clause,[],[f1665,f23826]) ).

fof(f23826,plain,
    ( spl0_2144
  <=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).

fof(f1665,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X79,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).

fof(f23824,plain,
    spl0_2143,
    inference(avatar_split_clause,[],[f1664,f23822]) ).

fof(f23822,plain,
    ( spl0_2143
  <=> ! [X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).

fof(f1664,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X76,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).

fof(f23820,plain,
    spl0_2142,
    inference(avatar_split_clause,[],[f1663,f23818]) ).

fof(f23818,plain,
    ( spl0_2142
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X72,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).

fof(f1663,axiom,
    ! [X72,X70,X73,X71,X80,X78,X3,X1,X68,X44,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).

fof(f23816,plain,
    spl0_2141,
    inference(avatar_split_clause,[],[f1662,f23814]) ).

fof(f23814,plain,
    ( spl0_2141
  <=> ! [X45,X3,X70,X73,X80,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).

fof(f1662,axiom,
    ! [X72,X70,X73,X71,X80,X3,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).

fof(f23812,plain,
    spl0_2140,
    inference(avatar_split_clause,[],[f1661,f23810]) ).

fof(f23810,plain,
    ( spl0_2140
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).

fof(f1661,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).

fof(f23808,plain,
    spl0_2139,
    inference(avatar_split_clause,[],[f1660,f23806]) ).

fof(f23806,plain,
    ( spl0_2139
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X71,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).

fof(f1660,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).

fof(f23804,plain,
    spl0_2138,
    inference(avatar_split_clause,[],[f1659,f23802]) ).

fof(f23802,plain,
    ( spl0_2138
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).

fof(f1659,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).

fof(f23800,plain,
    ( spl0_2137
    | ~ spl0_1834
    | ~ spl0_2062 ),
    inference(avatar_split_clause,[],[f23119,f22789,f17298,f23798]) ).

fof(f23798,plain,
    ( spl0_2137
  <=> ! [X0,X1] :
        ( ~ c_in(X0,c_insert(v_A,X1,tc_Message_Oagent),tc_Message_Oagent)
        | c_in(X0,X1,tc_Message_Oagent)
        | ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).

fof(f22789,plain,
    ( spl0_2062
  <=> ! [X0,X1] :
        ( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
        | ~ c_in(X1,c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).

fof(f23119,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X0,c_insert(v_A,X1,tc_Message_Oagent),tc_Message_Oagent)
        | c_in(X0,X1,tc_Message_Oagent)
        | ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) )
    | ~ spl0_1834
    | ~ spl0_2062 ),
    inference(resolution,[],[f22790,f17299]) ).

fof(f22790,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
        | ~ c_in(X1,c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent) )
    | ~ spl0_2062 ),
    inference(avatar_component_clause,[],[f22789]) ).

fof(f23796,plain,
    spl0_2136,
    inference(avatar_split_clause,[],[f1658,f23794]) ).

fof(f23794,plain,
    ( spl0_2136
  <=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X44,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).

fof(f1658,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).

fof(f23792,plain,
    spl0_2135,
    inference(avatar_split_clause,[],[f1657,f23790]) ).

fof(f23790,plain,
    ( spl0_2135
  <=> ! [X45,X3,X70,X73,X71,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).

fof(f1657,axiom,
    ! [X72,X70,X73,X71,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).

fof(f23788,plain,
    spl0_2134,
    inference(avatar_split_clause,[],[f1656,f23786]) ).

fof(f23786,plain,
    ( spl0_2134
  <=> ! [X45,X3,X70,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).

fof(f1656,axiom,
    ! [X72,X70,X3,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).

fof(f23784,plain,
    spl0_2133,
    inference(avatar_split_clause,[],[f1655,f23782]) ).

fof(f23782,plain,
    ( spl0_2133
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).

fof(f1655,axiom,
    ! [X3,X70,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).

fof(f23780,plain,
    spl0_2132,
    inference(avatar_split_clause,[],[f1654,f23778]) ).

fof(f23778,plain,
    ( spl0_2132
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).

fof(f1654,axiom,
    ! [X3,X70,X72,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).

fof(f23776,plain,
    spl0_2131,
    inference(avatar_split_clause,[],[f1653,f23774]) ).

fof(f23774,plain,
    ( spl0_2131
  <=> ! [X45,X3,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).

fof(f1653,axiom,
    ! [X3,X72,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).

fof(f23772,plain,
    spl0_2130,
    inference(avatar_split_clause,[],[f1652,f23770]) ).

fof(f23770,plain,
    ( spl0_2130
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).

fof(f1652,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X79,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).

fof(f23768,plain,
    spl0_2129,
    inference(avatar_split_clause,[],[f1651,f23766]) ).

fof(f23766,plain,
    ( spl0_2129
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).

fof(f1651,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).

fof(f23764,plain,
    spl0_2128,
    inference(avatar_split_clause,[],[f1650,f23762]) ).

fof(f23762,plain,
    ( spl0_2128
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).

fof(f1650,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).

fof(f23760,plain,
    spl0_2127,
    inference(avatar_split_clause,[],[f1649,f23758]) ).

fof(f23758,plain,
    ( spl0_2127
  <=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).

fof(f1649,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X79,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).

fof(f23749,plain,
    spl0_2126,
    inference(avatar_split_clause,[],[f1648,f23747]) ).

fof(f23747,plain,
    ( spl0_2126
  <=> ! [X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).

fof(f1648,axiom,
    ! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X76,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).

fof(f23745,plain,
    spl0_2125,
    inference(avatar_split_clause,[],[f1647,f23743]) ).

fof(f23743,plain,
    ( spl0_2125
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X72,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).

fof(f1647,axiom,
    ! [X72,X70,X73,X71,X80,X78,X3,X1,X68,X44,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).

fof(f23741,plain,
    spl0_2124,
    inference(avatar_split_clause,[],[f1646,f23739]) ).

fof(f23739,plain,
    ( spl0_2124
  <=> ! [X45,X3,X70,X73,X80,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).

fof(f1646,axiom,
    ! [X72,X70,X73,X71,X80,X3,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).

fof(f23737,plain,
    spl0_2123,
    inference(avatar_split_clause,[],[f1645,f23735]) ).

fof(f23735,plain,
    ( spl0_2123
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).

fof(f1645,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).

fof(f23733,plain,
    spl0_2122,
    inference(avatar_split_clause,[],[f1644,f23731]) ).

fof(f23731,plain,
    ( spl0_2122
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X71,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2122])]) ).

fof(f1644,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).

fof(f23729,plain,
    spl0_2121,
    inference(avatar_split_clause,[],[f1643,f23727]) ).

fof(f23727,plain,
    ( spl0_2121
  <=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2121])]) ).

fof(f1643,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).

fof(f23725,plain,
    spl0_2120,
    inference(avatar_split_clause,[],[f1642,f23723]) ).

fof(f23723,plain,
    ( spl0_2120
  <=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X44,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2120])]) ).

fof(f1642,axiom,
    ! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).

fof(f23721,plain,
    spl0_2119,
    inference(avatar_split_clause,[],[f1641,f23719]) ).

fof(f23719,plain,
    ( spl0_2119
  <=> ! [X45,X3,X70,X73,X71,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2119])]) ).

fof(f1641,axiom,
    ! [X72,X70,X73,X71,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).

fof(f23717,plain,
    spl0_2118,
    inference(avatar_split_clause,[],[f1629,f23715]) ).

fof(f23715,plain,
    ( spl0_2118
  <=> ! [X41,X60,X18,X65] :
        ( ~ c_in(X18,c_List_Oset(X65,X41),X41)
        | c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist_OCons(X18,c_List_Olist__inter(X60,X65,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2118])]) ).

fof(f1629,axiom,
    ! [X65,X41,X18,X60] :
      ( ~ c_in(X18,c_List_Oset(X65,X41),X41)
      | c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist_OCons(X18,c_List_Olist__inter(X60,X65,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).

fof(f23713,plain,
    spl0_2117,
    inference(avatar_split_clause,[],[f1614,f23711]) ).

fof(f23711,plain,
    ( spl0_2117
  <=> ! [X23,X25,X2,X1] : c_Nat_Osize(c_List_Ozip(X23,X25,X1,X2),tc_List_Olist(tc_prod(X1,X2))) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2117])]) ).

fof(f1614,axiom,
    ! [X2,X1,X25,X23] : c_Nat_Osize(c_List_Ozip(X23,X25,X1,X2),tc_List_Olist(tc_prod(X1,X2))) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).

fof(f23709,plain,
    ( spl0_2116
    | ~ spl0_892
    | ~ spl0_2074 ),
    inference(avatar_split_clause,[],[f23663,f23001,f7944,f23707]) ).

fof(f23663,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X0,c_insert(v_B,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) )
    | ~ spl0_892
    | ~ spl0_2074 ),
    inference(superposition,[],[f23002,f7945]) ).

fof(f23705,plain,
    spl0_2115,
    inference(avatar_split_clause,[],[f1523,f23703]) ).

fof(f23703,plain,
    ( spl0_2115
  <=> ! [X53,X23,X25,X52,X1] :
        ( X52 = X53
        | c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
        | c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2115])]) ).

fof(f1523,axiom,
    ! [X1,X52,X53,X25,X23] :
      ( X52 = X53
      | c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
      | c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).

fof(f23701,plain,
    spl0_2114,
    inference(avatar_split_clause,[],[f1522,f23699]) ).

fof(f23699,plain,
    ( spl0_2114
  <=> ! [X52,X53,X23,X25,X1] :
        ( X23 = X25
        | c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
        | c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).

fof(f1522,axiom,
    ! [X1,X52,X53,X25,X23] :
      ( X23 = X25
      | c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
      | c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).

fof(f23697,plain,
    spl0_2113,
    inference(avatar_split_clause,[],[f1521,f23695]) ).

fof(f23695,plain,
    ( spl0_2113
  <=> ! [X53,X23,X25,X52,X1] :
        ( X52 = X53
        | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
        | c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).

fof(f1521,axiom,
    ! [X1,X52,X53,X25,X23] :
      ( X52 = X53
      | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
      | c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).

fof(f23693,plain,
    spl0_2112,
    inference(avatar_split_clause,[],[f1520,f23691]) ).

fof(f23691,plain,
    ( spl0_2112
  <=> ! [X52,X53,X23,X25,X1] :
        ( X23 = X25
        | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
        | c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).

fof(f1520,axiom,
    ! [X1,X52,X53,X25,X23] :
      ( X23 = X25
      | c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
      | c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).

fof(f23689,plain,
    spl0_2111,
    inference(avatar_split_clause,[],[f1468,f23687]) ).

fof(f23687,plain,
    ( spl0_2111
  <=> ! [X11,X47] : c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).

fof(f1468,axiom,
    ! [X11,X47] : c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_0) ).

fof(f23685,plain,
    spl0_2110,
    inference(avatar_split_clause,[],[f1283,f23683]) ).

fof(f23683,plain,
    ( spl0_2110
  <=> ! [X18,X13,X12,X1] :
        ( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).

fof(f1283,axiom,
    ! [X1,X18,X12,X13] :
      ( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).

fof(f23681,plain,
    spl0_2109,
    inference(avatar_split_clause,[],[f1282,f23679]) ).

fof(f23679,plain,
    ( spl0_2109
  <=> ! [X18,X13,X12,X1] :
        ( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).

fof(f1282,axiom,
    ! [X1,X18,X12,X13] :
      ( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).

fof(f23677,plain,
    spl0_2108,
    inference(avatar_split_clause,[],[f79,f23675]) ).

fof(f23675,plain,
    ( spl0_2108
  <=> ! [X12,X1,X4] :
        ( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
        | c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).

fof(f79,axiom,
    ! [X1,X4,X12] :
      ( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
      | c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).

fof(f23673,plain,
    spl0_2107,
    inference(avatar_split_clause,[],[f75,f23671]) ).

fof(f23671,plain,
    ( spl0_2107
  <=> ! [X5,X27,X2,X1] :
        ( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
        | c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).

fof(f75,axiom,
    ! [X2,X1,X27,X5] :
      ( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
      | c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).

fof(f23669,plain,
    spl0_2106,
    inference(avatar_split_clause,[],[f69,f23667]) ).

fof(f23667,plain,
    ( spl0_2106
  <=> ! [X18,X5,X2,X1] :
        ( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
        | c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2106])]) ).

fof(f69,axiom,
    ! [X2,X18,X1,X5] :
      ( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
      | c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).

fof(f23652,plain,
    spl0_2105,
    inference(avatar_split_clause,[],[f60,f23650]) ).

fof(f23650,plain,
    ( spl0_2105
  <=> ! [X18,X12,X1,X26] :
        ( ~ c_in(X18,X12,X1)
        | ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).

fof(f60,axiom,
    ! [X18,X1,X26,X12] :
      ( ~ c_in(X18,X12,X1)
      | ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

fof(f23648,plain,
    spl0_2104,
    inference(avatar_split_clause,[],[f22,f23646]) ).

fof(f23646,plain,
    ( spl0_2104
  <=> ! [X13,X7,X12,X2,X1] :
        ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).

fof(f22,axiom,
    ! [X2,X1,X7,X12,X13] :
      ( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).

fof(f23644,plain,
    spl0_2103,
    inference(avatar_split_clause,[],[f21,f23642]) ).

fof(f23642,plain,
    ( spl0_2103
  <=> ! [X13,X12,X9,X2,X1] :
        ( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
        | c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).

fof(f21,axiom,
    ! [X2,X1,X9,X12,X13] :
      ( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
      | c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).

fof(f23543,plain,
    ( spl0_2102
    | ~ spl0_57
    | ~ spl0_1588
    | ~ spl0_2085 ),
    inference(avatar_split_clause,[],[f23060,f23057,f12886,f3714,f23541]) ).

fof(f23541,plain,
    ( spl0_2102
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).

fof(f23057,plain,
    ( spl0_2085
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).

fof(f23060,plain,
    ( ! [X83,X47] :
        ( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
    | ~ spl0_57
    | ~ spl0_1588
    | ~ spl0_2085 ),
    inference(forward_demodulation,[],[f23058,f14195]) ).

fof(f23058,plain,
    ( ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
    | ~ spl0_2085 ),
    inference(avatar_component_clause,[],[f23057]) ).

fof(f23528,plain,
    ( spl0_2101
    | ~ spl0_57
    | ~ spl0_1588
    | ~ spl0_2084 ),
    inference(avatar_split_clause,[],[f23044,f23041,f12886,f3714,f23526]) ).

fof(f23526,plain,
    ( spl0_2101
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2101])]) ).

fof(f23041,plain,
    ( spl0_2084
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).

fof(f23044,plain,
    ( ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
    | ~ spl0_57
    | ~ spl0_1588
    | ~ spl0_2084 ),
    inference(forward_demodulation,[],[f23042,f14195]) ).

fof(f23042,plain,
    ( ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) )
    | ~ spl0_2084 ),
    inference(avatar_component_clause,[],[f23041]) ).

fof(f23212,plain,
    ( spl0_2100
    | ~ spl0_892
    | ~ spl0_2062 ),
    inference(avatar_split_clause,[],[f23129,f22789,f7944,f23210]) ).

fof(f23129,plain,
    ( ! [X0] :
        ( ~ c_in(X0,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X0,c_insert(v_A,c_emptyset,tc_Message_Oagent),tc_Message_Oagent) )
    | ~ spl0_892
    | ~ spl0_2062 ),
    inference(superposition,[],[f22790,f7945]) ).

fof(f23195,plain,
    ( spl0_2099
    | ~ spl0_1664
    | ~ spl0_2098 ),
    inference(avatar_split_clause,[],[f23191,f23188,f14495,f23193]) ).

fof(f23193,plain,
    ( spl0_2099
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).

fof(f14495,plain,
    ( spl0_1664
  <=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).

fof(f23188,plain,
    ( spl0_2098
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2098])]) ).

fof(f23191,plain,
    ( ! [X0,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
    | ~ spl0_1664
    | ~ spl0_2098 ),
    inference(forward_demodulation,[],[f23189,f14497]) ).

fof(f14497,plain,
    ( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
    | ~ spl0_1664 ),
    inference(avatar_component_clause,[],[f14495]) ).

fof(f23189,plain,
    ( ! [X0,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
    | ~ spl0_2098 ),
    inference(avatar_component_clause,[],[f23188]) ).

fof(f23190,plain,
    spl0_2098,
    inference(avatar_split_clause,[],[f3428,f23188]) ).

fof(f3428,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
    inference(forward_demodulation,[],[f3214,f2156]) ).

fof(f3214,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    inference(definition_unfolding,[],[f1319,f2129]) ).

fof(f1319,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).

fof(f23186,plain,
    spl0_2097,
    inference(avatar_split_clause,[],[f3426,f23184]) ).

fof(f23184,plain,
    ( spl0_2097
  <=> ! [X1,X3] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2097])]) ).

fof(f3426,plain,
    ! [X3,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3212,f2156]) ).

fof(f3212,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1315,f2129]) ).

fof(f1315,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).

fof(f23182,plain,
    spl0_2096,
    inference(avatar_split_clause,[],[f3424,f23180]) ).

fof(f23180,plain,
    ( spl0_2096
  <=> ! [X0,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).

fof(f3424,plain,
    ! [X0,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
    inference(forward_demodulation,[],[f3210,f2156]) ).

fof(f3210,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
    inference(definition_unfolding,[],[f1327,f2129]) ).

fof(f1327,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X0)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).

fof(f23161,plain,
    ( spl0_2095
    | ~ spl0_1664
    | ~ spl0_2094 ),
    inference(avatar_split_clause,[],[f23157,f23154,f14495,f23159]) ).

fof(f23159,plain,
    ( spl0_2095
  <=> ! [X1,X3] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).

fof(f23154,plain,
    ( spl0_2094
  <=> ! [X1,X3] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).

fof(f23157,plain,
    ( ! [X3,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
    | ~ spl0_1664
    | ~ spl0_2094 ),
    inference(forward_demodulation,[],[f23155,f14497]) ).

fof(f23155,plain,
    ( ! [X3,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
    | ~ spl0_2094 ),
    inference(avatar_component_clause,[],[f23154]) ).

fof(f23156,plain,
    spl0_2094,
    inference(avatar_split_clause,[],[f3421,f23154]) ).

fof(f3421,plain,
    ! [X3,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3208,f2156]) ).

fof(f3208,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    inference(definition_unfolding,[],[f1323,f2129]) ).

fof(f1323,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).

fof(f23135,plain,
    ( spl0_2093
    | ~ spl0_1664
    | ~ spl0_2092 ),
    inference(avatar_split_clause,[],[f23118,f23115,f14495,f23133]) ).

fof(f23133,plain,
    ( spl0_2093
  <=> ! [X0,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).

fof(f23115,plain,
    ( spl0_2092
  <=> ! [X0,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).

fof(f23118,plain,
    ( ! [X0,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
    | ~ spl0_1664
    | ~ spl0_2092 ),
    inference(forward_demodulation,[],[f23116,f14497]) ).

fof(f23116,plain,
    ( ! [X0,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
    | ~ spl0_2092 ),
    inference(avatar_component_clause,[],[f23115]) ).

fof(f23117,plain,
    spl0_2092,
    inference(avatar_split_clause,[],[f3418,f23115]) ).

fof(f3418,plain,
    ! [X0,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
    inference(forward_demodulation,[],[f3206,f2156]) ).

fof(f3206,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    inference(definition_unfolding,[],[f1318,f2129]) ).

fof(f1318,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).

fof(f23113,plain,
    spl0_2091,
    inference(avatar_split_clause,[],[f3416,f23111]) ).

fof(f23111,plain,
    ( spl0_2091
  <=> ! [X1,X3] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).

fof(f3416,plain,
    ! [X3,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3204,f2156]) ).

fof(f3204,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1314,f2129]) ).

fof(f1314,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).

fof(f23109,plain,
    spl0_2090,
    inference(avatar_split_clause,[],[f3414,f23107]) ).

fof(f23107,plain,
    ( spl0_2090
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).

fof(f3414,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
    inference(forward_demodulation,[],[f3202,f2156]) ).

fof(f3202,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
    inference(definition_unfolding,[],[f1326,f2129]) ).

fof(f1326,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X0)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).

fof(f23096,plain,
    ( spl0_2089
    | ~ spl0_1664
    | ~ spl0_2088 ),
    inference(avatar_split_clause,[],[f23092,f23089,f14495,f23094]) ).

fof(f23094,plain,
    ( spl0_2089
  <=> ! [X1,X3] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).

fof(f23089,plain,
    ( spl0_2088
  <=> ! [X1,X3] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).

fof(f23092,plain,
    ( ! [X3,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
    | ~ spl0_1664
    | ~ spl0_2088 ),
    inference(forward_demodulation,[],[f23090,f14497]) ).

fof(f23090,plain,
    ( ! [X3,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
    | ~ spl0_2088 ),
    inference(avatar_component_clause,[],[f23089]) ).

fof(f23091,plain,
    spl0_2088,
    inference(avatar_split_clause,[],[f3411,f23089]) ).

fof(f3411,plain,
    ! [X3,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3200,f2156]) ).

fof(f3200,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    inference(definition_unfolding,[],[f1322,f2129]) ).

fof(f1322,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).

fof(f23070,plain,
    ( spl0_2087
    | ~ spl0_57
    | ~ spl0_1465
    | ~ spl0_2086 ),
    inference(avatar_split_clause,[],[f23066,f23062,f11350,f3714,f23068]) ).

fof(f23068,plain,
    ( spl0_2087
  <=> ! [X0] :
        ( c_1 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).

fof(f11350,plain,
    ( spl0_1465
  <=> ! [X1] :
        ( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).

fof(f23062,plain,
    ( spl0_2086
  <=> ! [X0] :
        ( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).

fof(f23066,plain,
    ( ! [X0] :
        ( c_1 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1465
    | ~ spl0_2086 ),
    inference(forward_demodulation,[],[f23065,f12369]) ).

fof(f12369,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_57
    | ~ spl0_1465 ),
    inference(resolution,[],[f11351,f3716]) ).

fof(f11351,plain,
    ( ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1) )
    | ~ spl0_1465 ),
    inference(avatar_component_clause,[],[f11350]) ).

fof(f23065,plain,
    ( ! [X0] :
        ( c_0 = c_Divides_Oop_Amod(X0,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1465
    | ~ spl0_2086 ),
    inference(forward_demodulation,[],[f23063,f12369]) ).

fof(f23063,plain,
    ( ! [X0] :
        ( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_2086 ),
    inference(avatar_component_clause,[],[f23062]) ).

fof(f23064,plain,
    spl0_2086,
    inference(avatar_split_clause,[],[f3369,f23062]) ).

fof(f3369,plain,
    ! [X0] :
      ( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3368,f2156]) ).

fof(f3368,plain,
    ! [X0] :
      ( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3367,f2154]) ).

fof(f3367,plain,
    ! [X0] :
      ( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3366,f2156]) ).

fof(f3366,plain,
    ! [X0] :
      ( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3365,f2156]) ).

fof(f3365,plain,
    ! [X0] :
      ( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3364,f2154]) ).

fof(f3364,plain,
    ! [X0] :
      ( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f2308,f2156]) ).

fof(f2308,axiom,
    ! [X0] :
      ( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_0) ).

fof(f23059,plain,
    spl0_2085,
    inference(avatar_split_clause,[],[f3193,f23057]) ).

fof(f3193,plain,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1855,f2129]) ).

fof(f1855,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).

fof(f23043,plain,
    spl0_2084,
    inference(avatar_split_clause,[],[f3192,f23041]) ).

fof(f3192,plain,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X83),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1858,f2129]) ).

fof(f1858,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).

fof(f23039,plain,
    spl0_2083,
    inference(avatar_split_clause,[],[f2954,f23037]) ).

fof(f23037,plain,
    ( spl0_2083
  <=> ! [X86,X12,X88] :
        ( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).

fof(f2954,axiom,
    ! [X88,X86,X12] :
      ( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Oanalz__shrK__Decrypt_0) ).

fof(f23035,plain,
    spl0_2082,
    inference(avatar_split_clause,[],[f2936,f23033]) ).

fof(f23033,plain,
    ( spl0_2082
  <=> ! [X102,X86,X13] :
        ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OGets(X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).

fof(f2936,axiom,
    ! [X86,X102,X13] :
      ( ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OGets(X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).

fof(f23031,plain,
    spl0_2081,
    inference(avatar_split_clause,[],[f2352,f23029]) ).

fof(f23029,plain,
    ( spl0_2081
  <=> ! [X15,X18,X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1)
        | X15 = X21
        | ~ c_less(c_1,X18,X1)
        | c_Nat_Opower(X18,X21,X1) != c_Nat_Opower(X18,X15,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).

fof(f2352,axiom,
    ! [X21,X1,X18,X15] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__semidom(X1)
      | X15 = X21
      | ~ c_less(c_1,X18,X1)
      | c_Nat_Opower(X18,X21,X1) != c_Nat_Opower(X18,X15,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).

fof(f23027,plain,
    spl0_2080,
    inference(avatar_split_clause,[],[f2327,f23025]) ).

fof(f23025,plain,
    ( spl0_2080
  <=> ! [X21,X1,X0] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_Parity_Oeven(X21,tc_nat)
        | c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_uminus(c_Nat_Opower(X0,X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).

fof(f2327,axiom,
    ! [X21,X0,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_Parity_Oeven(X21,tc_nat)
      | c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_uminus(c_Nat_Opower(X0,X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).

fof(f23023,plain,
    spl0_2079,
    inference(avatar_split_clause,[],[f2320,f23021]) ).

fof(f23021,plain,
    ( spl0_2079
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = X0
        | c_lessequals(X0,c_0,X1)
        | ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).

fof(f2320,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = X0
      | c_lessequals(X0,c_0,X1)
      | ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).

fof(f23019,plain,
    spl0_2078,
    inference(avatar_split_clause,[],[f1973,f23017]) ).

fof(f23017,plain,
    ( spl0_2078
  <=> ! [X2,X18,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
        | c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).

fof(f1973,axiom,
    ! [X2,X47,X18] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
      | c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).

fof(f23015,plain,
    spl0_2077,
    inference(avatar_split_clause,[],[f1972,f23013]) ).

fof(f23013,plain,
    ( spl0_2077
  <=> ! [X2,X18,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
        | c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).

fof(f1972,axiom,
    ! [X2,X18,X47] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
      | c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).

fof(f23011,plain,
    spl0_2076,
    inference(avatar_split_clause,[],[f1969,f23009]) ).

fof(f23009,plain,
    ( spl0_2076
  <=> ! [X2,X18,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
        | c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).

fof(f1969,axiom,
    ! [X2,X47,X18] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
      | c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).

fof(f23007,plain,
    spl0_2075,
    inference(avatar_split_clause,[],[f1968,f23005]) ).

fof(f23005,plain,
    ( spl0_2075
  <=> ! [X2,X18,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
        | c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).

fof(f1968,axiom,
    ! [X2,X18,X47] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
      | c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).

fof(f23003,plain,
    ( spl0_2074
    | ~ spl0_1427
    | ~ spl0_2037 ),
    inference(avatar_split_clause,[],[f22412,f22217,f11185,f23001]) ).

fof(f11185,plain,
    ( spl0_1427
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X13,X1)
        | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).

fof(f22412,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
        | ~ c_in(X1,c_insert(v_B,X0,tc_Message_Oagent),tc_Message_Oagent) )
    | ~ spl0_1427
    | ~ spl0_2037 ),
    inference(superposition,[],[f11186,f22218]) ).

fof(f11186,plain,
    ( ! [X1,X4,X12,X13] :
        ( ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1)
        | ~ c_in(X4,X13,X1) )
    | ~ spl0_1427 ),
    inference(avatar_component_clause,[],[f11185]) ).

fof(f22999,plain,
    spl0_2073,
    inference(avatar_split_clause,[],[f1962,f22997]) ).

fof(f22997,plain,
    ( spl0_2073
  <=> ! [X2,X27,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
        | c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).

fof(f1962,axiom,
    ! [X2,X47,X27] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
      | c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).

fof(f22995,plain,
    spl0_2072,
    inference(avatar_split_clause,[],[f1961,f22993]) ).

fof(f22993,plain,
    ( spl0_2072
  <=> ! [X2,X27,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
        | c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).

fof(f1961,axiom,
    ! [X2,X47,X27] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
      | c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).

fof(f22991,plain,
    spl0_2071,
    inference(avatar_split_clause,[],[f1946,f22989]) ).

fof(f22989,plain,
    ( spl0_2071
  <=> ! [X2,X27,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
        | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).

fof(f1946,axiom,
    ! [X2,X47,X27] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
      | c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).

fof(f22987,plain,
    spl0_2070,
    inference(avatar_split_clause,[],[f1945,f22985]) ).

fof(f22985,plain,
    ( spl0_2070
  <=> ! [X2,X27,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
        | c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).

fof(f1945,axiom,
    ! [X2,X47,X27] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
      | c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).

fof(f22983,plain,
    spl0_2069,
    inference(avatar_split_clause,[],[f1876,f22981]) ).

fof(f22981,plain,
    ( spl0_2069
  <=> ! [X11,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).

fof(f1876,axiom,
    ! [X11,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).

fof(f22979,plain,
    spl0_2068,
    inference(avatar_split_clause,[],[f1755,f22977]) ).

fof(f22977,plain,
    ( spl0_2068
  <=> ! [X0,X1,X23] :
        ( ~ c_List_Odistinct(X23,X1)
        | c_List_Oset(c_List_Oremove1(X0,X23,X1),X1) = c_minus(c_List_Oset(X23,X1),c_insert(X0,c_emptyset,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2068])]) ).

fof(f1755,axiom,
    ! [X0,X1,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | c_List_Oset(c_List_Oremove1(X0,X23,X1),X1) = c_minus(c_List_Oset(X23,X1),c_insert(X0,c_emptyset,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).

fof(f22975,plain,
    spl0_2067,
    inference(avatar_split_clause,[],[f1274,f22973]) ).

fof(f22973,plain,
    ( spl0_2067
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X0,X12,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_lessequals(c_Finite__Set_OMin(X12,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).

fof(f1274,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X0,X12,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_lessequals(c_Finite__Set_OMin(X12,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).

fof(f22971,plain,
    spl0_2066,
    inference(avatar_split_clause,[],[f1256,f22969]) ).

fof(f22969,plain,
    ( spl0_2066
  <=> ! [X12,X0,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X0,X12,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_lessequals(X0,c_Finite__Set_OMax(X12,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).

fof(f1256,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X0,X12,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_lessequals(X0,c_Finite__Set_OMax(X12,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).

fof(f22967,plain,
    spl0_2065,
    inference(avatar_split_clause,[],[f33,f22965]) ).

fof(f22965,plain,
    ( spl0_2065
  <=> ! [X12,X1] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
        | ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).

fof(f33,axiom,
    ! [X1,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
      | ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).

fof(f22963,plain,
    spl0_2064,
    inference(avatar_split_clause,[],[f32,f22961]) ).

fof(f22961,plain,
    ( spl0_2064
  <=> ! [X12,X1] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
        | c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
        | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).

fof(f32,axiom,
    ! [X1,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
      | c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
      | c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).

fof(f22959,plain,
    ( spl0_2063
    | ~ spl0_1424
    | ~ spl0_2037 ),
    inference(avatar_split_clause,[],[f22410,f22217,f11167,f22957]) ).

fof(f22957,plain,
    ( spl0_2063
  <=> ! [X0] :
        ( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
        | c_lessequals(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).

fof(f22410,plain,
    ( ! [X0] :
        ( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
        | c_lessequals(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) )
    | ~ spl0_1424
    | ~ spl0_2037 ),
    inference(superposition,[],[f11168,f22218]) ).

fof(f22791,plain,
    ( spl0_2062
    | ~ spl0_1427
    | ~ spl0_2036 ),
    inference(avatar_split_clause,[],[f22347,f22076,f11185,f22789]) ).

fof(f22347,plain,
    ( ! [X0,X1] :
        ( ~ c_in(X1,c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
        | ~ c_in(X1,c_insert(v_A,X0,tc_Message_Oagent),tc_Message_Oagent) )
    | ~ spl0_1427
    | ~ spl0_2036 ),
    inference(superposition,[],[f11186,f22077]) ).

fof(f22553,plain,
    ( spl0_2061
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_2045 ),
    inference(avatar_split_clause,[],[f22381,f22378,f17663,f7510,f7490,f22551]) ).

fof(f22551,plain,
    ( spl0_2061
  <=> ! [X3,X23,X25,X1] :
        ( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
        | c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).

fof(f22378,plain,
    ( spl0_2045
  <=> ! [X3,X23,X25,X1] :
        ( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
        | c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).

fof(f22381,plain,
    ( ! [X3,X1,X25,X23] :
        ( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
        | c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) )
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_2045 ),
    inference(forward_demodulation,[],[f22379,f17696]) ).

fof(f22379,plain,
    ( ! [X3,X1,X25,X23] :
        ( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
        | c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 )
    | ~ spl0_2045 ),
    inference(avatar_component_clause,[],[f22378]) ).

fof(f22518,plain,
    ( spl0_2060
    | ~ spl0_1850
    | ~ spl0_2042 ),
    inference(avatar_split_clause,[],[f22368,f22365,f17549,f22516]) ).

fof(f22516,plain,
    ( spl0_2060
  <=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).

fof(f22365,plain,
    ( spl0_2042
  <=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).

fof(f22368,plain,
    ( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ spl0_1850
    | ~ spl0_2042 ),
    inference(forward_demodulation,[],[f22366,f17551]) ).

fof(f22366,plain,
    ( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
    | ~ spl0_2042 ),
    inference(avatar_component_clause,[],[f22365]) ).

fof(f22488,plain,
    ( spl0_2059
    | ~ spl0_1424
    | ~ spl0_2036 ),
    inference(avatar_split_clause,[],[f22345,f22076,f11167,f22486]) ).

fof(f22486,plain,
    ( spl0_2059
  <=> ! [X0] :
        ( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
        | c_lessequals(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).

fof(f22345,plain,
    ( ! [X0] :
        ( c_emptyset != c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
        | c_lessequals(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) )
    | ~ spl0_1424
    | ~ spl0_2036 ),
    inference(superposition,[],[f11168,f22077]) ).

fof(f22456,plain,
    spl0_2058,
    inference(avatar_split_clause,[],[f3342,f22454]) ).

fof(f22454,plain,
    ( spl0_2058
  <=> ! [X83] :
        ( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).

fof(f3342,plain,
    ! [X83] :
      ( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3154,f2979]) ).

fof(f2979,plain,
    c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2016,f2544]) ).

fof(f2016,axiom,
    c_Suc(c_0) = c_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).

fof(f3154,plain,
    ! [X83] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1872,f2544]) ).

fof(f1872,axiom,
    ! [X83] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).

fof(f22452,plain,
    spl0_2057,
    inference(avatar_split_clause,[],[f3160,f22450]) ).

fof(f22450,plain,
    ( spl0_2057
  <=> ! [X5,X1,X28] :
        ( ~ c_in(X28,X5,tc_prod(X1,X1))
        | c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).

fof(f3160,plain,
    ! [X28,X1,X5] :
      ( ~ c_in(X28,X5,tc_prod(X1,X1))
      | c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
    inference(definition_unfolding,[],[f119,f2716]) ).

fof(f119,axiom,
    ! [X28,X1,X5] :
      ( ~ c_in(X28,X5,tc_prod(X1,X1))
      | c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).

fof(f22448,plain,
    spl0_2056,
    inference(avatar_split_clause,[],[f3158,f22446]) ).

fof(f22446,plain,
    ( spl0_2056
  <=> ! [X25,X1,X23] :
        ( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
        | c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).

fof(f3158,plain,
    ! [X1,X25,X23] :
      ( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
      | c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ),
    inference(definition_unfolding,[],[f1557,f2373]) ).

fof(f1557,axiom,
    ! [X1,X25,X23] :
      ( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
      | c_emptyset = c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).

fof(f22444,plain,
    spl0_2055,
    inference(avatar_split_clause,[],[f3105,f22442]) ).

fof(f22442,plain,
    ( spl0_2055
  <=> ! [X11,X48,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1),X48,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).

fof(f3105,plain,
    ! [X48,X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1),X48,X1) ),
    inference(definition_unfolding,[],[f2165,f2129]) ).

fof(f2165,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1),X48,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).

fof(f22440,plain,
    spl0_2054,
    inference(avatar_split_clause,[],[f3076,f22438]) ).

fof(f22438,plain,
    ( spl0_2054
  <=> ! [X41,X0,X23,X25] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).

fof(f3076,plain,
    ! [X41,X0,X25,X23] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41),
    inference(definition_unfolding,[],[f1587,f1585,f1585]) ).

fof(f1585,axiom,
    ! [X0,X1,X23] : c_List_Oitrev(X23,X0,X1) = c_append(c_List_Orev(X23,X1),X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).

fof(f1587,axiom,
    ! [X41,X0,X25,X23] : c_List_Oitrev(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Oitrev(X23,c_List_Olist_OCons(X0,X25,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).

fof(f22436,plain,
    spl0_2053,
    inference(avatar_split_clause,[],[f2858,f22434]) ).

fof(f22434,plain,
    ( spl0_2053
  <=> ! [X91,X88] :
        ( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
        | c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).

fof(f2858,axiom,
    ! [X91,X88] :
      ( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
      | c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).

fof(f22432,plain,
    spl0_2052,
    inference(avatar_split_clause,[],[f2846,f22430]) ).

fof(f22430,plain,
    ( spl0_2052
  <=> ! [X86,X91,X88] :
        ( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2052])]) ).

fof(f2846,axiom,
    ! [X91,X88,X86] :
      ( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).

fof(f22405,plain,
    spl0_2051,
    inference(avatar_split_clause,[],[f2797,f22403]) ).

fof(f22403,plain,
    ( spl0_2051
  <=> ! [X102,X86,X12] :
        ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).

fof(f2797,axiom,
    ! [X86,X12,X102] :
      ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_0) ).

fof(f22401,plain,
    spl0_2050,
    inference(avatar_split_clause,[],[f2122,f22399]) ).

fof(f22399,plain,
    ( spl0_2050
  <=> ! [X0,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
        | c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).

fof(f2122,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).

fof(f22397,plain,
    spl0_2049,
    inference(avatar_split_clause,[],[f1864,f22395]) ).

fof(f22395,plain,
    ( spl0_2049
  <=> ! [X83,X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).

fof(f1864,axiom,
    ! [X83,X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).

fof(f22393,plain,
    spl0_2048,
    inference(avatar_split_clause,[],[f1800,f22391]) ).

fof(f22391,plain,
    ( spl0_2048
  <=> ! [X16,X59,X43] :
        ( ~ c_lessequals(X16,X59,tc_nat)
        | c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).

fof(f1800,axiom,
    ! [X59,X16,X43] :
      ( ~ c_lessequals(X16,X59,tc_nat)
      | c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).

fof(f22389,plain,
    spl0_2047,
    inference(avatar_split_clause,[],[f1796,f22387]) ).

fof(f22387,plain,
    ( spl0_2047
  <=> ! [X16,X59,X43] :
        ( ~ c_lessequals(X16,X59,tc_nat)
        | c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).

fof(f1796,axiom,
    ! [X59,X16,X43] :
      ( ~ c_lessequals(X16,X59,tc_nat)
      | c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).

fof(f22385,plain,
    spl0_2046,
    inference(avatar_split_clause,[],[f1795,f22383]) ).

fof(f22383,plain,
    ( spl0_2046
  <=> ! [X16,X59,X43] :
        ( ~ c_lessequals(X16,X59,tc_nat)
        | c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).

fof(f1795,axiom,
    ! [X59,X16,X43] :
      ( ~ c_lessequals(X16,X59,tc_nat)
      | c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).

fof(f22380,plain,
    spl0_2045,
    inference(avatar_split_clause,[],[f1726,f22378]) ).

fof(f1726,axiom,
    ! [X3,X1,X25,X23] :
      ( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
      | c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).

fof(f22376,plain,
    spl0_2044,
    inference(avatar_split_clause,[],[f1714,f22374]) ).

fof(f1714,axiom,
    ! [X41,X0,X23] :
      ( c_in(X0,c_List_Oset(X23,X41),X41)
      | c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).

fof(f22372,plain,
    spl0_2043,
    inference(avatar_split_clause,[],[f1617,f22370]) ).

fof(f22370,plain,
    ( spl0_2043
  <=> ! [X61,X5,X1,X24] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).

fof(f1617,axiom,
    ! [X1,X24,X5,X61] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).

fof(f22367,plain,
    spl0_2042,
    inference(avatar_split_clause,[],[f1453,f22365]) ).

fof(f1453,axiom,
    ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).

fof(f22340,plain,
    spl0_2041,
    inference(avatar_split_clause,[],[f1219,f22338]) ).

fof(f22338,plain,
    ( spl0_2041
  <=> ! [X4,X27,X18] :
        ( ~ c_less(c_0,X4,tc_nat)
        | c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).

fof(f1219,axiom,
    ! [X18,X27,X4] :
      ( ~ c_less(c_0,X4,tc_nat)
      | c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).

fof(f22336,plain,
    spl0_2040,
    inference(avatar_split_clause,[],[f1218,f22334]) ).

fof(f22334,plain,
    ( spl0_2040
  <=> ! [X4,X27,X18] :
        ( ~ c_less(c_0,X4,tc_nat)
        | c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).

fof(f1218,axiom,
    ! [X18,X27,X4] :
      ( ~ c_less(c_0,X4,tc_nat)
      | c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).

fof(f22332,plain,
    spl0_2039,
    inference(avatar_split_clause,[],[f57,f22330]) ).

fof(f22330,plain,
    ( spl0_2039
  <=> ! [X5,X1,X23] :
        ( c_List_Olist_ONil = X23
        | ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).

fof(f57,axiom,
    ! [X1,X5,X23] :
      ( c_List_Olist_ONil = X23
      | ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).

fof(f22328,plain,
    spl0_2038,
    inference(avatar_split_clause,[],[f56,f22326]) ).

fof(f22326,plain,
    ( spl0_2038
  <=> ! [X5,X1,X23] :
        ( c_List_Olist_ONil = X23
        | ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).

fof(f56,axiom,
    ! [X1,X5,X23] :
      ( c_List_Olist_ONil = X23
      | ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).

fof(f22219,plain,
    ( spl0_2037
    | spl0_3
    | ~ spl0_2010 ),
    inference(avatar_split_clause,[],[f21831,f20913,f3444,f22217]) ).

fof(f3444,plain,
    ( spl0_3
  <=> c_in(v_B,c_Event_Obad,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f21831,plain,
    ( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_B,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
    | spl0_3
    | ~ spl0_2010 ),
    inference(resolution,[],[f20914,f3446]) ).

fof(f3446,plain,
    ( ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent)
    | spl0_3 ),
    inference(avatar_component_clause,[],[f3444]) ).

fof(f22078,plain,
    ( spl0_2036
    | spl0_2
    | ~ spl0_2010 ),
    inference(avatar_split_clause,[],[f21830,f20913,f3439,f22076]) ).

fof(f3439,plain,
    ( spl0_2
  <=> c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f21830,plain,
    ( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_A,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
    | spl0_2
    | ~ spl0_2010 ),
    inference(resolution,[],[f20914,f3441]) ).

fof(f3441,plain,
    ( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f3439]) ).

fof(f21724,plain,
    ( spl0_2035
    | ~ spl0_1793
    | ~ spl0_1883 ),
    inference(avatar_split_clause,[],[f19183,f18930,f17080,f21722]) ).

fof(f21722,plain,
    ( spl0_2035
  <=> ! [X0,X1] :
        ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Obutlast(X1,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Obutlast(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent),tc_Event_Oevent))
        | c_List_Olist_ONil = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).

fof(f17080,plain,
    ( spl0_1793
  <=> ! [X41,X0,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).

fof(f18930,plain,
    ( spl0_1883
  <=> ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X1),X0,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).

fof(f19183,plain,
    ( ! [X0,X1] :
        ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Obutlast(X1,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Obutlast(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent),tc_Event_Oevent))
        | c_List_Olist_ONil = X1 )
    | ~ spl0_1793
    | ~ spl0_1883 ),
    inference(superposition,[],[f18931,f17081]) ).

fof(f17081,plain,
    ( ! [X41,X0,X23] :
        ( c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41)
        | c_List_Olist_ONil = X23 )
    | ~ spl0_1793 ),
    inference(avatar_component_clause,[],[f17080]) ).

fof(f18931,plain,
    ( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X1),X0,tc_Event_Oevent))
    | ~ spl0_1883 ),
    inference(avatar_component_clause,[],[f18930]) ).

fof(f21359,plain,
    ( spl0_2034
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_1992 ),
    inference(avatar_split_clause,[],[f20843,f20839,f17663,f7510,f7490,f21357]) ).

fof(f21357,plain,
    ( spl0_2034
  <=> ! [X3,X0,X23,X25,X1] :
        ( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
        | X0 = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).

fof(f20839,plain,
    ( spl0_1992
  <=> ! [X23,X0,X3,X25,X1] :
        ( X0 = X3
        | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).

fof(f20843,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
        | X0 = X3 )
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_1992 ),
    inference(forward_demodulation,[],[f20842,f17696]) ).

fof(f20842,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
        | X0 = X3 )
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_1992 ),
    inference(forward_demodulation,[],[f20840,f17696]) ).

fof(f20840,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( X0 = X3
        | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
    | ~ spl0_1992 ),
    inference(avatar_component_clause,[],[f20839]) ).

fof(f21355,plain,
    ( spl0_2033
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_1990 ),
    inference(avatar_split_clause,[],[f20833,f20829,f17663,f7510,f7490,f21353]) ).

fof(f21353,plain,
    ( spl0_2033
  <=> ! [X3,X0,X23,X25,X1] :
        ( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
        | X23 = X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2033])]) ).

fof(f20829,plain,
    ( spl0_1990
  <=> ! [X3,X0,X23,X25,X1] :
        ( X23 = X25
        | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).

fof(f20833,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
        | X23 = X25 )
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_1990 ),
    inference(forward_demodulation,[],[f20832,f17696]) ).

fof(f20832,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
        | X23 = X25 )
    | ~ spl0_782
    | ~ spl0_787
    | ~ spl0_1854
    | ~ spl0_1990 ),
    inference(forward_demodulation,[],[f20830,f17696]) ).

fof(f20830,plain,
    ( ! [X3,X0,X1,X25,X23] :
        ( X23 = X25
        | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
    | ~ spl0_1990 ),
    inference(avatar_component_clause,[],[f20829]) ).

fof(f21177,plain,
    ( spl0_2032
    | ~ spl0_1763
    | ~ spl0_1882 ),
    inference(avatar_split_clause,[],[f19286,f18723,f16003,f21174]) ).

fof(f21174,plain,
    ( spl0_2032
  <=> c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Osublist(c_List_Oremdups(v_evso,tc_Event_Oevent),c_SetInterval_OlessThan(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).

fof(f16003,plain,
    ( spl0_1763
  <=> ! [X21,X1,X3] :
        ( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
        | ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).

fof(f18723,plain,
    ( spl0_1882
  <=> c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).

fof(f19286,plain,
    ( c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Osublist(c_List_Oremdups(v_evso,tc_Event_Oevent),c_SetInterval_OlessThan(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat),tc_Event_Oevent)
    | ~ spl0_1763
    | ~ spl0_1882 ),
    inference(resolution,[],[f18725,f16004]) ).

fof(f16004,plain,
    ( ! [X21,X3,X1] :
        ( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat)
        | c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3 )
    | ~ spl0_1763 ),
    inference(avatar_component_clause,[],[f16003]) ).

fof(f18725,plain,
    ( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
    | ~ spl0_1882 ),
    inference(avatar_component_clause,[],[f18723]) ).

fof(f21027,plain,
    ( spl0_2031
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2030 ),
    inference(avatar_split_clause,[],[f21023,f21019,f11334,f10936,f7067,f6122,f21025]) ).

fof(f21019,plain,
    ( spl0_2030
  <=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).

fof(f21023,plain,
    ( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2030 ),
    inference(forward_demodulation,[],[f21022,f12301]) ).

fof(f21022,plain,
    ( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(c_1,X21,tc_nat),tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_2030 ),
    inference(forward_demodulation,[],[f21020,f12301]) ).

fof(f21020,plain,
    ( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
    | ~ spl0_2030 ),
    inference(avatar_component_clause,[],[f21019]) ).

fof(f21021,plain,
    spl0_2030,
    inference(avatar_split_clause,[],[f3264,f21019]) ).

fof(f21017,plain,
    spl0_2029,
    inference(avatar_split_clause,[],[f3186,f21015]) ).

fof(f21015,plain,
    ( spl0_2029
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X13,X1)
        | ~ c_in(X4,X12,X1)
        | c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).

fof(f3186,plain,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X13,X1)
      | ~ c_in(X4,X12,X1)
      | c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
    inference(definition_unfolding,[],[f2608,f2373]) ).

fof(f2608,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X13,X1)
      | ~ c_in(X4,X12,X1)
      | c_in(X4,c_inter(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).

fof(f21013,plain,
    spl0_2028,
    inference(avatar_split_clause,[],[f3181,f21011]) ).

fof(f21011,plain,
    ( spl0_2028
  <=> ! [X0,X1,X3] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).

fof(f3181,plain,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f2142,f2129]) ).

fof(f2142,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).

fof(f21009,plain,
    spl0_2027,
    inference(avatar_split_clause,[],[f3180,f21007]) ).

fof(f21007,plain,
    ( spl0_2027
  <=> ! [X0,X1,X3] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
        | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).

fof(f3180,plain,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f2141,f2129]) ).

fof(f2141,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).

fof(f21005,plain,
    spl0_2026,
    inference(avatar_split_clause,[],[f3137,f21003]) ).

fof(f21003,plain,
    ( spl0_2026
  <=> ! [X43,X23,X21,X1] :
        ( ~ c_less(X43,X21,tc_nat)
        | c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).

fof(f3137,plain,
    ! [X21,X1,X23,X43] :
      ( ~ c_less(X43,X21,tc_nat)
      | c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ),
    inference(definition_unfolding,[],[f1703,f1766]) ).

fof(f1703,axiom,
    ! [X21,X1,X23,X43] :
      ( ~ c_less(X43,X21,tc_nat)
      | c_List_Onth(c_List_Otake(X21,X23,X1),X43,X1) = c_List_Onth(X23,X43,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).

fof(f21001,plain,
    spl0_2025,
    inference(avatar_split_clause,[],[f3102,f20999]) ).

fof(f20999,plain,
    ( spl0_2025
  <=> ! [X11,X1,X47] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).

fof(f3102,plain,
    ! [X11,X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ),
    inference(definition_unfolding,[],[f2120,f2129]) ).

fof(f2120,axiom,
    ! [X11,X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1) = c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).

fof(f20997,plain,
    spl0_2024,
    inference(avatar_split_clause,[],[f2940,f20995]) ).

fof(f20995,plain,
    ( spl0_2024
  <=> ! [X102,X12] :
        ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).

fof(f2940,axiom,
    ! [X12,X102] :
      ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_1) ).

fof(f20993,plain,
    spl0_2023,
    inference(avatar_split_clause,[],[f2939,f20991]) ).

fof(f20991,plain,
    ( spl0_2023
  <=> ! [X102,X12] :
        ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).

fof(f2939,axiom,
    ! [X12,X102] :
      ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_0) ).

fof(f20976,plain,
    spl0_2022,
    inference(avatar_split_clause,[],[f2938,f20974]) ).

fof(f20974,plain,
    ( spl0_2022
  <=> ! [X102,X12] :
        ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).

fof(f2938,axiom,
    ! [X12,X102] :
      ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_1) ).

fof(f20972,plain,
    spl0_2021,
    inference(avatar_split_clause,[],[f2937,f20970]) ).

fof(f20970,plain,
    ( spl0_2021
  <=> ! [X102,X12] :
        ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
        | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).

fof(f2937,axiom,
    ! [X12,X102] :
      ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
      | ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_0) ).

fof(f20968,plain,
    spl0_2020,
    inference(avatar_split_clause,[],[f2873,f20966]) ).

fof(f20966,plain,
    ( spl0_2020
  <=> ! [X86,X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).

fof(f2873,axiom,
    ! [X91,X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).

fof(f20964,plain,
    spl0_2019,
    inference(avatar_split_clause,[],[f2867,f20962]) ).

fof(f20962,plain,
    ( spl0_2019
  <=> ! [X20,X88,X4] :
        ( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
        | c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
        | ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).

fof(f2867,axiom,
    ! [X88,X4,X20] :
      ( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
      | c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
      | ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).

fof(f20960,plain,
    spl0_2018,
    inference(avatar_split_clause,[],[f2839,f20958]) ).

fof(f20958,plain,
    ( spl0_2018
  <=> ! [X86,X87,X88] :
        ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).

fof(f2839,axiom,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).

fof(f20956,plain,
    spl0_2017,
    inference(avatar_split_clause,[],[f2838,f20954]) ).

fof(f20954,plain,
    ( spl0_2017
  <=> ! [X87,X86,X88] :
        ( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).

fof(f2838,axiom,
    ! [X88,X86,X87] :
      ( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).

fof(f20952,plain,
    spl0_2016,
    inference(avatar_split_clause,[],[f2805,f20950]) ).

fof(f20950,plain,
    ( spl0_2016
  <=> ! [X86,X91,X88] :
        ( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
        | c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).

fof(f2805,axiom,
    ! [X91,X88,X86] :
      ( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).

fof(f20948,plain,
    spl0_2015,
    inference(avatar_split_clause,[],[f2804,f20946]) ).

fof(f20946,plain,
    ( spl0_2015
  <=> ! [X86,X91,X88] :
        ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).

fof(f2804,axiom,
    ! [X91,X88,X86] :
      ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).

fof(f20944,plain,
    spl0_2014,
    inference(avatar_split_clause,[],[f2802,f20942]) ).

fof(f20942,plain,
    ( spl0_2014
  <=> ! [X102,X13,X12,X86] : c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).

fof(f2802,axiom,
    ! [X86,X102,X12,X13] : c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Says_0) ).

fof(f20940,plain,
    spl0_2013,
    inference(avatar_split_clause,[],[f2791,f20938]) ).

fof(f20938,plain,
    ( spl0_2013
  <=> ! [X91,X88] :
        ( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
        | ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
        | c_in(c_Message_Omsg_OKey(v_sko__uhi(X88,X91)),X88,tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).

fof(f2791,axiom,
    ! [X91,X88] :
      ( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
      | ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
      | c_in(c_Message_Omsg_OKey(v_sko__uhi(X88,X91)),X88,tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).

fof(f20923,plain,
    spl0_2012,
    inference(avatar_split_clause,[],[f2674,f20921]) ).

fof(f2674,axiom,
    ! [X0,X1,X12,X13] :
      ( ~ c_in(X0,X13,X1)
      | c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).

fof(f20919,plain,
    spl0_2011,
    inference(avatar_split_clause,[],[f2647,f20917]) ).

fof(f20917,plain,
    ( spl0_2011
  <=> ! [X13,X12,X32,X1] :
        ( ~ c_lessequals(X13,X32,tc_set(X1))
        | ~ c_lessequals(X12,X32,tc_set(X1))
        | c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).

fof(f2647,axiom,
    ! [X1,X12,X32,X13] :
      ( ~ c_lessequals(X13,X32,tc_set(X1))
      | ~ c_lessequals(X12,X32,tc_set(X1))
      | c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).

fof(f20915,plain,
    spl0_2010,
    inference(avatar_split_clause,[],[f2597,f20913]) ).

fof(f2597,axiom,
    ! [X0,X1,X12,X13] :
      ( c_in(X0,X12,X1)
      | c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).

fof(f20911,plain,
    spl0_2009,
    inference(avatar_split_clause,[],[f2337,f20909]) ).

fof(f20909,plain,
    ( spl0_2009
  <=> ! [X0,X11] :
        ( c_less(c_0,X0,tc_nat)
        | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
        | ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).

fof(f2337,axiom,
    ! [X0,X11] :
      ( c_less(c_0,X0,tc_nat)
      | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
      | ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).

fof(f20907,plain,
    spl0_2008,
    inference(avatar_split_clause,[],[f2329,f20905]) ).

fof(f20905,plain,
    ( spl0_2008
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).

fof(f2329,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).

fof(f20903,plain,
    spl0_2007,
    inference(avatar_split_clause,[],[f2326,f20901]) ).

fof(f20901,plain,
    ( spl0_2007
  <=> ! [X21,X1,X0] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Parity_Oeven(X21,tc_nat)
        | c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).

fof(f2326,axiom,
    ! [X21,X0,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | ~ c_Parity_Oeven(X21,tc_nat)
      | c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).

fof(f20899,plain,
    spl0_2006,
    inference(avatar_split_clause,[],[f2323,f20897]) ).

fof(f20897,plain,
    ( spl0_2006
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
        | ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).

fof(f2323,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
      | ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).

fof(f20895,plain,
    spl0_2005,
    inference(avatar_split_clause,[],[f2077,f20893]) ).

fof(f20893,plain,
    ( spl0_2005
  <=> ! [X21,X16,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | ~ c_less(c_0,X16,tc_nat)
        | c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).

fof(f2077,axiom,
    ! [X21,X16,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | ~ c_less(c_0,X16,tc_nat)
      | c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).

fof(f20891,plain,
    spl0_2004,
    inference(avatar_split_clause,[],[f2074,f20889]) ).

fof(f20889,plain,
    ( spl0_2004
  <=> ! [X21,X16,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | ~ c_less(c_0,X16,tc_nat)
        | c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).

fof(f2074,axiom,
    ! [X21,X16,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | ~ c_less(c_0,X16,tc_nat)
      | c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).

fof(f20887,plain,
    spl0_2003,
    inference(avatar_split_clause,[],[f2069,f20885]) ).

fof(f20885,plain,
    ( spl0_2003
  <=> ! [X16,X21,X15] :
        ( ~ c_less(c_0,X16,tc_nat)
        | c_lessequals(X15,X21,tc_nat)
        | ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).

fof(f2069,axiom,
    ! [X21,X16,X15] :
      ( ~ c_less(c_0,X16,tc_nat)
      | c_lessequals(X15,X21,tc_nat)
      | ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).

fof(f20883,plain,
    ( spl0_2002
    | ~ spl0_1712
    | ~ spl0_1884 ),
    inference(avatar_split_clause,[],[f19230,f19128,f15746,f20881]) ).

fof(f20881,plain,
    ( spl0_2002
  <=> ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).

fof(f15746,plain,
    ( spl0_1712
  <=> ! [X41,X0,X23,X25] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).

fof(f19128,plain,
    ( spl0_1884
  <=> ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X1),X0,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).

fof(f19230,plain,
    ( ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent))
    | ~ spl0_1712
    | ~ spl0_1884 ),
    inference(superposition,[],[f19129,f15747]) ).

fof(f15747,plain,
    ( ! [X41,X0,X25,X23] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41)
    | ~ spl0_1712 ),
    inference(avatar_component_clause,[],[f15746]) ).

fof(f19129,plain,
    ( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X1),X0,tc_Event_Oevent))
    | ~ spl0_1884 ),
    inference(avatar_component_clause,[],[f19128]) ).

fof(f20879,plain,
    spl0_2001,
    inference(avatar_split_clause,[],[f2066,f20877]) ).

fof(f20877,plain,
    ( spl0_2001
  <=> ! [X16,X21,X15] :
        ( ~ c_less(c_0,X16,tc_nat)
        | c_lessequals(X15,X21,tc_nat)
        | ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).

fof(f2066,axiom,
    ! [X21,X16,X15] :
      ( ~ c_less(c_0,X16,tc_nat)
      | c_lessequals(X15,X21,tc_nat)
      | ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).

fof(f20875,plain,
    spl0_2000,
    inference(avatar_split_clause,[],[f1929,f20873]) ).

fof(f20873,plain,
    ( spl0_2000
  <=> ! [X2,X27,X47] :
        ( ~ class_Numeral_Onumber(X2)
        | ~ class_OrderedGroup_Oab__group__add(X2)
        | c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
        | c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).

fof(f1929,axiom,
    ! [X2,X47,X27] :
      ( ~ class_Numeral_Onumber(X2)
      | ~ class_OrderedGroup_Oab__group__add(X2)
      | c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
      | c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).

fof(f20871,plain,
    spl0_1999,
    inference(avatar_split_clause,[],[f1830,f20869]) ).

fof(f20869,plain,
    ( spl0_1999
  <=> ! [X0,X3] :
        ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
        | c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).

fof(f1830,axiom,
    ! [X3,X0] :
      ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
      | c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).

fof(f20867,plain,
    spl0_1998,
    inference(avatar_split_clause,[],[f1829,f20865]) ).

fof(f20865,plain,
    ( spl0_1998
  <=> ! [X0,X3] :
        ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
        | c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).

fof(f1829,axiom,
    ! [X3,X0] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
      | c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).

fof(f20863,plain,
    spl0_1997,
    inference(avatar_split_clause,[],[f1721,f20861]) ).

fof(f20861,plain,
    ( spl0_1997
  <=> ! [X41,X0,X23,X3] :
        ( X0 = X3
        | c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).

fof(f1721,axiom,
    ! [X3,X41,X0,X23] :
      ( X0 = X3
      | c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).

fof(f20859,plain,
    spl0_1996,
    inference(avatar_split_clause,[],[f1704,f20857]) ).

fof(f20857,plain,
    ( spl0_1996
  <=> ! [X16,X59,X43] :
        ( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
        | c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).

fof(f1704,axiom,
    ! [X59,X16,X43] :
      ( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
      | c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).

fof(f20855,plain,
    spl0_1995,
    inference(avatar_split_clause,[],[f1697,f20853]) ).

fof(f20853,plain,
    ( spl0_1995
  <=> ! [X21,X23,X25,X1] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).

fof(f1697,axiom,
    ! [X21,X1,X25,X23] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).

fof(f20851,plain,
    spl0_1994,
    inference(avatar_split_clause,[],[f1630,f20849]) ).

fof(f1630,axiom,
    ! [X65,X41,X18,X60] :
      ( c_in(X18,c_List_Oset(X65,X41),X41)
      | c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).

fof(f20847,plain,
    spl0_1993,
    inference(avatar_split_clause,[],[f1599,f20845]) ).

fof(f20845,plain,
    ( spl0_1993
  <=> ! [X25,X1,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).

fof(f1599,axiom,
    ! [X1,X25,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).

fof(f20841,plain,
    spl0_1992,
    inference(avatar_split_clause,[],[f1517,f20839]) ).

fof(f1517,axiom,
    ! [X3,X0,X1,X25,X23] :
      ( X0 = X3
      | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).

fof(f20837,plain,
    ( spl0_1991
    | ~ spl0_1712
    | ~ spl0_1883 ),
    inference(avatar_split_clause,[],[f19181,f18930,f15746,f20835]) ).

fof(f20835,plain,
    ( spl0_1991
  <=> ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).

fof(f19181,plain,
    ( ! [X2,X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,c_append(X1,X2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_append(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent),X2,tc_Event_Oevent))
    | ~ spl0_1712
    | ~ spl0_1883 ),
    inference(superposition,[],[f18931,f15747]) ).

fof(f20831,plain,
    spl0_1990,
    inference(avatar_split_clause,[],[f1516,f20829]) ).

fof(f1516,axiom,
    ! [X3,X0,X1,X25,X23] :
      ( X23 = X25
      | c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).

fof(f20827,plain,
    spl0_1989,
    inference(avatar_split_clause,[],[f1481,f20825]) ).

fof(f1481,axiom,
    ! [X3,X0] :
      ( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).

fof(f20823,plain,
    spl0_1988,
    inference(avatar_split_clause,[],[f1480,f20821]) ).

fof(f20821,plain,
    ( spl0_1988
  <=> ! [X0,X3] :
        ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).

fof(f1480,axiom,
    ! [X3,X0] :
      ( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).

fof(f20819,plain,
    spl0_1987,
    inference(avatar_split_clause,[],[f1473,f20817]) ).

fof(f20817,plain,
    ( spl0_1987
  <=> ! [X18,X27] :
        ( c_0 = X18
        | c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).

fof(f1473,axiom,
    ! [X18,X27] :
      ( c_0 = X18
      | c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).

fof(f20815,plain,
    spl0_1986,
    inference(avatar_split_clause,[],[f1472,f20813]) ).

fof(f20813,plain,
    ( spl0_1986
  <=> ! [X18,X27] :
        ( c_0 = X18
        | c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).

fof(f1472,axiom,
    ! [X18,X27] :
      ( c_0 = X18
      | c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).

fof(f20811,plain,
    spl0_1985,
    inference(avatar_split_clause,[],[f1292,f20809]) ).

fof(f20809,plain,
    ( spl0_1985
  <=> ! [X2,X12] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
        | c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).

fof(f1292,axiom,
    ! [X2,X12] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
      | c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).

fof(f20807,plain,
    spl0_1984,
    inference(avatar_split_clause,[],[f1288,f20805]) ).

fof(f20805,plain,
    ( spl0_1984
  <=> ! [X20,X1,X19] :
        ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).

fof(f1288,axiom,
    ! [X1,X19,X20] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).

fof(f20333,plain,
    ( spl0_1983
    | ~ spl0_1760
    | ~ spl0_1981 ),
    inference(avatar_split_clause,[],[f20175,f19951,f15960,f20330]) ).

fof(f20330,plain,
    ( spl0_1983
  <=> c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).

fof(f19951,plain,
    ( spl0_1981
  <=> c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).

fof(f20175,plain,
    ( c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
    | ~ spl0_1760
    | ~ spl0_1981 ),
    inference(superposition,[],[f19953,f15961]) ).

fof(f19953,plain,
    ( c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
    | ~ spl0_1981 ),
    inference(avatar_component_clause,[],[f19951]) ).

fof(f20078,plain,
    ( spl0_1982
    | ~ spl0_1624
    | ~ spl0_1882 ),
    inference(avatar_split_clause,[],[f19287,f18723,f14335,f20076]) ).

fof(f20076,plain,
    ( spl0_1982
  <=> ! [X0] : c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Olist__update(c_List_Oremdups(v_evso,tc_Event_Oevent),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),X0,tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).

fof(f14335,plain,
    ( spl0_1624
  <=> ! [X0,X3,X43,X1] :
        ( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
        | c_List_Olist__update(X3,X43,X0,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).

fof(f19287,plain,
    ( ! [X0] : c_List_Oremdups(v_evso,tc_Event_Oevent) = c_List_Olist__update(c_List_Oremdups(v_evso,tc_Event_Oevent),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),X0,tc_Event_Oevent)
    | ~ spl0_1624
    | ~ spl0_1882 ),
    inference(resolution,[],[f18725,f14336]) ).

fof(f14336,plain,
    ( ! [X3,X0,X1,X43] :
        ( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
        | c_List_Olist__update(X3,X43,X0,X1) = X3 )
    | ~ spl0_1624 ),
    inference(avatar_component_clause,[],[f14335]) ).

fof(f19954,plain,
    ( spl0_1981
    | ~ spl0_1181
    | ~ spl0_1882 ),
    inference(avatar_split_clause,[],[f19282,f18723,f9531,f19951]) ).

fof(f9531,plain,
    ( spl0_1181
  <=> ! [X21,X15] :
        ( ~ c_lessequals(X15,X21,tc_nat)
        | c_0 = c_minus(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).

fof(f19282,plain,
    ( c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
    | ~ spl0_1181
    | ~ spl0_1882 ),
    inference(resolution,[],[f18725,f9532]) ).

fof(f9532,plain,
    ( ! [X21,X15] :
        ( ~ c_lessequals(X15,X21,tc_nat)
        | c_0 = c_minus(X15,X21,tc_nat) )
    | ~ spl0_1181 ),
    inference(avatar_component_clause,[],[f9531]) ).

fof(f19765,plain,
    spl0_1980,
    inference(avatar_split_clause,[],[f3427,f19763]) ).

fof(f19763,plain,
    ( spl0_1980
  <=> ! [X1,X3] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).

fof(f3427,plain,
    ! [X3,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3213,f2114]) ).

fof(f2114,axiom,
    ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).

fof(f3213,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1313,f2129]) ).

fof(f1313,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).

fof(f19761,plain,
    spl0_1979,
    inference(avatar_split_clause,[],[f3425,f19759]) ).

fof(f19759,plain,
    ( spl0_1979
  <=> ! [X0,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).

fof(f3425,plain,
    ! [X0,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
    inference(forward_demodulation,[],[f3211,f2114]) ).

fof(f3211,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
    inference(definition_unfolding,[],[f1325,f2129]) ).

fof(f1325,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).

fof(f19757,plain,
    spl0_1978,
    inference(avatar_split_clause,[],[f3417,f19755]) ).

fof(f19755,plain,
    ( spl0_1978
  <=> ! [X1,X3] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).

fof(f3417,plain,
    ! [X3,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3205,f2114]) ).

fof(f3205,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1312,f2129]) ).

fof(f1312,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).

fof(f19753,plain,
    spl0_1977,
    inference(avatar_split_clause,[],[f3415,f19751]) ).

fof(f19751,plain,
    ( spl0_1977
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).

fof(f3415,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
    inference(forward_demodulation,[],[f3203,f2114]) ).

fof(f3203,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
    inference(definition_unfolding,[],[f1324,f2129]) ).

fof(f1324,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).

fof(f19749,plain,
    spl0_1976,
    inference(avatar_split_clause,[],[f3383,f19747]) ).

fof(f19747,plain,
    ( spl0_1976
  <=> ! [X1,X3] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 = c_Numeral_Onumber__of(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).

fof(f3383,plain,
    ! [X3,X1] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_1 = c_Numeral_Onumber__of(X3,X1) ),
    inference(forward_demodulation,[],[f3177,f2156]) ).

fof(f3177,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 = c_Numeral_Onumber__of(X3,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1336,f2129]) ).

fof(f1336,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 = c_Numeral_Onumber__of(X3,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).

fof(f19733,plain,
    ( spl0_1975
    | ~ spl0_1664
    | ~ spl0_1974 ),
    inference(avatar_split_clause,[],[f19729,f19726,f14495,f19731]) ).

fof(f19731,plain,
    ( spl0_1975
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).

fof(f19726,plain,
    ( spl0_1974
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).

fof(f19729,plain,
    ( ! [X0,X1] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 = c_Numeral_Onumber__of(X0,X1) )
    | ~ spl0_1664
    | ~ spl0_1974 ),
    inference(forward_demodulation,[],[f19727,f14497]) ).

fof(f19727,plain,
    ( ! [X0,X1] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 = c_Numeral_Onumber__of(X0,X1) )
    | ~ spl0_1974 ),
    inference(avatar_component_clause,[],[f19726]) ).

fof(f19728,plain,
    spl0_1974,
    inference(avatar_split_clause,[],[f3382,f19726]) ).

fof(f3382,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_1 = c_Numeral_Onumber__of(X0,X1) ),
    inference(forward_demodulation,[],[f3176,f2156]) ).

fof(f3176,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 = c_Numeral_Onumber__of(X0,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    inference(definition_unfolding,[],[f1340,f2129]) ).

fof(f1340,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 = c_Numeral_Onumber__of(X0,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).

fof(f19724,plain,
    spl0_1973,
    inference(avatar_split_clause,[],[f3377,f19722]) ).

fof(f19722,plain,
    ( spl0_1973
  <=> ! [X1,X3] :
        ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 != c_Numeral_Onumber__of(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).

fof(f3377,plain,
    ! [X3,X1] :
      ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_1 != c_Numeral_Onumber__of(X3,X1) ),
    inference(forward_demodulation,[],[f3173,f2156]) ).

fof(f3173,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 != c_Numeral_Onumber__of(X3,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1335,f2129]) ).

fof(f1335,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 != c_Numeral_Onumber__of(X3,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).

fof(f19711,plain,
    ( spl0_1972
    | ~ spl0_1664
    | ~ spl0_1971 ),
    inference(avatar_split_clause,[],[f19707,f19704,f14495,f19709]) ).

fof(f19709,plain,
    ( spl0_1972
  <=> ! [X0,X1] :
        ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).

fof(f19704,plain,
    ( spl0_1971
  <=> ! [X0,X1] :
        ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).

fof(f19707,plain,
    ( ! [X0,X1] :
        ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 != c_Numeral_Onumber__of(X0,X1) )
    | ~ spl0_1664
    | ~ spl0_1971 ),
    inference(forward_demodulation,[],[f19705,f14497]) ).

fof(f19705,plain,
    ( ! [X0,X1] :
        ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_1 != c_Numeral_Onumber__of(X0,X1) )
    | ~ spl0_1971 ),
    inference(avatar_component_clause,[],[f19704]) ).

fof(f19706,plain,
    spl0_1971,
    inference(avatar_split_clause,[],[f3376,f19704]) ).

fof(f3376,plain,
    ! [X0,X1] :
      ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_1 != c_Numeral_Onumber__of(X0,X1) ),
    inference(forward_demodulation,[],[f3172,f2156]) ).

fof(f3172,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 != c_Numeral_Onumber__of(X0,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    inference(definition_unfolding,[],[f1339,f2129]) ).

fof(f1339,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 != c_Numeral_Onumber__of(X0,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).

fof(f19700,plain,
    ( spl0_1970
    | ~ spl0_57
    | ~ spl0_1465
    | ~ spl0_1969 ),
    inference(avatar_split_clause,[],[f19696,f19693,f11350,f3714,f19698]) ).

fof(f19698,plain,
    ( spl0_1970
  <=> ! [X47] :
        ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).

fof(f19693,plain,
    ( spl0_1969
  <=> ! [X47] :
        ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).

fof(f19696,plain,
    ( ! [X47] :
        ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1465
    | ~ spl0_1969 ),
    inference(forward_demodulation,[],[f19694,f12369]) ).

fof(f19694,plain,
    ( ! [X47] :
        ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1969 ),
    inference(avatar_component_clause,[],[f19693]) ).

fof(f19695,plain,
    spl0_1969,
    inference(avatar_split_clause,[],[f3345,f19693]) ).

fof(f3345,plain,
    ! [X47] :
      ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3344,f2156]) ).

fof(f3344,plain,
    ! [X47] :
      ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3343,f2154]) ).

fof(f3343,plain,
    ! [X47] :
      ( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f2273,f2156]) ).

fof(f2273,axiom,
    ! [X47] :
      ( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/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(f19691,plain,
    ( spl0_1968
    | ~ spl0_1444
    | ~ spl0_1884 ),
    inference(avatar_split_clause,[],[f19235,f19128,f11266,f19689]) ).

fof(f19689,plain,
    ( spl0_1968
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
        | c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).

fof(f19235,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
        | c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) )
    | ~ spl0_1444
    | ~ spl0_1884 ),
    inference(superposition,[],[f11267,f19129]) ).

fof(f19685,plain,
    ( spl0_1967
    | ~ spl0_57
    | ~ spl0_1465
    | ~ spl0_1966 ),
    inference(avatar_split_clause,[],[f19681,f19678,f11350,f3714,f19683]) ).

fof(f19683,plain,
    ( spl0_1967
  <=> ! [X47] :
        ( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).

fof(f19678,plain,
    ( spl0_1966
  <=> ! [X47] :
        ( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).

fof(f19681,plain,
    ( ! [X47] :
        ( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_57
    | ~ spl0_1465
    | ~ spl0_1966 ),
    inference(forward_demodulation,[],[f19679,f12369]) ).

fof(f19679,plain,
    ( ! [X47] :
        ( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1966 ),
    inference(avatar_component_clause,[],[f19678]) ).

fof(f19680,plain,
    spl0_1966,
    inference(avatar_split_clause,[],[f3341,f19678]) ).

fof(f3341,plain,
    ! [X47] :
      ( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3340,f2156]) ).

fof(f3340,plain,
    ! [X47] :
      ( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3339,f2154]) ).

fof(f3339,plain,
    ! [X47] :
      ( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f2272,f2156]) ).

fof(f2272,axiom,
    ! [X47] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/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(f19675,plain,
    ( spl0_1965
    | ~ spl0_1664
    | ~ spl0_1964 ),
    inference(avatar_split_clause,[],[f19671,f19668,f14495,f19673]) ).

fof(f19673,plain,
    ( spl0_1965
  <=> ! [X1,X47] :
        ( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OMin),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).

fof(f19668,plain,
    ( spl0_1964
  <=> ! [X1,X47] :
        ( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).

fof(f19671,plain,
    ( ! [X47,X1] :
        ( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OMin),X1)
        | ~ class_Numeral_Onumber__ring(X1) )
    | ~ spl0_1664
    | ~ spl0_1964 ),
    inference(forward_demodulation,[],[f19669,f14497]) ).

fof(f19669,plain,
    ( ! [X47,X1] :
        ( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
        | ~ class_Numeral_Onumber__ring(X1) )
    | ~ spl0_1964 ),
    inference(avatar_component_clause,[],[f19668]) ).

fof(f19670,plain,
    spl0_1964,
    inference(avatar_split_clause,[],[f3310,f19668]) ).

fof(f3310,plain,
    ! [X47,X1] :
      ( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f3104,f2156]) ).

fof(f3104,plain,
    ! [X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
    inference(definition_unfolding,[],[f1332,f2129]) ).

fof(f1332,axiom,
    ! [X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).

fof(f19666,plain,
    spl0_1963,
    inference(avatar_split_clause,[],[f3309,f19664]) ).

fof(f19664,plain,
    ( spl0_1963
  <=> ! [X11,X1] :
        ( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).

fof(f3309,plain,
    ! [X11,X1] :
      ( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f3103,f2156]) ).

fof(f3103,plain,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ),
    inference(definition_unfolding,[],[f1331,f2129]) ).

fof(f1331,axiom,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X11)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).

fof(f19662,plain,
    spl0_1962,
    inference(avatar_split_clause,[],[f3277,f19660]) ).

fof(f3277,plain,
    ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat),
    inference(forward_demodulation,[],[f3084,f2979]) ).

fof(f3084,plain,
    ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2765,f2544]) ).

fof(f2765,axiom,
    ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__6_0) ).

fof(f19658,plain,
    spl0_1961,
    inference(avatar_split_clause,[],[f3268,f19656]) ).

fof(f19656,plain,
    ( spl0_1961
  <=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).

fof(f3268,plain,
    ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),
    inference(forward_demodulation,[],[f3267,f2156]) ).

fof(f3267,plain,
    ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),
    inference(forward_demodulation,[],[f3266,f2154]) ).

fof(f3266,plain,
    ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),
    inference(forward_demodulation,[],[f3265,f2156]) ).

fof(f3265,plain,
    ! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3072,f3264]) ).

fof(f3072,plain,
    ! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1881,f2544,f2544]) ).

fof(f1881,axiom,
    ! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_Suc(c_Suc(X21)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).

fof(f19636,plain,
    ( spl0_1960
    | ~ spl0_1444
    | ~ spl0_1883 ),
    inference(avatar_split_clause,[],[f19186,f18930,f11266,f19634]) ).

fof(f19634,plain,
    ( spl0_1960
  <=> ! [X2,X0,X1] :
        ( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
        | c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).

fof(f19186,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X2,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
        | c_in(X2,c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) )
    | ~ spl0_1444
    | ~ spl0_1883 ),
    inference(superposition,[],[f11267,f18931]) ).

fof(f19632,plain,
    ( spl0_1959
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1958 ),
    inference(avatar_split_clause,[],[f19628,f19625,f11334,f10936,f7067,f6122,f19630]) ).

fof(f19630,plain,
    ( spl0_1959
  <=> ! [X47] :
        ( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).

fof(f19625,plain,
    ( spl0_1958
  <=> ! [X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).

fof(f19628,plain,
    ( ! [X47] :
        ( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1958 ),
    inference(forward_demodulation,[],[f19626,f12301]) ).

fof(f19626,plain,
    ( ! [X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
    | ~ spl0_1958 ),
    inference(avatar_component_clause,[],[f19625]) ).

fof(f19627,plain,
    spl0_1958,
    inference(avatar_split_clause,[],[f3153,f19625]) ).

fof(f3153,plain,
    ! [X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1823,f2544]) ).

fof(f1823,axiom,
    ! [X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).

fof(f19623,plain,
    spl0_1957,
    inference(avatar_split_clause,[],[f3077,f19621]) ).

fof(f19621,plain,
    ( spl0_1957
  <=> ! [X43,X0,X16,X1] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).

fof(f3077,plain,
    ! [X0,X1,X16,X43] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1),
    inference(definition_unfolding,[],[f1775,f1766]) ).

fof(f1775,axiom,
    ! [X0,X1,X16,X43] : c_List_Otake(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).

fof(f19619,plain,
    spl0_1956,
    inference(avatar_split_clause,[],[f3075,f19617]) ).

fof(f19617,plain,
    ( spl0_1956
  <=> ! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).

fof(f3075,plain,
    ! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)),
    inference(definition_unfolding,[],[f1611,f1766]) ).

fof(f1611,axiom,
    ! [X21,X1,X23] : c_Nat_Osize(c_List_Otake(X21,X23,X1),tc_List_Olist(X1)) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).

fof(f19615,plain,
    spl0_1955,
    inference(avatar_split_clause,[],[f3071,f19613]) ).

fof(f3071,plain,
    ! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1),
    inference(definition_unfolding,[],[f2623,f2373]) ).

fof(f2623,axiom,
    ! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_inter(X18,c_Inter(X13,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).

fof(f19610,plain,
    ( spl0_1954
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1953 ),
    inference(avatar_split_clause,[],[f19606,f19603,f11334,f10936,f7067,f6122,f19608]) ).

fof(f19608,plain,
    ( spl0_1954
  <=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).

fof(f19603,plain,
    ( spl0_1953
  <=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).

fof(f19606,plain,
    ( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1953 ),
    inference(forward_demodulation,[],[f19604,f12301]) ).

fof(f19604,plain,
    ( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
    | ~ spl0_1953 ),
    inference(avatar_component_clause,[],[f19603]) ).

fof(f19605,plain,
    spl0_1953,
    inference(avatar_split_clause,[],[f3070,f19603]) ).

fof(f3070,plain,
    ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1207,f2544]) ).

fof(f1207,axiom,
    ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).

fof(f19600,plain,
    ( spl0_1952
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1951 ),
    inference(avatar_split_clause,[],[f19588,f19585,f11334,f10936,f7067,f6122,f19598]) ).

fof(f19598,plain,
    ( spl0_1952
  <=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).

fof(f19585,plain,
    ( spl0_1951
  <=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).

fof(f19588,plain,
    ( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1951 ),
    inference(forward_demodulation,[],[f19586,f12301]) ).

fof(f19586,plain,
    ( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
    | ~ spl0_1951 ),
    inference(avatar_component_clause,[],[f19585]) ).

fof(f19587,plain,
    spl0_1951,
    inference(avatar_split_clause,[],[f3069,f19585]) ).

fof(f3069,plain,
    ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1206,f2544]) ).

fof(f1206,axiom,
    ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).

fof(f19582,plain,
    ( spl0_1950
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1949 ),
    inference(avatar_split_clause,[],[f19578,f19575,f11334,f10936,f7067,f6122,f19580]) ).

fof(f19580,plain,
    ( spl0_1950
  <=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).

fof(f19575,plain,
    ( spl0_1949
  <=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).

fof(f19578,plain,
    ( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1949 ),
    inference(forward_demodulation,[],[f19576,f12301]) ).

fof(f19576,plain,
    ( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
    | ~ spl0_1949 ),
    inference(avatar_component_clause,[],[f19575]) ).

fof(f19577,plain,
    spl0_1949,
    inference(avatar_split_clause,[],[f3068,f19575]) ).

fof(f3068,plain,
    ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1203,f2544]) ).

fof(f1203,axiom,
    ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).

fof(f19573,plain,
    spl0_1948,
    inference(avatar_split_clause,[],[f3056,f19571]) ).

fof(f19571,plain,
    ( spl0_1948
  <=> ! [X18,X5,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).

fof(f3056,plain,
    ! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)),
    inference(definition_unfolding,[],[f120,f2716]) ).

fof(f120,axiom,
    ! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

fof(f19569,plain,
    spl0_1947,
    inference(avatar_split_clause,[],[f3048,f19567]) ).

fof(f19567,plain,
    ( spl0_1947
  <=> ! [X5,X1] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).

fof(f3048,plain,
    ! [X1,X5] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
    inference(definition_unfolding,[],[f2708,f2716]) ).

fof(f2708,axiom,
    ! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).

fof(f19544,plain,
    ( spl0_1946
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1945 ),
    inference(avatar_split_clause,[],[f19540,f19537,f11334,f10936,f7067,f6122,f19542]) ).

fof(f19542,plain,
    ( spl0_1946
  <=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).

fof(f19537,plain,
    ( spl0_1945
  <=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).

fof(f19540,plain,
    ( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1945 ),
    inference(forward_demodulation,[],[f19538,f12301]) ).

fof(f19538,plain,
    ( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
    | ~ spl0_1945 ),
    inference(avatar_component_clause,[],[f19537]) ).

fof(f19539,plain,
    spl0_1945,
    inference(avatar_split_clause,[],[f3046,f19537]) ).

fof(f3046,plain,
    ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2027,f2544,f2544]) ).

fof(f2027,axiom,
    ! [X21,X15] : c_plus(X15,c_Suc(X21),tc_nat) = c_Suc(c_plus(X15,X21,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).

fof(f19454,plain,
    ( spl0_1944
    | ~ spl0_1071
    | ~ spl0_1882 ),
    inference(avatar_split_clause,[],[f19283,f18723,f8872,f19451]) ).

fof(f19451,plain,
    ( spl0_1944
  <=> c_List_Olist_ONil = c_List_Oupt(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).

fof(f19283,plain,
    ( c_List_Olist_ONil = c_List_Oupt(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)))
    | ~ spl0_1071
    | ~ spl0_1882 ),
    inference(resolution,[],[f18725,f8873]) ).

fof(f19449,plain,
    ( spl0_1943
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1942 ),
    inference(avatar_split_clause,[],[f19445,f19441,f11334,f10936,f7067,f6122,f19447]) ).

fof(f19447,plain,
    ( spl0_1943
  <=> ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).

fof(f19441,plain,
    ( spl0_1942
  <=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).

fof(f19445,plain,
    ( ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1942 ),
    inference(forward_demodulation,[],[f19444,f12301]) ).

fof(f19444,plain,
    ( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1942 ),
    inference(forward_demodulation,[],[f19442,f12301]) ).

fof(f19442,plain,
    ( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
    | ~ spl0_1942 ),
    inference(avatar_component_clause,[],[f19441]) ).

fof(f19443,plain,
    spl0_1942,
    inference(avatar_split_clause,[],[f3045,f19441]) ).

fof(f19417,plain,
    ( spl0_1941
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1940 ),
    inference(avatar_split_clause,[],[f19413,f19409,f11334,f10936,f7067,f6122,f19415]) ).

fof(f19415,plain,
    ( spl0_1941
  <=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).

fof(f19409,plain,
    ( spl0_1940
  <=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).

fof(f19413,plain,
    ( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1940 ),
    inference(forward_demodulation,[],[f19412,f12301]) ).

fof(f19412,plain,
    ( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1940 ),
    inference(forward_demodulation,[],[f19410,f12301]) ).

fof(f19410,plain,
    ( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
    | ~ spl0_1940 ),
    inference(avatar_component_clause,[],[f19409]) ).

fof(f19411,plain,
    spl0_1940,
    inference(avatar_split_clause,[],[f3044,f19409]) ).

fof(f3044,plain,
    ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2035,f2544,f2544]) ).

fof(f2035,axiom,
    ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Suc(X15),c_Suc(X21),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).

fof(f19407,plain,
    spl0_1939,
    inference(avatar_split_clause,[],[f2947,f19405]) ).

fof(f19405,plain,
    ( spl0_1939
  <=> ! [X102,X12,X114,X91,X22,X86] :
        ( c_Message_Oagent_OServer = X22
        | c_Yahalom_OKeyWithNonce(X91,X114,X102)
        | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(X22,X12,X86),X102,tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).

fof(f2947,axiom,
    ! [X91,X86,X114,X22,X102,X12] :
      ( c_Message_Oagent_OServer = X22
      | c_Yahalom_OKeyWithNonce(X91,X114,X102)
      | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(X22,X12,X86),X102,tc_Event_Oevent)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_0) ).

fof(f19403,plain,
    spl0_1938,
    inference(avatar_split_clause,[],[f2887,f19401]) ).

fof(f19401,plain,
    ( spl0_1938
  <=> ! [X87,X86,X88] :
        ( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
        | ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).

fof(f2887,axiom,
    ! [X88,X86,X87] :
      ( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
      | ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).

fof(f19399,plain,
    spl0_1937,
    inference(avatar_split_clause,[],[f2884,f19397]) ).

fof(f19397,plain,
    ( spl0_1937
  <=> ! [X86,X91,X88] :
        ( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
        | c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).

fof(f2884,axiom,
    ! [X91,X88,X86] :
      ( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
      | c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).

fof(f19395,plain,
    spl0_1936,
    inference(avatar_split_clause,[],[f2801,f19393]) ).

fof(f19393,plain,
    ( spl0_1936
  <=> ! [X102,X86,X12] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).

fof(f2801,axiom,
    ! [X86,X12,X102] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) = c_union(c_Message_Oparts(c_insert(X86,c_emptyset,tc_Message_Omsg)),c_Event_Oused(X102),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Notes_0) ).

fof(f19391,plain,
    spl0_1935,
    inference(avatar_split_clause,[],[f2792,f19389]) ).

fof(f19389,plain,
    ( spl0_1935
  <=> ! [X91,X88] :
        ( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
        | ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
        | c_Message_OinvKey(v_sko__uhi(X88,X91)) = X91 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).

fof(f2792,axiom,
    ! [X91,X88] :
      ( c_in(X91,c_Message_OkeysFor(X88),tc_nat)
      | ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
      | c_Message_OinvKey(v_sko__uhi(X88,X91)) = X91 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).

fof(f19376,plain,
    spl0_1934,
    inference(avatar_split_clause,[],[f2697,f19374]) ).

fof(f19374,plain,
    ( spl0_1934
  <=> ! [X12,X0,X1] :
        ( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
        | c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).

fof(f2697,axiom,
    ! [X0,X1,X12] :
      ( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
      | c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).

fof(f19372,plain,
    spl0_1933,
    inference(avatar_split_clause,[],[f2696,f19370]) ).

fof(f19370,plain,
    ( spl0_1933
  <=> ! [X12,X27,X1,X18] :
        ( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
        | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).

fof(f2696,axiom,
    ! [X1,X18,X27,X12] :
      ( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
      | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).

fof(f19368,plain,
    spl0_1932,
    inference(avatar_split_clause,[],[f2690,f19366]) ).

fof(f19366,plain,
    ( spl0_1932
  <=> ! [X13,X0,X12,X1] :
        ( ~ c_in(X0,X13,X1)
        | ~ c_lessequals(X12,X13,tc_set(X1))
        | c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).

fof(f2690,axiom,
    ! [X0,X1,X12,X13] :
      ( ~ c_in(X0,X13,X1)
      | ~ c_lessequals(X12,X13,tc_set(X1))
      | c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).

fof(f19364,plain,
    spl0_1931,
    inference(avatar_split_clause,[],[f2573,f19362]) ).

fof(f19362,plain,
    ( spl0_1931
  <=> ! [X16,X1] :
        ( ~ class_Orderings_Oorder(X1)
        | c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).

fof(f2573,axiom,
    ! [X1,X16] :
      ( ~ class_Orderings_Oorder(X1)
      | c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).

fof(f19360,plain,
    spl0_1930,
    inference(avatar_split_clause,[],[f2565,f19358]) ).

fof(f19358,plain,
    ( spl0_1930
  <=> ! [X15,X59,X43,X21,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_lessequals(X59,X43,X1)
        | c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).

fof(f2565,axiom,
    ! [X21,X59,X1,X15,X43] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_lessequals(X59,X43,X1)
      | c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).

fof(f19356,plain,
    spl0_1929,
    inference(avatar_split_clause,[],[f2556,f19354]) ).

fof(f19354,plain,
    ( spl0_1929
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_less(X26,X43,X1)
        | ~ c_less(X43,X14,X1)
        | c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).

fof(f2556,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_less(X26,X43,X1)
      | ~ c_less(X43,X14,X1)
      | c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).

fof(f19352,plain,
    spl0_1928,
    inference(avatar_split_clause,[],[f2553,f19350]) ).

fof(f19350,plain,
    ( spl0_1928
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_lessequals(X43,X14,X1)
        | ~ c_less(X26,X43,X1)
        | c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).

fof(f2553,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_lessequals(X43,X14,X1)
      | ~ c_less(X26,X43,X1)
      | c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).

fof(f19348,plain,
    spl0_1927,
    inference(avatar_split_clause,[],[f2526,f19346]) ).

fof(f19346,plain,
    ( spl0_1927
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_lessequals(X26,X43,X1)
        | ~ c_less(X43,X14,X1)
        | c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).

fof(f2526,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_lessequals(X26,X43,X1)
      | ~ c_less(X43,X14,X1)
      | c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).

fof(f19344,plain,
    spl0_1926,
    inference(avatar_split_clause,[],[f2521,f19342]) ).

fof(f19342,plain,
    ( spl0_1926
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_lessequals(X26,X43,X1)
        | ~ c_lessequals(X43,X14,X1)
        | c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).

fof(f2521,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_lessequals(X26,X43,X1)
      | ~ c_lessequals(X43,X14,X1)
      | c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).

fof(f19340,plain,
    spl0_1925,
    inference(avatar_split_clause,[],[f2324,f19338]) ).

fof(f19338,plain,
    ( spl0_1925
  <=> ! [X11,X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(X0,c_0,X1)
        | ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).

fof(f2324,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(X0,c_0,X1)
      | ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).

fof(f19336,plain,
    ( spl0_1924
    | ~ spl0_1492
    | ~ spl0_1882 ),
    inference(avatar_split_clause,[],[f19288,f18723,f12470,f19333]) ).

fof(f19333,plain,
    ( spl0_1924
  <=> c_List_Olist_ONil = c_List_Odrop(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).

fof(f12470,plain,
    ( spl0_1492
  <=> ! [X21,X1,X23] :
        ( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
        | ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).

fof(f19288,plain,
    ( c_List_Olist_ONil = c_List_Odrop(c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_List_Oremdups(v_evso,tc_Event_Oevent),tc_Event_Oevent)
    | ~ spl0_1492
    | ~ spl0_1882 ),
    inference(resolution,[],[f18725,f12471]) ).

fof(f12471,plain,
    ( ! [X21,X1,X23] :
        ( ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat)
        | c_List_Olist_ONil = c_List_Odrop(X21,X23,X1) )
    | ~ spl0_1492 ),
    inference(avatar_component_clause,[],[f12470]) ).

fof(f19331,plain,
    spl0_1923,
    inference(avatar_split_clause,[],[f2307,f19329]) ).

fof(f19329,plain,
    ( spl0_1923
  <=> ! [X0,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Power_Orecpower(X1)
        | c_Parity_Oeven(X0,tc_nat)
        | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).

fof(f2307,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Power_Orecpower(X1)
      | c_Parity_Oeven(X0,tc_nat)
      | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).

fof(f19327,plain,
    spl0_1922,
    inference(avatar_split_clause,[],[f2305,f19325]) ).

fof(f19325,plain,
    ( spl0_1922
  <=> ! [X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_Parity_Oeven(X0,tc_nat)
        | c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).

fof(f2305,axiom,
    ! [X0,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_Parity_Oeven(X0,tc_nat)
      | c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).

fof(f19323,plain,
    spl0_1921,
    inference(avatar_split_clause,[],[f2266,f19321]) ).

fof(f19321,plain,
    ( spl0_1921
  <=> ! [X48,X0,X3,X2] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_lessequals(X0,X48,X2)
        | ~ c_lessequals(X3,X48,X2)
        | c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).

fof(f2266,axiom,
    ! [X2,X3,X48,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_lessequals(X0,X48,X2)
      | ~ c_lessequals(X3,X48,X2)
      | c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).

fof(f19319,plain,
    spl0_1920,
    inference(avatar_split_clause,[],[f2261,f19317]) ).

fof(f19317,plain,
    ( spl0_1920
  <=> ! [X48,X0,X3,X2] :
        ( ~ class_Orderings_Olinorder(X2)
        | ~ c_lessequals(X0,X3,X2)
        | ~ c_lessequals(X0,X48,X2)
        | c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).

fof(f2261,axiom,
    ! [X2,X3,X48,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | ~ c_lessequals(X0,X3,X2)
      | ~ c_lessequals(X0,X48,X2)
      | c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).

fof(f19315,plain,
    spl0_1919,
    inference(avatar_split_clause,[],[f2258,f19313]) ).

fof(f19313,plain,
    ( spl0_1919
  <=> ! [X48,X0,X3,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_less(X48,X0,X1)
        | ~ c_less(X48,X3,X1)
        | c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).

fof(f2258,axiom,
    ! [X3,X48,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_less(X48,X0,X1)
      | ~ c_less(X48,X3,X1)
      | c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).

fof(f19311,plain,
    spl0_1918,
    inference(avatar_split_clause,[],[f2255,f19309]) ).

fof(f19309,plain,
    ( spl0_1918
  <=> ! [X48,X0,X3,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_less(X0,X48,X1)
        | ~ c_less(X3,X48,X1)
        | c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).

fof(f2255,axiom,
    ! [X3,X48,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_less(X0,X48,X1)
      | ~ c_less(X3,X48,X1)
      | c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).

fof(f19307,plain,
    spl0_1917,
    inference(avatar_split_clause,[],[f2237,f19305]) ).

fof(f19305,plain,
    ( spl0_1917
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).

fof(f2237,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).

fof(f19303,plain,
    spl0_1916,
    inference(avatar_split_clause,[],[f2228,f19301]) ).

fof(f19301,plain,
    ( spl0_1916
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).

fof(f2228,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).

fof(f19299,plain,
    spl0_1915,
    inference(avatar_split_clause,[],[f2214,f19297]) ).

fof(f2214,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).

fof(f19295,plain,
    spl0_1914,
    inference(avatar_split_clause,[],[f1843,f19293]) ).

fof(f19293,plain,
    ( spl0_1914
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).

fof(f1843,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).

fof(f19278,plain,
    spl0_1913,
    inference(avatar_split_clause,[],[f1836,f19276]) ).

fof(f19276,plain,
    ( spl0_1913
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).

fof(f1836,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).

fof(f19274,plain,
    spl0_1912,
    inference(avatar_split_clause,[],[f1824,f19272]) ).

fof(f19272,plain,
    ( spl0_1912
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).

fof(f1824,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).

fof(f19270,plain,
    spl0_1911,
    inference(avatar_split_clause,[],[f1821,f19268]) ).

fof(f19268,plain,
    ( spl0_1911
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).

fof(f1821,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).

fof(f19266,plain,
    spl0_1910,
    inference(avatar_split_clause,[],[f1809,f19264]) ).

fof(f19264,plain,
    ( spl0_1910
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).

fof(f1809,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).

fof(f19262,plain,
    spl0_1909,
    inference(avatar_split_clause,[],[f1781,f19260]) ).

fof(f19260,plain,
    ( spl0_1909
  <=> ! [X21,X1,X0] :
        ( c_0 = X21
        | c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).

fof(f1781,axiom,
    ! [X21,X0,X1] :
      ( c_0 = X21
      | c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).

fof(f19258,plain,
    spl0_1908,
    inference(avatar_split_clause,[],[f1699,f19256]) ).

fof(f19256,plain,
    ( spl0_1908
  <=> ! [X43,X23,X3,X1] :
        ( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
        | c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).

fof(f1699,axiom,
    ! [X3,X1,X23,X43] :
      ( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
      | c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).

fof(f19254,plain,
    spl0_1907,
    inference(avatar_split_clause,[],[f1633,f19252]) ).

fof(f19252,plain,
    ( spl0_1907
  <=> ! [X1,X43,X3] :
        ( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
        | c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).

fof(f1633,axiom,
    ! [X3,X1,X43] :
      ( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
      | c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).

fof(f19250,plain,
    spl0_1906,
    inference(avatar_split_clause,[],[f1592,f19248]) ).

fof(f19248,plain,
    ( spl0_1906
  <=> ! [X21,X1,X23] :
        ( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
        | c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).

fof(f1592,axiom,
    ! [X21,X1,X23] :
      ( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
      | c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).

fof(f19246,plain,
    spl0_1905,
    inference(avatar_split_clause,[],[f1525,f19244]) ).

fof(f19244,plain,
    ( spl0_1905
  <=> ! [X12,X1,X23,X25] :
        ( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).

fof(f1525,axiom,
    ! [X1,X25,X12,X23] :
      ( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).

fof(f19242,plain,
    spl0_1904,
    inference(avatar_split_clause,[],[f1524,f19240]) ).

fof(f19240,plain,
    ( spl0_1904
  <=> ! [X23,X12,X25,X1] :
        ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).

fof(f1524,axiom,
    ! [X1,X12,X23,X25] :
      ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).

fof(f19229,plain,
    spl0_1903,
    inference(avatar_split_clause,[],[f1417,f19227]) ).

fof(f19227,plain,
    ( spl0_1903
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).

fof(f1417,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).

fof(f19225,plain,
    spl0_1902,
    inference(avatar_split_clause,[],[f1403,f19223]) ).

fof(f19223,plain,
    ( spl0_1902
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).

fof(f1403,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).

fof(f19221,plain,
    spl0_1901,
    inference(avatar_split_clause,[],[f1402,f19219]) ).

fof(f19219,plain,
    ( spl0_1901
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).

fof(f1402,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).

fof(f19217,plain,
    spl0_1900,
    inference(avatar_split_clause,[],[f1366,f19215]) ).

fof(f19215,plain,
    ( spl0_1900
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | ~ c_in(X18,c_IntDef_ONats,X1)
        | ~ c_in(X27,c_IntDef_ONats,X1)
        | c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).

fof(f1366,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | ~ c_in(X18,c_IntDef_ONats,X1)
      | ~ c_in(X27,c_IntDef_ONats,X1)
      | c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).

fof(f19213,plain,
    spl0_1899,
    inference(avatar_split_clause,[],[f1365,f19211]) ).

fof(f19211,plain,
    ( spl0_1899
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | ~ c_in(X18,c_IntDef_ONats,X1)
        | ~ c_in(X27,c_IntDef_ONats,X1)
        | c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).

fof(f1365,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | ~ c_in(X18,c_IntDef_ONats,X1)
      | ~ c_in(X27,c_IntDef_ONats,X1)
      | c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).

fof(f19209,plain,
    spl0_1898,
    inference(avatar_split_clause,[],[f1362,f19207]) ).

fof(f19207,plain,
    ( spl0_1898
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_in(X18,c_IntDef_OInts,X1)
        | ~ c_in(X27,c_IntDef_OInts,X1)
        | c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).

fof(f1362,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | ~ c_in(X18,c_IntDef_OInts,X1)
      | ~ c_in(X27,c_IntDef_OInts,X1)
      | c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).

fof(f19205,plain,
    spl0_1897,
    inference(avatar_split_clause,[],[f1360,f19203]) ).

fof(f19203,plain,
    ( spl0_1897
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_in(X18,c_IntDef_OInts,X1)
        | ~ c_in(X27,c_IntDef_OInts,X1)
        | c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).

fof(f1360,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | ~ c_in(X18,c_IntDef_OInts,X1)
      | ~ c_in(X27,c_IntDef_OInts,X1)
      | c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).

fof(f19201,plain,
    spl0_1896,
    inference(avatar_split_clause,[],[f1359,f19199]) ).

fof(f19199,plain,
    ( spl0_1896
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_in(X18,c_IntDef_OInts,X1)
        | ~ c_in(X27,c_IntDef_OInts,X1)
        | c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).

fof(f1359,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | ~ c_in(X18,c_IntDef_OInts,X1)
      | ~ c_in(X27,c_IntDef_OInts,X1)
      | c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).

fof(f19197,plain,
    spl0_1895,
    inference(avatar_split_clause,[],[f1306,f19195]) ).

fof(f19195,plain,
    ( spl0_1895
  <=> ! [X21,X16,X15] :
        ( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
        | ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
        | c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).

fof(f1306,axiom,
    ! [X21,X16,X15] :
      ( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
      | ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
      | c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).

fof(f19193,plain,
    spl0_1894,
    inference(avatar_split_clause,[],[f1290,f19191]) ).

fof(f19191,plain,
    ( spl0_1894
  <=> ! [X2,X5,X1] :
        ( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
        | c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).

fof(f1290,axiom,
    ! [X2,X1,X5] :
      ( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
      | c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).

fof(f19180,plain,
    spl0_1893,
    inference(avatar_split_clause,[],[f1289,f19178]) ).

fof(f19178,plain,
    ( spl0_1893
  <=> ! [X2,X5,X1] :
        ( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
        | ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).

fof(f1289,axiom,
    ! [X2,X1,X5] :
      ( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
      | ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).

fof(f19176,plain,
    spl0_1892,
    inference(avatar_split_clause,[],[f114,f19174]) ).

fof(f19174,plain,
    ( spl0_1892
  <=> ! [X13,X12,X27,X2,X1] :
        ( ~ c_in(X27,X13,X1)
        | c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).

fof(f114,axiom,
    ! [X2,X1,X27,X12,X13] :
      ( ~ c_in(X27,X13,X1)
      | c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).

fof(f19172,plain,
    spl0_1891,
    inference(avatar_split_clause,[],[f113,f19170]) ).

fof(f19170,plain,
    ( spl0_1891
  <=> ! [X18,X13,X12,X2,X1] :
        ( ~ c_in(X18,X12,X1)
        | c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).

fof(f113,axiom,
    ! [X2,X18,X1,X12,X13] :
      ( ~ c_in(X18,X12,X1)
      | c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).

fof(f19168,plain,
    spl0_1890,
    inference(avatar_split_clause,[],[f76,f19166]) ).

fof(f76,axiom,
    ! [X2,X1,X18,X27,X5] :
      ( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
      | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).

fof(f19164,plain,
    spl0_1889,
    inference(avatar_split_clause,[],[f72,f19162]) ).

fof(f19162,plain,
    ( spl0_1889
  <=> ! [X12,X5,X27,X2,X1] :
        ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
        | c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).

fof(f72,axiom,
    ! [X2,X1,X27,X5,X12] :
      ( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
      | c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).

fof(f19160,plain,
    spl0_1888,
    inference(avatar_split_clause,[],[f71,f19158]) ).

fof(f19158,plain,
    ( spl0_1888
  <=> ! [X1,X28] :
        ( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
        | c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).

fof(f71,axiom,
    ! [X28,X1] :
      ( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
      | c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).

fof(f19156,plain,
    spl0_1887,
    inference(avatar_split_clause,[],[f70,f19154]) ).

fof(f70,axiom,
    ! [X2,X18,X1,X27,X5] :
      ( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
      | ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).

fof(f19152,plain,
    spl0_1886,
    inference(avatar_split_clause,[],[f58,f19150]) ).

fof(f19150,plain,
    ( spl0_1886
  <=> ! [X12,X0,X1,X26] :
        ( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).

fof(f58,axiom,
    ! [X0,X1,X26,X12] :
      ( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

fof(f19148,plain,
    spl0_1885,
    inference(avatar_split_clause,[],[f46,f19146]) ).

fof(f19146,plain,
    ( spl0_1885
  <=> ! [X24,X23,X12,X1] :
        ( c_in(X24,X12,X1)
        | ~ c_in(X24,c_List_Oset(X23,X1),X1)
        | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).

fof(f46,axiom,
    ! [X1,X24,X12,X23] :
      ( c_in(X24,X12,X1)
      | ~ c_in(X24,c_List_Oset(X23,X1),X1)
      | ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

fof(f19130,plain,
    ( spl0_1884
    | spl0_3
    | ~ spl0_1837 ),
    inference(avatar_split_clause,[],[f18901,f17310,f3444,f19128]) ).

fof(f17310,plain,
    ( spl0_1837
  <=> ! [X102,X86,X12] :
        ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).

fof(f18901,plain,
    ( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_B,X1),X0,tc_Event_Oevent))
    | spl0_3
    | ~ spl0_1837 ),
    inference(resolution,[],[f17311,f3446]) ).

fof(f17311,plain,
    ( ! [X86,X12,X102] :
        ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) )
    | ~ spl0_1837 ),
    inference(avatar_component_clause,[],[f17310]) ).

fof(f18932,plain,
    ( spl0_1883
    | spl0_2
    | ~ spl0_1837 ),
    inference(avatar_split_clause,[],[f18900,f17310,f3439,f18930]) ).

fof(f18900,plain,
    ( ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X1),X0,tc_Event_Oevent))
    | spl0_2
    | ~ spl0_1837 ),
    inference(resolution,[],[f17311,f3441]) ).

fof(f18726,plain,
    ( spl0_1882
    | ~ spl0_1060
    | ~ spl0_1328
    | ~ spl0_1765
    | ~ spl0_1854
    | ~ spl0_1881 ),
    inference(avatar_split_clause,[],[f18414,f18322,f17663,f16011,f10753,f8828,f18723]) ).

fof(f8828,plain,
    ( spl0_1060
  <=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f10753,plain,
    ( spl0_1328
  <=> ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).

fof(f16011,plain,
    ( spl0_1765
  <=> ! [X18,X64,X1] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).

fof(f18322,plain,
    ( spl0_1881
  <=> c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evso,tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).

fof(f18414,plain,
    ( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
    | ~ spl0_1060
    | ~ spl0_1328
    | ~ spl0_1765
    | ~ spl0_1854
    | ~ spl0_1881 ),
    inference(forward_demodulation,[],[f18413,f17698]) ).

fof(f17698,plain,
    ( ! [X1] : c_plus(X1,c_1,tc_nat) = c_plus(c_1,X1,tc_nat)
    | ~ spl0_1060
    | ~ spl0_1765
    | ~ spl0_1854 ),
    inference(forward_demodulation,[],[f17697,f8829]) ).

fof(f8829,plain,
    ( ! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3
    | ~ spl0_1060 ),
    inference(avatar_component_clause,[],[f8828]) ).

fof(f17697,plain,
    ( ! [X2,X0,X1] : c_plus(c_1,X1,tc_nat) = c_plus(c_Nat_Osize(c_List_Oreplicate(X1,X0,X2),tc_List_Olist(X2)),c_1,tc_nat)
    | ~ spl0_1060
    | ~ spl0_1765
    | ~ spl0_1854 ),
    inference(forward_demodulation,[],[f17686,f8829]) ).

fof(f17686,plain,
    ( ! [X2,X0,X1] : c_plus(c_Nat_Osize(c_List_Oreplicate(X1,X0,X2),tc_List_Olist(X2)),c_1,tc_nat) = c_Nat_Osize(c_List_Oreplicate(c_plus(c_1,X1,tc_nat),X0,X2),tc_List_Olist(X2))
    | ~ spl0_1765
    | ~ spl0_1854 ),
    inference(superposition,[],[f16012,f17664]) ).

fof(f16012,plain,
    ( ! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat)
    | ~ spl0_1765 ),
    inference(avatar_component_clause,[],[f16011]) ).

fof(f18413,plain,
    ( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_Nat_Osize(v_evso,tc_List_Olist(tc_Event_Oevent)),c_1,tc_nat),tc_nat)
    | ~ spl0_1328
    | ~ spl0_1765
    | ~ spl0_1881 ),
    inference(forward_demodulation,[],[f18409,f16012]) ).

fof(f18409,plain,
    ( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),v_evso,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat)
    | ~ spl0_1328
    | ~ spl0_1881 ),
    inference(superposition,[],[f10754,f18324]) ).

fof(f18324,plain,
    ( c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evso,tc_Event_Oevent)
    | ~ spl0_1881 ),
    inference(avatar_component_clause,[],[f18322]) ).

fof(f10754,plain,
    ( ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
    | ~ spl0_1328 ),
    inference(avatar_component_clause,[],[f10753]) ).

fof(f18325,plain,
    ( spl0_1881
    | ~ spl0_749
    | ~ spl0_1799 ),
    inference(avatar_split_clause,[],[f18182,f17104,f7355,f18322]) ).

fof(f18182,plain,
    ( c_List_Oremdups(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),v_evso,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evso,tc_Event_Oevent)
    | ~ spl0_749
    | ~ spl0_1799 ),
    inference(resolution,[],[f17105,f7357]) ).

fof(f18142,plain,
    ( spl0_1880
    | ~ spl0_797
    | ~ spl0_1180 ),
    inference(avatar_split_clause,[],[f9893,f9527,f7550,f18140]) ).

fof(f18140,plain,
    ( spl0_1880
  <=> ! [X0] :
        ( c_0 != X0
        | c_lessequals(X0,c_0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).

fof(f7550,plain,
    ( spl0_797
  <=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f9527,plain,
    ( spl0_1180
  <=> ! [X21,X15] :
        ( c_lessequals(X15,X21,tc_nat)
        | c_0 != c_minus(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).

fof(f9893,plain,
    ( ! [X0] :
        ( c_0 != X0
        | c_lessequals(X0,c_0,tc_nat) )
    | ~ spl0_797
    | ~ spl0_1180 ),
    inference(superposition,[],[f9528,f7551]) ).

fof(f7551,plain,
    ( ! [X3] : c_minus(X3,c_0,tc_nat) = X3
    | ~ spl0_797 ),
    inference(avatar_component_clause,[],[f7550]) ).

fof(f9528,plain,
    ( ! [X21,X15] :
        ( c_0 != c_minus(X15,X21,tc_nat)
        | c_lessequals(X15,X21,tc_nat) )
    | ~ spl0_1180 ),
    inference(avatar_component_clause,[],[f9527]) ).

fof(f18013,plain,
    ( spl0_1879
    | ~ spl0_1019
    | ~ spl0_1103 ),
    inference(avatar_split_clause,[],[f9296,f9000,f8532,f18011]) ).

fof(f18011,plain,
    ( spl0_1879
  <=> ! [X0,X1] : ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oknows(X1,c_List_Olist_ONil),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).

fof(f8532,plain,
    ( spl0_1019
  <=> ! [X13,X7] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_Oknows(X13,c_List_Olist_ONil)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f9000,plain,
    ( spl0_1103
  <=> ! [X86,X88] :
        ( ~ c_in(X86,X88,tc_Message_Omsg)
        | c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f9296,plain,
    ( ! [X0,X1] : ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oknows(X1,c_List_Olist_ONil),tc_Message_Omsg)
    | ~ spl0_1019
    | ~ spl0_1103 ),
    inference(resolution,[],[f9001,f8533]) ).

fof(f8533,plain,
    ( ! [X7,X13] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_Oknows(X13,c_List_Olist_ONil)),tc_Message_Omsg)
    | ~ spl0_1019 ),
    inference(avatar_component_clause,[],[f8532]) ).

fof(f9001,plain,
    ( ! [X88,X86] :
        ( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
        | ~ c_in(X86,X88,tc_Message_Omsg) )
    | ~ spl0_1103 ),
    inference(avatar_component_clause,[],[f9000]) ).

fof(f17868,plain,
    ( spl0_1876
    | spl0_1878 ),
    inference(avatar_split_clause,[],[f3432,f17866,f17845]) ).

fof(f17845,plain,
    ( spl0_1876
  <=> ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).

fof(f17866,plain,
    ( spl0_1878
  <=> ! [X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).

fof(f3432,plain,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 != c_Numeral_Onumber__of(X11,tc_nat)
      | c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1) ),
    inference(inner_rewriting,[],[f2334]) ).

fof(f2334,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 != c_Numeral_Onumber__of(X11,tc_nat)
      | c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).

fof(f17854,plain,
    ( ~ spl0_715
    | ~ spl0_1876 ),
    inference(avatar_contradiction_clause,[],[f17853]) ).

fof(f17853,plain,
    ( $false
    | ~ spl0_715
    | ~ spl0_1876 ),
    inference(trivial_inequality_removal,[],[f17851]) ).

fof(f17851,plain,
    ( c_0 != c_0
    | ~ spl0_715
    | ~ spl0_1876 ),
    inference(superposition,[],[f17846,f7197]) ).

fof(f7197,plain,
    ( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
    | ~ spl0_715 ),
    inference(avatar_component_clause,[],[f7195]) ).

fof(f7195,plain,
    ( spl0_715
  <=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f17846,plain,
    ( ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat)
    | ~ spl0_1876 ),
    inference(avatar_component_clause,[],[f17845]) ).

fof(f17850,plain,
    ( spl0_1876
    | spl0_1877 ),
    inference(avatar_split_clause,[],[f3431,f17848,f17845]) ).

fof(f17848,plain,
    ( spl0_1877
  <=> ! [X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).

fof(f3431,plain,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 != c_Numeral_Onumber__of(X11,tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1) ),
    inference(inner_rewriting,[],[f2317]) ).

fof(f2317,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 != c_Numeral_Onumber__of(X11,tc_nat)
      | ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).

fof(f17817,plain,
    ( spl0_1875
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_787
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1760
    | ~ spl0_1874 ),
    inference(avatar_split_clause,[],[f17813,f17809,f15960,f11334,f10936,f7510,f7067,f6122,f17815]) ).

fof(f17815,plain,
    ( spl0_1875
  <=> ! [X3] :
        ( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
        | ~ c_less(c_0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).

fof(f17809,plain,
    ( spl0_1874
  <=> ! [X3] :
        ( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
        | ~ c_less(c_0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).

fof(f17813,plain,
    ( ! [X3] :
        ( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
        | ~ c_less(c_0,X3,tc_nat) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_787
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1760
    | ~ spl0_1874 ),
    inference(forward_demodulation,[],[f17812,f15963]) ).

fof(f15963,plain,
    ( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
    | ~ spl0_787
    | ~ spl0_1760 ),
    inference(superposition,[],[f15961,f7511]) ).

fof(f17812,plain,
    ( ! [X3] :
        ( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat) = X3
        | ~ c_less(c_0,X3,tc_nat) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1874 ),
    inference(forward_demodulation,[],[f17810,f12301]) ).

fof(f17810,plain,
    ( ! [X3] :
        ( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
        | ~ c_less(c_0,X3,tc_nat) )
    | ~ spl0_1874 ),
    inference(avatar_component_clause,[],[f17809]) ).

fof(f17811,plain,
    spl0_1874,
    inference(avatar_split_clause,[],[f3321,f17809]) ).

fof(f3321,plain,
    ! [X3] :
      ( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
      | ~ c_less(c_0,X3,tc_nat) ),
    inference(forward_demodulation,[],[f3126,f3051]) ).

fof(f3126,plain,
    ! [X3] :
      ( ~ c_less(c_0,X3,tc_nat)
      | c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X3 ),
    inference(definition_unfolding,[],[f2024,f2544,f2544]) ).

fof(f2024,axiom,
    ! [X3] :
      ( ~ c_less(c_0,X3,tc_nat)
      | c_Suc(c_minus(X3,c_Suc(c_0),tc_nat)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).

fof(f17807,plain,
    spl0_1873,
    inference(avatar_split_clause,[],[f3156,f17805]) ).

fof(f17805,plain,
    ( spl0_1873
  <=> ! [X13,X12,X32,X1] :
        ( c_lessequals(X32,X13,tc_set(X1))
        | ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).

fof(f3156,plain,
    ! [X1,X12,X32,X13] :
      ( c_lessequals(X32,X13,tc_set(X1))
      | ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
    inference(definition_unfolding,[],[f2610,f2373]) ).

fof(f2610,axiom,
    ! [X1,X12,X32,X13] :
      ( c_lessequals(X32,X13,tc_set(X1))
      | ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).

fof(f17803,plain,
    spl0_1872,
    inference(avatar_split_clause,[],[f3155,f17801]) ).

fof(f17801,plain,
    ( spl0_1872
  <=> ! [X13,X12,X32,X1] :
        ( c_lessequals(X32,X12,tc_set(X1))
        | ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).

fof(f3155,plain,
    ! [X1,X12,X32,X13] :
      ( c_lessequals(X32,X12,tc_set(X1))
      | ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
    inference(definition_unfolding,[],[f2609,f2373]) ).

fof(f2609,axiom,
    ! [X1,X12,X32,X13] :
      ( c_lessequals(X32,X12,tc_set(X1))
      | ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).

fof(f17799,plain,
    spl0_1871,
    inference(avatar_split_clause,[],[f3151,f17797]) ).

fof(f17797,plain,
    ( spl0_1871
  <=> ! [X20,X1,X19] :
        ( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).

fof(f3151,plain,
    ! [X1,X19,X20] :
      ( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    inference(definition_unfolding,[],[f30,f2373]) ).

fof(f30,axiom,
    ! [X1,X19,X20] :
      ( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).

fof(f17795,plain,
    spl0_1870,
    inference(avatar_split_clause,[],[f3150,f17793]) ).

fof(f17793,plain,
    ( spl0_1870
  <=> ! [X20,X1,X19] :
        ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).

fof(f3150,plain,
    ! [X1,X19,X20] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    inference(definition_unfolding,[],[f31,f2373]) ).

fof(f31,axiom,
    ! [X1,X19,X20] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

fof(f17789,plain,
    spl0_1869,
    inference(avatar_split_clause,[],[f3144,f17787]) ).

fof(f17787,plain,
    ( spl0_1869
  <=> ! [X21,X15] :
        ( c_less(X15,X21,tc_nat)
        | ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).

fof(f3144,plain,
    ! [X21,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2021,f2544,f2544]) ).

fof(f2021,axiom,
    ! [X21,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).

fof(f17783,plain,
    spl0_1868,
    inference(avatar_split_clause,[],[f3142,f17781]) ).

fof(f17781,plain,
    ( spl0_1868
  <=> ! [X21,X15] :
        ( c_lessequals(X21,X15,tc_nat)
        | ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).

fof(f3142,plain,
    ! [X21,X15] :
      ( c_lessequals(X21,X15,tc_nat)
      | ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2019,f2544,f2544]) ).

fof(f2019,axiom,
    ! [X21,X15] :
      ( c_lessequals(X21,X15,tc_nat)
      | ~ c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).

fof(f17779,plain,
    ( spl0_1867
    | ~ spl0_895
    | ~ spl0_1089 ),
    inference(avatar_split_clause,[],[f9271,f8944,f7956,f17777]) ).

fof(f17777,plain,
    ( spl0_1867
  <=> ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).

fof(f7956,plain,
    ( spl0_895
  <=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).

fof(f9271,plain,
    ( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
    | ~ spl0_895
    | ~ spl0_1089 ),
    inference(superposition,[],[f7957,f8945]) ).

fof(f7957,plain,
    ( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
    | ~ spl0_895 ),
    inference(avatar_component_clause,[],[f7956]) ).

fof(f17773,plain,
    spl0_1866,
    inference(avatar_split_clause,[],[f3136,f17771]) ).

fof(f17771,plain,
    ( spl0_1866
  <=> ! [X21,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).

fof(f3136,plain,
    ! [X21,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2022,f2544,f2544]) ).

fof(f2022,axiom,
    ! [X21,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).

fof(f17767,plain,
    spl0_1865,
    inference(avatar_split_clause,[],[f3132,f17765]) ).

fof(f17765,plain,
    ( spl0_1865
  <=> ! [X21,X15] :
        ( ~ c_lessequals(X21,X15,tc_nat)
        | c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).

fof(f3132,plain,
    ! [X21,X15] :
      ( ~ c_lessequals(X21,X15,tc_nat)
      | c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2020,f2544,f2544]) ).

fof(f2020,axiom,
    ! [X21,X15] :
      ( ~ c_lessequals(X21,X15,tc_nat)
      | c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).

fof(f17763,plain,
    spl0_1864,
    inference(avatar_split_clause,[],[f3130,f17761]) ).

fof(f3130,plain,
    ! [X18,X1,X12,X13] :
      ( ~ c_in(X18,X13,X1)
      | c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
    inference(definition_unfolding,[],[f2677,f2373]) ).

fof(f2677,axiom,
    ! [X18,X1,X12,X13] :
      ( ~ c_in(X18,X13,X1)
      | c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).

fof(f17759,plain,
    spl0_1863,
    inference(avatar_split_clause,[],[f3128,f17757]) ).

fof(f17757,plain,
    ( spl0_1863
  <=> ! [X13,X12,X27,X1] :
        ( ~ c_in(X27,X12,X1)
        | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).

fof(f3128,plain,
    ! [X1,X27,X12,X13] :
      ( ~ c_in(X27,X12,X1)
      | c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ),
    inference(definition_unfolding,[],[f2664,f2373]) ).

fof(f2664,axiom,
    ! [X1,X27,X12,X13] :
      ( ~ c_in(X27,X12,X1)
      | c_emptyset != c_inter(X12,c_insert(X27,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).

fof(f17755,plain,
    spl0_1862,
    inference(avatar_split_clause,[],[f3112,f17753]) ).

fof(f17753,plain,
    ( spl0_1862
  <=> ! [X107,X108,X87,X86] :
        ( X86 = X107
        | c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X107,X108)),X108) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).

fof(f3112,plain,
    ! [X108,X86,X87,X107] :
      ( X86 = X107
      | c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X107,X108)),X108) ),
    inference(definition_unfolding,[],[f2808,f2812,f2812]) ).

fof(f2808,axiom,
    ! [X108,X86,X87,X107] :
      ( X86 = X107
      | c_Message_OHPair(X107,X108) != c_Message_OHPair(X86,X87) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_0) ).

fof(f17747,plain,
    ( spl0_1861
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1860 ),
    inference(avatar_split_clause,[],[f17743,f17740,f11334,f10936,f7067,f6122,f17745]) ).

fof(f17745,plain,
    ( spl0_1861
  <=> ! [X41,X15] :
        ( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
        | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).

fof(f17740,plain,
    ( spl0_1860
  <=> ! [X41,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
        | c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).

fof(f17743,plain,
    ( ! [X41,X15] :
        ( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
        | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1860 ),
    inference(forward_demodulation,[],[f17741,f12301]) ).

fof(f17741,plain,
    ( ! [X41,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
        | c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) )
    | ~ spl0_1860 ),
    inference(avatar_component_clause,[],[f17740]) ).

fof(f17742,plain,
    spl0_1860,
    inference(avatar_split_clause,[],[f3108,f17740]) ).

fof(f3108,plain,
    ! [X41,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ),
    inference(definition_unfolding,[],[f1802,f2544]) ).

fof(f1802,axiom,
    ! [X41,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
      | c_NatArith_Oof__nat(c_Suc(X15),X41) = c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).

fof(f17734,plain,
    ( spl0_1859
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1857 ),
    inference(avatar_split_clause,[],[f17726,f17723,f11334,f10936,f7067,f6122,f17732]) ).

fof(f17732,plain,
    ( spl0_1859
  <=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).

fof(f17723,plain,
    ( spl0_1857
  <=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).

fof(f17726,plain,
    ( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1857 ),
    inference(forward_demodulation,[],[f17724,f12301]) ).

fof(f17724,plain,
    ( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1)
    | ~ spl0_1857 ),
    inference(avatar_component_clause,[],[f17723]) ).

fof(f17730,plain,
    ( spl0_1858
    | ~ spl0_14
    | ~ spl0_1078 ),
    inference(avatar_split_clause,[],[f9258,f8900,f3499,f17728]) ).

fof(f17728,plain,
    ( spl0_1858
  <=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).

fof(f8900,plain,
    ( spl0_1078
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f9258,plain,
    ( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
    | ~ spl0_14
    | ~ spl0_1078 ),
    inference(resolution,[],[f8901,f3501]) ).

fof(f8901,plain,
    ( ! [X3,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_uminus(c_uminus(X3,X1),X1) = X3 )
    | ~ spl0_1078 ),
    inference(avatar_component_clause,[],[f8900]) ).

fof(f17725,plain,
    spl0_1857,
    inference(avatar_split_clause,[],[f3065,f17723]) ).

fof(f3065,plain,
    ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1),
    inference(definition_unfolding,[],[f1693,f2544]) ).

fof(f1693,axiom,
    ! [X21,X0,X1,X23] : c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Suc(X21),X1) = c_List_Onth(X23,X21,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).

fof(f17707,plain,
    ( spl0_1856
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1855 ),
    inference(avatar_split_clause,[],[f17703,f17700,f11334,f10936,f7067,f6122,f17705]) ).

fof(f17705,plain,
    ( spl0_1856
  <=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).

fof(f17700,plain,
    ( spl0_1855
  <=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).

fof(f17703,plain,
    ( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1855 ),
    inference(forward_demodulation,[],[f17701,f12301]) ).

fof(f17701,plain,
    ( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
    | ~ spl0_1855 ),
    inference(avatar_component_clause,[],[f17700]) ).

fof(f17702,plain,
    spl0_1855,
    inference(avatar_split_clause,[],[f3064,f17700]) ).

fof(f3064,plain,
    ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1),
    inference(definition_unfolding,[],[f1572,f2544]) ).

fof(f1572,axiom,
    ! [X21,X0,X1,X23] : c_List_Odrop(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(X21,X23,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).

fof(f17665,plain,
    ( spl0_1854
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1853 ),
    inference(avatar_split_clause,[],[f17661,f17658,f11334,f10936,f7067,f6122,f17663]) ).

fof(f17658,plain,
    ( spl0_1853
  <=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).

fof(f17661,plain,
    ( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1853 ),
    inference(forward_demodulation,[],[f17659,f12301]) ).

fof(f17659,plain,
    ( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41)
    | ~ spl0_1853 ),
    inference(avatar_component_clause,[],[f17658]) ).

fof(f17660,plain,
    spl0_1853,
    inference(avatar_split_clause,[],[f3062,f17658]) ).

fof(f3062,plain,
    ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41),
    inference(definition_unfolding,[],[f1723,f2544]) ).

fof(f1723,axiom,
    ! [X21,X41,X0] : c_List_Oreplicate(c_Suc(X21),X0,X41) = c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).

fof(f17561,plain,
    ( spl0_1852
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1851 ),
    inference(avatar_split_clause,[],[f17557,f17554,f11334,f10936,f7067,f6122,f17559]) ).

fof(f17559,plain,
    ( spl0_1852
  <=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).

fof(f17554,plain,
    ( spl0_1851
  <=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).

fof(f17557,plain,
    ( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1851 ),
    inference(forward_demodulation,[],[f17555,f12301]) ).

fof(f17555,plain,
    ( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
    | ~ spl0_1851 ),
    inference(avatar_component_clause,[],[f17554]) ).

fof(f17556,plain,
    spl0_1851,
    inference(avatar_split_clause,[],[f3061,f17554]) ).

fof(f3061,plain,
    ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
    inference(definition_unfolding,[],[f2099,f2544]) ).

fof(f2099,axiom,
    ! [X21,X15] : c_times(c_Suc(X15),X21,tc_nat) = c_plus(X21,c_times(X15,X21,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).

fof(f17552,plain,
    ( spl0_1850
    | ~ spl0_57
    | ~ spl0_1074 ),
    inference(avatar_split_clause,[],[f9250,f8884,f3714,f17549]) ).

fof(f8884,plain,
    ( spl0_1074
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f9250,plain,
    ( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
    | ~ spl0_57
    | ~ spl0_1074 ),
    inference(resolution,[],[f8885,f3716]) ).

fof(f8885,plain,
    ( ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
    | ~ spl0_1074 ),
    inference(avatar_component_clause,[],[f8884]) ).

fof(f17456,plain,
    ( spl0_1849
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1848 ),
    inference(avatar_split_clause,[],[f17452,f17449,f11334,f10936,f7067,f6122,f17454]) ).

fof(f17454,plain,
    ( spl0_1849
  <=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).

fof(f17449,plain,
    ( spl0_1848
  <=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).

fof(f17452,plain,
    ( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1848 ),
    inference(forward_demodulation,[],[f17450,f12301]) ).

fof(f17450,plain,
    ( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
    | ~ spl0_1848 ),
    inference(avatar_component_clause,[],[f17449]) ).

fof(f17451,plain,
    spl0_1848,
    inference(avatar_split_clause,[],[f3060,f17449]) ).

fof(f3060,plain,
    ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2057,f2544]) ).

fof(f2057,axiom,
    ! [X21,X15] : c_times(X15,c_Suc(X21),tc_nat) = c_plus(X15,c_times(X15,X21,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).

fof(f17393,plain,
    ( spl0_1847
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1846 ),
    inference(avatar_split_clause,[],[f17389,f17386,f11334,f10936,f7067,f6122,f17391]) ).

fof(f17391,plain,
    ( spl0_1847
  <=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).

fof(f17386,plain,
    ( spl0_1846
  <=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).

fof(f17389,plain,
    ( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1846 ),
    inference(forward_demodulation,[],[f17387,f12301]) ).

fof(f17387,plain,
    ( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
    | ~ spl0_1846 ),
    inference(avatar_component_clause,[],[f17386]) ).

fof(f17388,plain,
    spl0_1846,
    inference(avatar_split_clause,[],[f3059,f17386]) ).

fof(f3059,plain,
    ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2345,f2544]) ).

fof(f2345,axiom,
    ! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_nat) = c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).

fof(f17360,plain,
    ( spl0_1845
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1844 ),
    inference(avatar_split_clause,[],[f17356,f17353,f11334,f10936,f7067,f6122,f17358]) ).

fof(f17358,plain,
    ( spl0_1845
  <=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).

fof(f17353,plain,
    ( spl0_1844
  <=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).

fof(f17356,plain,
    ( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1844 ),
    inference(forward_demodulation,[],[f17354,f12301]) ).

fof(f17354,plain,
    ( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint)
    | ~ spl0_1844 ),
    inference(avatar_component_clause,[],[f17353]) ).

fof(f17355,plain,
    spl0_1844,
    inference(avatar_split_clause,[],[f3058,f17353]) ).

fof(f3058,plain,
    ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint),
    inference(definition_unfolding,[],[f1465,f2544]) ).

fof(f1465,axiom,
    ! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_IntDef_Oint) = c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).

fof(f17351,plain,
    spl0_1843,
    inference(avatar_split_clause,[],[f3057,f17349]) ).

fof(f3057,plain,
    ! [X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
    inference(definition_unfolding,[],[f2586,f2373]) ).

fof(f2586,axiom,
    ! [X1,X12,X13] : c_inter(X12,X13,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).

fof(f17332,plain,
    spl0_1842,
    inference(avatar_split_clause,[],[f2933,f17330]) ).

fof(f2933,axiom,
    ! [X86,X102,X12,X13] :
      ( c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).

fof(f17328,plain,
    spl0_1841,
    inference(avatar_split_clause,[],[f2866,f17326]) ).

fof(f17326,plain,
    ( spl0_1841
  <=> ! [X20,X88] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).

fof(f2866,axiom,
    ! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).

fof(f17324,plain,
    spl0_1840,
    inference(avatar_split_clause,[],[f2828,f17322]) ).

fof(f17322,plain,
    ( spl0_1840
  <=> ! [X86,X88] :
        ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).

fof(f2828,axiom,
    ! [X88,X86] :
      ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).

fof(f17320,plain,
    spl0_1839,
    inference(avatar_split_clause,[],[f2807,f17318]) ).

fof(f17318,plain,
    ( spl0_1839
  <=> ! [X86,X88] :
        ( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | c_Message_Osynth(c_Message_Oanalz(X88)) = c_Message_Osynth(c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).

fof(f2807,axiom,
    ! [X88,X86] :
      ( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | c_Message_Osynth(c_Message_Oanalz(X88)) = c_Message_Osynth(c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).

fof(f17316,plain,
    spl0_1838,
    inference(avatar_split_clause,[],[f2799,f17314]) ).

fof(f17314,plain,
    ( spl0_1838
  <=> ! [X102,X13,X12,X86] : c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).

fof(f2799,axiom,
    ! [X86,X102,X12,X13] : c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Says_0) ).

fof(f17312,plain,
    spl0_1837,
    inference(avatar_split_clause,[],[f2798,f17310]) ).

fof(f2798,axiom,
    ! [X86,X12,X102] :
      ( c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_1) ).

fof(f17308,plain,
    spl0_1836,
    inference(avatar_split_clause,[],[f2675,f17306]) ).

fof(f17306,plain,
    ( spl0_1836
  <=> ! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).

fof(f2675,axiom,
    ! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).

fof(f17304,plain,
    spl0_1835,
    inference(avatar_split_clause,[],[f2650,f17302]) ).

fof(f17302,plain,
    ( spl0_1835
  <=> ! [X13,X12,X1] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).

fof(f2650,axiom,
    ! [X1,X12,X13] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).

fof(f17300,plain,
    spl0_1834,
    inference(avatar_split_clause,[],[f2596,f17298]) ).

fof(f2596,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X12,X1)
      | c_in(X4,X13,X1)
      | c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).

fof(f17296,plain,
    spl0_1833,
    inference(avatar_split_clause,[],[f2585,f17294]) ).

fof(f17294,plain,
    ( spl0_1833
  <=> ! [X13,X12,X1] :
        ( ~ c_lessequals(X13,X12,tc_set(X1))
        | c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).

fof(f2585,axiom,
    ! [X1,X12,X13] :
      ( ~ c_lessequals(X13,X12,tc_set(X1))
      | c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).

fof(f17239,plain,
    spl0_1832,
    inference(avatar_split_clause,[],[f2584,f17237]) ).

fof(f17237,plain,
    ( spl0_1832
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X13,X12,tc_set(X1))
        | ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).

fof(f2584,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X13,X12,tc_set(X1))
      | ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).

fof(f17235,plain,
    spl0_1831,
    inference(avatar_split_clause,[],[f2574,f17233]) ).

fof(f17233,plain,
    ( spl0_1831
  <=> ! [X13,X12,X1] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).

fof(f2574,axiom,
    ! [X1,X12,X13] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).

fof(f17231,plain,
    spl0_1830,
    inference(avatar_split_clause,[],[f2360,f17229]) ).

fof(f17229,plain,
    ( spl0_1830
  <=> ! [X18,X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = X18
        | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).

fof(f2360,axiom,
    ! [X21,X1,X18] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = X18
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).

fof(f17227,plain,
    spl0_1829,
    inference(avatar_split_clause,[],[f2359,f17225]) ).

fof(f17225,plain,
    ( spl0_1829
  <=> ! [X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = X21
        | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).

fof(f2359,axiom,
    ! [X21,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = X21
      | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).

fof(f17223,plain,
    spl0_1828,
    inference(avatar_split_clause,[],[f2194,f17221]) ).

fof(f17221,plain,
    ( spl0_1828
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | ~ c_less(X18,X27,X1)
        | c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).

fof(f2194,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | ~ c_less(X18,X27,X1)
      | c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).

fof(f17219,plain,
    spl0_1827,
    inference(avatar_split_clause,[],[f2193,f17217]) ).

fof(f17217,plain,
    ( spl0_1827
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_less(X18,X27,X1)
        | ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).

fof(f2193,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | c_less(X18,X27,X1)
      | ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).

fof(f17215,plain,
    spl0_1826,
    inference(avatar_split_clause,[],[f2192,f17213]) ).

fof(f17213,plain,
    ( spl0_1826
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | ~ c_less(X18,X27,X1)
        | c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).

fof(f2192,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | ~ c_less(X18,X27,X1)
      | c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).

fof(f17211,plain,
    spl0_1825,
    inference(avatar_split_clause,[],[f2191,f17209]) ).

fof(f17209,plain,
    ( spl0_1825
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_less(X18,X27,X1)
        | ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).

fof(f2191,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | c_less(X18,X27,X1)
      | ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).

fof(f17207,plain,
    spl0_1824,
    inference(avatar_split_clause,[],[f2189,f17205]) ).

fof(f17205,plain,
    ( spl0_1824
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | ~ c_lessequals(X18,X27,X1)
        | c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).

fof(f2189,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | ~ c_lessequals(X18,X27,X1)
      | c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).

fof(f17203,plain,
    spl0_1823,
    inference(avatar_split_clause,[],[f2188,f17201]) ).

fof(f17201,plain,
    ( spl0_1823
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X18,X27,X1)
        | ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).

fof(f2188,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | c_lessequals(X18,X27,X1)
      | ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).

fof(f17199,plain,
    ( spl0_1822
    | ~ spl0_812
    | ~ spl0_1750 ),
    inference(avatar_split_clause,[],[f16752,f15898,f7611,f17197]) ).

fof(f16752,plain,
    ( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
    | ~ spl0_812
    | ~ spl0_1750 ),
    inference(forward_demodulation,[],[f16722,f7612]) ).

fof(f16722,plain,
    ( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
    | ~ spl0_812
    | ~ spl0_1750 ),
    inference(superposition,[],[f15899,f7612]) ).

fof(f17195,plain,
    spl0_1821,
    inference(avatar_split_clause,[],[f2187,f17193]) ).

fof(f17193,plain,
    ( spl0_1821
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | ~ c_lessequals(X18,X27,X1)
        | c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).

fof(f2187,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | ~ c_lessequals(X18,X27,X1)
      | c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).

fof(f17191,plain,
    spl0_1820,
    inference(avatar_split_clause,[],[f2186,f17189]) ).

fof(f17189,plain,
    ( spl0_1820
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X18,X27,X1)
        | ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).

fof(f2186,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
      | c_lessequals(X18,X27,X1)
      | ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).

fof(f17187,plain,
    spl0_1819,
    inference(avatar_split_clause,[],[f2146,f17185]) ).

fof(f17185,plain,
    ( spl0_1819
  <=> ! [X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
        | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).

fof(f2146,axiom,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).

fof(f17183,plain,
    spl0_1818,
    inference(avatar_split_clause,[],[f2145,f17181]) ).

fof(f17181,plain,
    ( spl0_1818
  <=> ! [X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).

fof(f2145,axiom,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).

fof(f17179,plain,
    spl0_1817,
    inference(avatar_split_clause,[],[f2138,f17177]) ).

fof(f17177,plain,
    ( spl0_1817
  <=> ! [X11,X0,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).

fof(f2138,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).

fof(f17175,plain,
    spl0_1816,
    inference(avatar_split_clause,[],[f2137,f17173]) ).

fof(f17173,plain,
    ( spl0_1816
  <=> ! [X11,X0,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).

fof(f2137,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).

fof(f17171,plain,
    spl0_1815,
    inference(avatar_split_clause,[],[f2119,f17169]) ).

fof(f2119,axiom,
    ! [X11,X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).

fof(f17167,plain,
    spl0_1814,
    inference(avatar_split_clause,[],[f2116,f17165]) ).

fof(f2116,axiom,
    ! [X11,X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).

fof(f17163,plain,
    spl0_1813,
    inference(avatar_split_clause,[],[f1971,f17161]) ).

fof(f17161,plain,
    ( spl0_1813
  <=> ! [X2,X18] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_less(c_uminus(c_1,X2),X18,X2)
        | c_less(c_uminus(X18,X2),c_1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).

fof(f1971,axiom,
    ! [X2,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_less(c_uminus(c_1,X2),X18,X2)
      | c_less(c_uminus(X18,X2),c_1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).

fof(f17159,plain,
    spl0_1812,
    inference(avatar_split_clause,[],[f1970,f17157]) ).

fof(f17157,plain,
    ( spl0_1812
  <=> ! [X2,X18] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_less(c_uminus(X18,X2),c_1,X2)
        | c_less(c_uminus(c_1,X2),X18,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).

fof(f1970,axiom,
    ! [X2,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_less(c_uminus(X18,X2),c_1,X2)
      | c_less(c_uminus(c_1,X2),X18,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).

fof(f17155,plain,
    ( spl0_1811
    | ~ spl0_672
    | ~ spl0_1743 ),
    inference(avatar_split_clause,[],[f16629,f15870,f7003,f17153]) ).

fof(f17153,plain,
    ( spl0_1811
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).

fof(f15870,plain,
    ( spl0_1743
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_lessequals(X3,X0,X1)
        | ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).

fof(f16629,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_672
    | ~ spl0_1743 ),
    inference(resolution,[],[f15871,f7004]) ).

fof(f15871,plain,
    ( ! [X3,X0,X1] :
        ( ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
        | c_lessequals(X3,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_1743 ),
    inference(avatar_component_clause,[],[f15870]) ).

fof(f17151,plain,
    spl0_1810,
    inference(avatar_split_clause,[],[f1967,f17149]) ).

fof(f17149,plain,
    ( spl0_1810
  <=> ! [X2,X18] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
        | c_lessequals(c_uminus(X18,X2),c_1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).

fof(f1967,axiom,
    ! [X2,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
      | c_lessequals(c_uminus(X18,X2),c_1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).

fof(f17147,plain,
    spl0_1809,
    inference(avatar_split_clause,[],[f1966,f17145]) ).

fof(f17145,plain,
    ( spl0_1809
  <=> ! [X2,X18] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
        | c_lessequals(c_uminus(c_1,X2),X18,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).

fof(f1966,axiom,
    ! [X2,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
      | c_lessequals(c_uminus(c_1,X2),X18,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).

fof(f17143,plain,
    spl0_1808,
    inference(avatar_split_clause,[],[f1960,f17141]) ).

fof(f17141,plain,
    ( spl0_1808
  <=> ! [X2,X27] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_less(X27,c_uminus(c_1,X2),X2)
        | c_less(c_1,c_uminus(X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).

fof(f1960,axiom,
    ! [X2,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_less(X27,c_uminus(c_1,X2),X2)
      | c_less(c_1,c_uminus(X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).

fof(f17139,plain,
    spl0_1807,
    inference(avatar_split_clause,[],[f1959,f17137]) ).

fof(f17137,plain,
    ( spl0_1807
  <=> ! [X2,X27] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_less(c_1,c_uminus(X27,X2),X2)
        | c_less(X27,c_uminus(c_1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).

fof(f1959,axiom,
    ! [X2,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_less(c_1,c_uminus(X27,X2),X2)
      | c_less(X27,c_uminus(c_1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).

fof(f17135,plain,
    spl0_1806,
    inference(avatar_split_clause,[],[f1944,f17133]) ).

fof(f17133,plain,
    ( spl0_1806
  <=> ! [X2,X27] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
        | c_lessequals(c_1,c_uminus(X27,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).

fof(f1944,axiom,
    ! [X2,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
      | c_lessequals(c_1,c_uminus(X27,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).

fof(f17131,plain,
    spl0_1805,
    inference(avatar_split_clause,[],[f1943,f17129]) ).

fof(f17129,plain,
    ( spl0_1805
  <=> ! [X2,X27] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
        | ~ class_HOL_Oone(X2)
        | ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
        | c_lessequals(X27,c_uminus(c_1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).

fof(f1943,axiom,
    ! [X2,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
      | ~ class_HOL_Oone(X2)
      | ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
      | c_lessequals(X27,c_uminus(c_1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).

fof(f17127,plain,
    spl0_1804,
    inference(avatar_split_clause,[],[f1869,f17125]) ).

fof(f17125,plain,
    ( spl0_1804
  <=> ! [X1,X47] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).

fof(f1869,axiom,
    ! [X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).

fof(f17123,plain,
    spl0_1803,
    inference(avatar_split_clause,[],[f1780,f17121]) ).

fof(f17121,plain,
    ( spl0_1803
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).

fof(f1780,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).

fof(f17119,plain,
    spl0_1802,
    inference(avatar_split_clause,[],[f1764,f17117]) ).

fof(f17117,plain,
    ( spl0_1802
  <=> ! [X0,X12,X1] :
        ( ~ c_in(c_0,X12,tc_nat)
        | c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).

fof(f1764,axiom,
    ! [X0,X1,X12] :
      ( ~ c_in(c_0,X12,tc_nat)
      | c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).

fof(f17114,plain,
    spl0_1801,
    inference(avatar_split_clause,[],[f1727,f17112]) ).

fof(f17112,plain,
    ( spl0_1801
  <=> ! [X25,X1,X3] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).

fof(f1727,axiom,
    ! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).

fof(f17110,plain,
    spl0_1800,
    inference(avatar_split_clause,[],[f1724,f17108]) ).

fof(f17108,plain,
    ( spl0_1800
  <=> ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).

fof(f1724,axiom,
    ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).

fof(f17106,plain,
    spl0_1799,
    inference(avatar_split_clause,[],[f1713,f17104]) ).

fof(f1713,axiom,
    ! [X41,X0,X23] :
      ( ~ c_in(X0,c_List_Oset(X23,X41),X41)
      | c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).

fof(f17102,plain,
    spl0_1798,
    inference(avatar_split_clause,[],[f1701,f17100]) ).

fof(f17100,plain,
    ( spl0_1798
  <=> ! [X21,X1,X23] :
        ( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
        | c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).

fof(f1701,axiom,
    ! [X21,X1,X23] :
      ( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
      | c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).

fof(f17098,plain,
    spl0_1797,
    inference(avatar_split_clause,[],[f1700,f17096]) ).

fof(f17096,plain,
    ( spl0_1797
  <=> ! [X59,X0,X23,X43,X1] :
        ( X43 = X59
        | c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).

fof(f1700,axiom,
    ! [X59,X0,X1,X23,X43] :
      ( X43 = X59
      | c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).

fof(f17094,plain,
    spl0_1796,
    inference(avatar_split_clause,[],[f1618,f17092]) ).

fof(f17092,plain,
    ( spl0_1796
  <=> ! [X5,X1,X0] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).

fof(f1618,axiom,
    ! [X0,X1,X5] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).

fof(f17090,plain,
    spl0_1795,
    inference(avatar_split_clause,[],[f1605,f17088]) ).

fof(f17088,plain,
    ( spl0_1795
  <=> ! [X1,X23] :
        ( c_List_Oremdups(X23,X1) = X23
        | c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).

fof(f1605,axiom,
    ! [X1,X23] :
      ( c_List_Oremdups(X23,X1) = X23
      | c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).

fof(f17086,plain,
    spl0_1794,
    inference(avatar_split_clause,[],[f1545,f17084]) ).

fof(f17084,plain,
    ( spl0_1794
  <=> ! [X25,X1,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).

fof(f1545,axiom,
    ! [X1,X25,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).

fof(f17082,plain,
    spl0_1793,
    inference(avatar_split_clause,[],[f1538,f17080]) ).

fof(f1538,axiom,
    ! [X41,X0,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).

fof(f17078,plain,
    spl0_1792,
    inference(avatar_split_clause,[],[f1519,f17076]) ).

fof(f17076,plain,
    ( spl0_1792
  <=> ! [X1,X3] :
        ( c_List_Olist_ONil = X3
        | c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).

fof(f1519,axiom,
    ! [X3,X1] :
      ( c_List_Olist_ONil = X3
      | c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).

fof(f17074,plain,
    spl0_1791,
    inference(avatar_split_clause,[],[f1515,f17072]) ).

fof(f17072,plain,
    ( spl0_1791
  <=> ! [X25,X5,X1] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).

fof(f1515,axiom,
    ! [X1,X5,X25] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).

fof(f17070,plain,
    ( spl0_1790
    | ~ spl0_750
    | ~ spl0_1756 ),
    inference(avatar_split_clause,[],[f16821,f15922,f7360,f17067]) ).

fof(f17067,plain,
    ( spl0_1790
  <=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).

fof(f15922,plain,
    ( spl0_1756
  <=> ! [X102,X86,X12,X13] :
        ( c_in(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)
        | ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).

fof(f16821,plain,
    ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
    | ~ spl0_750
    | ~ spl0_1756 ),
    inference(resolution,[],[f15923,f7362]) ).

fof(f15923,plain,
    ( ! [X86,X12,X102,X13] :
        ( ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
        | c_in(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) )
    | ~ spl0_1756 ),
    inference(avatar_component_clause,[],[f15922]) ).

fof(f17065,plain,
    spl0_1789,
    inference(avatar_split_clause,[],[f1507,f17063]) ).

fof(f17063,plain,
    ( spl0_1789
  <=> ! [X50,X1,X24] :
        ( c_List_Olist_ONil = X24
        | c_List_Olist_ONil != c_List_Oconcat(X50,X1)
        | ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).

fof(f1507,axiom,
    ! [X50,X1,X24] :
      ( c_List_Olist_ONil = X24
      | c_List_Olist_ONil != c_List_Oconcat(X50,X1)
      | ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).

fof(f17061,plain,
    spl0_1788,
    inference(avatar_split_clause,[],[f1506,f17059]) ).

fof(f17059,plain,
    ( spl0_1788
  <=> ! [X5,X1,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).

fof(f1506,axiom,
    ! [X1,X5,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).

fof(f17057,plain,
    spl0_1787,
    inference(avatar_split_clause,[],[f1311,f17055]) ).

fof(f17055,plain,
    ( spl0_1787
  <=> ! [X21,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).

fof(f1311,axiom,
    ! [X21,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).

fof(f17053,plain,
    spl0_1786,
    inference(avatar_split_clause,[],[f1303,f17051]) ).

fof(f17051,plain,
    ( spl0_1786
  <=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).

fof(f1303,axiom,
    ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).

fof(f17049,plain,
    spl0_1785,
    inference(avatar_split_clause,[],[f1302,f17047]) ).

fof(f17047,plain,
    ( spl0_1785
  <=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).

fof(f1302,axiom,
    ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).

fof(f17045,plain,
    spl0_1784,
    inference(avatar_split_clause,[],[f1301,f17043]) ).

fof(f17043,plain,
    ( spl0_1784
  <=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).

fof(f1301,axiom,
    ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).

fof(f17041,plain,
    spl0_1783,
    inference(avatar_split_clause,[],[f1272,f17039]) ).

fof(f17039,plain,
    ( spl0_1783
  <=> ! [X12,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).

fof(f1272,axiom,
    ! [X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).

fof(f17037,plain,
    spl0_1782,
    inference(avatar_split_clause,[],[f1257,f17035]) ).

fof(f17035,plain,
    ( spl0_1782
  <=> ! [X12,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_emptyset = X12
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).

fof(f1257,axiom,
    ! [X1,X12] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_emptyset = X12
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).

fof(f17033,plain,
    spl0_1781,
    inference(avatar_split_clause,[],[f81,f17031]) ).

fof(f17031,plain,
    ( spl0_1781
  <=> ! [X12,X1,X18] :
        ( ~ c_in(X18,X12,X1)
        | c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).

fof(f81,axiom,
    ! [X18,X1,X12] :
      ( ~ c_in(X18,X12,X1)
      | c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).

fof(f17029,plain,
    spl0_1780,
    inference(avatar_split_clause,[],[f47,f17027]) ).

fof(f17027,plain,
    ( spl0_1780
  <=> ! [X12,X1,X23] :
        ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
        | c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).

fof(f47,axiom,
    ! [X1,X12,X23] :
      ( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
      | c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

fof(f16848,plain,
    ( spl0_1779
    | ~ spl0_749
    | ~ spl0_1756 ),
    inference(avatar_split_clause,[],[f16820,f15922,f7355,f16845]) ).

fof(f16845,plain,
    ( spl0_1779
  <=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).

fof(f16820,plain,
    ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
    | ~ spl0_749
    | ~ spl0_1756 ),
    inference(resolution,[],[f15923,f7357]) ).

fof(f16582,plain,
    ( spl0_1778
    | ~ spl0_758
    | ~ spl0_1714 ),
    inference(avatar_split_clause,[],[f16387,f15754,f7393,f16580]) ).

fof(f16580,plain,
    ( spl0_1778
  <=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).

fof(f15754,plain,
    ( spl0_1714
  <=> ! [X21,X1,X3] :
        ( c_List_Orotate(X21,X3,X1) = X3
        | c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).

fof(f16387,plain,
    ( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
    | ~ spl0_758
    | ~ spl0_1714 ),
    inference(trivial_inequality_removal,[],[f16377]) ).

fof(f16377,plain,
    ( ! [X0,X1] :
        ( c_0 != c_0
        | c_List_Orotate(c_0,X0,X1) = X0 )
    | ~ spl0_758
    | ~ spl0_1714 ),
    inference(superposition,[],[f15755,f7394]) ).

fof(f15755,plain,
    ( ! [X21,X3,X1] :
        ( c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
        | c_List_Orotate(X21,X3,X1) = X3 )
    | ~ spl0_1714 ),
    inference(avatar_component_clause,[],[f15754]) ).

fof(f16339,plain,
    ( ~ spl0_1776
    | spl0_1777
    | ~ spl0_114
    | ~ spl0_1704 ),
    inference(avatar_split_clause,[],[f16171,f15714,f3994,f16337,f16333]) ).

fof(f16333,plain,
    ( spl0_1776
  <=> c_List_Odistinct(v_evso,tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).

fof(f16337,plain,
    ( spl0_1777
  <=> ! [X0] : c_List_Odistinct(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).

fof(f15714,plain,
    ( spl0_1704
  <=> ! [X41,X0,X23] :
        ( ~ c_List_Odistinct(X23,X41)
        | c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
        | c_in(X0,c_List_Oset(X23,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).

fof(f16171,plain,
    ( ! [X0] :
        ( c_List_Odistinct(c_List_Olist_OCons(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),v_evso,tc_Event_Oevent),tc_Event_Oevent)
        | ~ c_List_Odistinct(v_evso,tc_Event_Oevent) )
    | ~ spl0_114
    | ~ spl0_1704 ),
    inference(resolution,[],[f15715,f3995]) ).

fof(f15715,plain,
    ( ! [X41,X0,X23] :
        ( c_in(X0,c_List_Oset(X23,X41),X41)
        | c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
        | ~ c_List_Odistinct(X23,X41) )
    | ~ spl0_1704 ),
    inference(avatar_component_clause,[],[f15714]) ).

fof(f16142,plain,
    ( spl0_1775
    | ~ spl0_895
    | ~ spl0_1061 ),
    inference(avatar_split_clause,[],[f9214,f8832,f7956,f16140]) ).

fof(f16140,plain,
    ( spl0_1775
  <=> ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).

fof(f9214,plain,
    ( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
    | ~ spl0_895
    | ~ spl0_1061 ),
    inference(superposition,[],[f7957,f8833]) ).

fof(f16050,plain,
    spl0_1774,
    inference(avatar_split_clause,[],[f3430,f16048]) ).

fof(f16048,plain,
    ( spl0_1774
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).

fof(f3430,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
    inference(forward_demodulation,[],[f3429,f2115]) ).

fof(f2115,axiom,
    ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).

fof(f3429,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
    inference(forward_demodulation,[],[f3215,f2978]) ).

fof(f2978,plain,
    c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
    inference(definition_unfolding,[],[f2126,f2129]) ).

fof(f2126,axiom,
    c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).

fof(f3215,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
    inference(definition_unfolding,[],[f1317,f2129]) ).

fof(f1317,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).

fof(f16046,plain,
    spl0_1773,
    inference(avatar_split_clause,[],[f3423,f16044]) ).

fof(f16044,plain,
    ( spl0_1773
  <=> ! [X1,X3] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).

fof(f3423,plain,
    ! [X3,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3422,f2115]) ).

fof(f3422,plain,
    ! [X3,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3209,f2978]) ).

fof(f3209,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
    inference(definition_unfolding,[],[f1321,f2129]) ).

fof(f1321,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).

fof(f16042,plain,
    ( spl0_1772
    | ~ spl0_997
    | ~ spl0_998 ),
    inference(avatar_split_clause,[],[f8656,f8446,f8441,f16039]) ).

fof(f16039,plain,
    ( spl0_1772
  <=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).

fof(f8656,plain,
    ( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
    | ~ spl0_997
    | ~ spl0_998 ),
    inference(superposition,[],[f8447,f8443]) ).

fof(f16037,plain,
    spl0_1771,
    inference(avatar_split_clause,[],[f3420,f16035]) ).

fof(f16035,plain,
    ( spl0_1771
  <=> ! [X0,X1] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).

fof(f3420,plain,
    ! [X0,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
    inference(forward_demodulation,[],[f3419,f2115]) ).

fof(f3419,plain,
    ! [X0,X1] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
    inference(forward_demodulation,[],[f3207,f2978]) ).

fof(f3207,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
    inference(definition_unfolding,[],[f1316,f2129]) ).

fof(f1316,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).

fof(f16033,plain,
    spl0_1770,
    inference(avatar_split_clause,[],[f3413,f16031]) ).

fof(f16031,plain,
    ( spl0_1770
  <=> ! [X1,X3] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).

fof(f3413,plain,
    ! [X3,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3412,f2115]) ).

fof(f3412,plain,
    ! [X3,X1] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
    inference(forward_demodulation,[],[f3201,f2978]) ).

fof(f3201,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
    inference(definition_unfolding,[],[f1320,f2129]) ).

fof(f1320,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).

fof(f16029,plain,
    spl0_1769,
    inference(avatar_split_clause,[],[f3394,f16027]) ).

fof(f16027,plain,
    ( spl0_1769
  <=> ! [X21,X15] :
        ( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
        | ~ c_lessequals(c_1,X21,tc_nat)
        | ~ c_lessequals(c_1,X15,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).

fof(f3394,plain,
    ! [X21,X15] :
      ( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
      | ~ c_lessequals(c_1,X21,tc_nat)
      | ~ c_lessequals(c_1,X15,tc_nat) ),
    inference(forward_demodulation,[],[f3185,f2979]) ).

fof(f3185,plain,
    ! [X21,X15] :
      ( ~ c_lessequals(c_1,X21,tc_nat)
      | ~ c_lessequals(c_1,X15,tc_nat)
      | c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2097,f2544]) ).

fof(f2097,axiom,
    ! [X21,X15] :
      ( ~ c_lessequals(c_1,X21,tc_nat)
      | ~ c_lessequals(c_1,X15,tc_nat)
      | c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).

fof(f16025,plain,
    spl0_1768,
    inference(avatar_split_clause,[],[f3308,f16023]) ).

fof(f16023,plain,
    ( spl0_1768
  <=> ! [X1,X47] :
        ( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).

fof(f3308,plain,
    ! [X47,X1] :
      ( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f1330,f2156]) ).

fof(f1330,axiom,
    ! [X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).

fof(f16021,plain,
    spl0_1767,
    inference(avatar_split_clause,[],[f3307,f16019]) ).

fof(f16019,plain,
    ( spl0_1767
  <=> ! [X11,X1] :
        ( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).

fof(f3307,plain,
    ! [X11,X1] :
      ( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f1329,f2156]) ).

fof(f1329,axiom,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X11),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).

fof(f16017,plain,
    spl0_1766,
    inference(avatar_split_clause,[],[f3278,f16015]) ).

fof(f16015,plain,
    ( spl0_1766
  <=> ! [X5,X1] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).

fof(f3278,plain,
    ! [X1,X5] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)),
    inference(forward_demodulation,[],[f1636,f1639]) ).

fof(f1639,axiom,
    ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).

fof(f1636,axiom,
    ! [X1,X5] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)),tc_List_Olist(X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).

fof(f16013,plain,
    spl0_1765,
    inference(avatar_split_clause,[],[f3274,f16011]) ).

fof(f3274,plain,
    ! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat),
    inference(forward_demodulation,[],[f3081,f2979]) ).

fof(f3081,plain,
    ! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1627,f2544]) ).

fof(f1627,axiom,
    ! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_Suc(c_0),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).

fof(f16009,plain,
    spl0_1764,
    inference(avatar_split_clause,[],[f3270,f16007]) ).

fof(f16007,plain,
    ( spl0_1764
  <=> ! [X18,X13,X32,X1] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).

fof(f3270,plain,
    ! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1),
    inference(forward_demodulation,[],[f2643,f2644]) ).

fof(f2644,axiom,
    ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).

fof(f2643,axiom,
    ! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_insert(X18,c_union(X13,X32,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).

fof(f16005,plain,
    spl0_1763,
    inference(avatar_split_clause,[],[f3167,f16003]) ).

fof(f3167,plain,
    ! [X21,X3,X1] :
      ( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
      | ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
    inference(definition_unfolding,[],[f1770,f1766]) ).

fof(f1770,axiom,
    ! [X21,X3,X1] :
      ( c_List_Otake(X21,X3,X1) = X3
      | ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).

fof(f15985,plain,
    ( spl0_1762
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1761 ),
    inference(avatar_split_clause,[],[f15981,f15978,f11334,f10936,f7067,f6122,f15983]) ).

fof(f15983,plain,
    ( spl0_1762
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).

fof(f15978,plain,
    ( spl0_1761
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).

fof(f15981,plain,
    ( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1761 ),
    inference(forward_demodulation,[],[f15979,f12301]) ).

fof(f15979,plain,
    ( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat)
    | ~ spl0_1761 ),
    inference(avatar_component_clause,[],[f15978]) ).

fof(f15980,plain,
    spl0_1761,
    inference(avatar_split_clause,[],[f3052,f15978]) ).

fof(f15962,plain,
    ( spl0_1760
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1759 ),
    inference(avatar_split_clause,[],[f15958,f15955,f11334,f10936,f7067,f6122,f15960]) ).

fof(f15955,plain,
    ( spl0_1759
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).

fof(f15958,plain,
    ( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1759 ),
    inference(forward_demodulation,[],[f15956,f12301]) ).

fof(f15956,plain,
    ( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat)
    | ~ spl0_1759 ),
    inference(avatar_component_clause,[],[f15955]) ).

fof(f15957,plain,
    spl0_1759,
    inference(avatar_split_clause,[],[f3051,f15955]) ).

fof(f15933,plain,
    ( spl0_1758
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1757 ),
    inference(avatar_split_clause,[],[f15929,f15926,f11334,f10936,f7067,f6122,f15931]) ).

fof(f15931,plain,
    ( spl0_1758
  <=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).

fof(f15926,plain,
    ( spl0_1757
  <=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).

fof(f15929,plain,
    ( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1757 ),
    inference(forward_demodulation,[],[f15927,f12301]) ).

fof(f15927,plain,
    ( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1)
    | ~ spl0_1757 ),
    inference(avatar_component_clause,[],[f15926]) ).

fof(f15928,plain,
    spl0_1757,
    inference(avatar_split_clause,[],[f3050,f15926]) ).

fof(f3050,plain,
    ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1),
    inference(definition_unfolding,[],[f1738,f2544]) ).

fof(f1738,axiom,
    ! [X21,X1,X23] : c_List_Orotate(c_Suc(X21),X23,X1) = c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).

fof(f15924,plain,
    spl0_1756,
    inference(avatar_split_clause,[],[f2953,f15922]) ).

fof(f2953,axiom,
    ! [X86,X102,X12,X13] :
      ( c_in(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg)
      | ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSays__imp__spies_0) ).

fof(f15920,plain,
    spl0_1755,
    inference(avatar_split_clause,[],[f2722,f15918]) ).

fof(f15918,plain,
    ( spl0_1755
  <=> ! [X5,X1,X0,X3] :
        ( c_Wellfounded__Recursion_Owf(X5,X1)
        | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).

fof(f2722,axiom,
    ! [X3,X0,X1,X5] :
      ( c_Wellfounded__Recursion_Owf(X5,X1)
      | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).

fof(f15916,plain,
    ( spl0_1753
    | ~ spl0_1754
    | ~ spl0_870
    | ~ spl0_976 ),
    inference(avatar_split_clause,[],[f8625,f8356,f7856,f15913,f15910]) ).

fof(f15910,plain,
    ( spl0_1753
  <=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).

fof(f15913,plain,
    ( spl0_1754
  <=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).

fof(f8625,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
        | c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
    | ~ spl0_870
    | ~ spl0_976 ),
    inference(resolution,[],[f8357,f7857]) ).

fof(f15908,plain,
    spl0_1752,
    inference(avatar_split_clause,[],[f2719,f15906]) ).

fof(f15906,plain,
    ( spl0_1752
  <=> ! [X5,X1,X0,X3] :
        ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).

fof(f2719,axiom,
    ! [X3,X0,X1,X5] :
      ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).

fof(f15904,plain,
    spl0_1751,
    inference(avatar_split_clause,[],[f2657,f15902]) ).

fof(f15902,plain,
    ( spl0_1751
  <=> ! [X24,X12,X32,X1] :
        ( ~ c_in(X12,X24,X1)
        | ~ c_in(X24,X32,tc_set(X1))
        | c_in(X12,c_Union(X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).

fof(f2657,axiom,
    ! [X1,X24,X12,X32] :
      ( ~ c_in(X12,X24,X1)
      | ~ c_in(X24,X32,tc_set(X1))
      | c_in(X12,c_Union(X32,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).

fof(f15900,plain,
    spl0_1750,
    inference(avatar_split_clause,[],[f2644,f15898]) ).

fof(f15896,plain,
    spl0_1749,
    inference(avatar_split_clause,[],[f2640,f15894]) ).

fof(f15894,plain,
    ( spl0_1749
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X12,X1)
        | c_in(X4,X13,X1)
        | ~ c_in(X4,c_union(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).

fof(f2640,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X12,X1)
      | c_in(X4,X13,X1)
      | ~ c_in(X4,c_union(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).

fof(f15892,plain,
    spl0_1748,
    inference(avatar_split_clause,[],[f2620,f15890]) ).

fof(f15890,plain,
    ( spl0_1748
  <=> ! [X24,X12,X32,X1] :
        ( c_in(X12,X24,X1)
        | ~ c_in(X24,X32,tc_set(X1))
        | ~ c_in(X12,c_Inter(X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).

fof(f2620,axiom,
    ! [X1,X24,X12,X32] :
      ( c_in(X12,X24,X1)
      | ~ c_in(X24,X32,tc_set(X1))
      | ~ c_in(X12,c_Inter(X32,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).

fof(f15888,plain,
    spl0_1747,
    inference(avatar_split_clause,[],[f2593,f15886]) ).

fof(f15886,plain,
    ( spl0_1747
  <=> ! [X13,X12,X1] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).

fof(f2593,axiom,
    ! [X1,X12,X13] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).

fof(f15884,plain,
    spl0_1746,
    inference(avatar_split_clause,[],[f2572,f15882]) ).

fof(f15882,plain,
    ( spl0_1746
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_lessequals(X0,X3,X1)
        | c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).

fof(f2572,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_lessequals(X0,X3,X1)
      | c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).

fof(f15880,plain,
    spl0_1745,
    inference(avatar_split_clause,[],[f2571,f15878]) ).

fof(f15878,plain,
    ( spl0_1745
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_lessequals(X0,X3,X1)
        | ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).

fof(f2571,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_lessequals(X0,X3,X1)
      | ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).

fof(f15876,plain,
    spl0_1744,
    inference(avatar_split_clause,[],[f2561,f15874]) ).

fof(f15874,plain,
    ( spl0_1744
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | ~ c_lessequals(X3,X0,X1)
        | c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).

fof(f2561,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | ~ c_lessequals(X3,X0,X1)
      | c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).

fof(f15872,plain,
    spl0_1743,
    inference(avatar_split_clause,[],[f2560,f15870]) ).

fof(f2560,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_lessequals(X3,X0,X1)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).

fof(f15868,plain,
    ( spl0_1742
    | ~ spl0_646
    | ~ spl0_943 ),
    inference(avatar_split_clause,[],[f8565,f8223,f6122,f15866]) ).

fof(f15866,plain,
    ( spl0_1742
  <=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).

fof(f8223,plain,
    ( spl0_943
  <=> ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f8565,plain,
    ( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_943 ),
    inference(superposition,[],[f8224,f6124]) ).

fof(f8224,plain,
    ( ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_943 ),
    inference(avatar_component_clause,[],[f8223]) ).

fof(f15864,plain,
    spl0_1741,
    inference(avatar_split_clause,[],[f2548,f15862]) ).

fof(f15862,plain,
    ( spl0_1741
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).

fof(f2548,axiom,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).

fof(f15860,plain,
    spl0_1740,
    inference(avatar_split_clause,[],[f2541,f15858]) ).

fof(f15858,plain,
    ( spl0_1740
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).

fof(f2541,axiom,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).

fof(f15856,plain,
    spl0_1739,
    inference(avatar_split_clause,[],[f2539,f15854]) ).

fof(f15854,plain,
    ( spl0_1739
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_lessequals(X0,X3,X1)
        | c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).

fof(f2539,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_lessequals(X0,X3,X1)
      | c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).

fof(f15852,plain,
    spl0_1738,
    inference(avatar_split_clause,[],[f2538,f15850]) ).

fof(f15850,plain,
    ( spl0_1738
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | c_lessequals(X0,X3,X1)
        | ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).

fof(f2538,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | c_lessequals(X0,X3,X1)
      | ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).

fof(f15848,plain,
    spl0_1737,
    inference(avatar_split_clause,[],[f2533,f15846]) ).

fof(f15846,plain,
    ( spl0_1737
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | ~ c_lessequals(X3,X0,X1)
        | c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).

fof(f2533,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_lessequals(X3,X0,X1)
      | c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).

fof(f15844,plain,
    spl0_1736,
    inference(avatar_split_clause,[],[f2532,f15842]) ).

fof(f15842,plain,
    ( spl0_1736
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Oorder(X1)
        | c_lessequals(X3,X0,X1)
        | ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).

fof(f2532,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | c_lessequals(X3,X0,X1)
      | ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).

fof(f15840,plain,
    spl0_1735,
    inference(avatar_split_clause,[],[f2490,f15838]) ).

fof(f15838,plain,
    ( spl0_1735
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Oring(X1)
        | c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).

fof(f2490,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Oring(X1)
      | c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).

fof(f15836,plain,
    spl0_1734,
    inference(avatar_split_clause,[],[f2489,f15834]) ).

fof(f15834,plain,
    ( spl0_1734
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Oring(X1)
        | c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).

fof(f2489,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Oring(X1)
      | c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).

fof(f15832,plain,
    spl0_1733,
    inference(avatar_split_clause,[],[f2467,f15830]) ).

fof(f15830,plain,
    ( spl0_1733
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Oring(X1)
        | c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).

fof(f2467,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Oring(X1)
      | c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).

fof(f15828,plain,
    spl0_1732,
    inference(avatar_split_clause,[],[f2312,f15826]) ).

fof(f15826,plain,
    ( spl0_1732
  <=> ! [X11,X1] :
        ( ~ class_Power_Orecpower(X1)
        | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
        | c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).

fof(f2312,axiom,
    ! [X11,X1] :
      ( ~ class_Power_Orecpower(X1)
      | c_0 = c_Numeral_Onumber__of(X11,tc_nat)
      | c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).

fof(f15824,plain,
    ( spl0_1731
    | ~ spl0_647
    | ~ spl0_943 ),
    inference(avatar_split_clause,[],[f8564,f8223,f6127,f15822]) ).

fof(f15822,plain,
    ( spl0_1731
  <=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).

fof(f8564,plain,
    ( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_943 ),
    inference(superposition,[],[f8224,f6129]) ).

fof(f15820,plain,
    spl0_1730,
    inference(avatar_split_clause,[],[f2306,f15818]) ).

fof(f15818,plain,
    ( spl0_1730
  <=> ! [X0,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Power_Orecpower(X1)
        | ~ c_Parity_Oeven(X0,tc_nat)
        | c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).

fof(f2306,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Power_Orecpower(X1)
      | ~ c_Parity_Oeven(X0,tc_nat)
      | c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).

fof(f15816,plain,
    spl0_1729,
    inference(avatar_split_clause,[],[f2304,f15814]) ).

fof(f15814,plain,
    ( spl0_1729
  <=> ! [X0,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Parity_Oeven(X0,tc_nat)
        | c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).

fof(f2304,axiom,
    ! [X0,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | ~ c_Parity_Oeven(X0,tc_nat)
      | c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).

fof(f15812,plain,
    spl0_1728,
    inference(avatar_split_clause,[],[f2209,f15810]) ).

fof(f15810,plain,
    ( spl0_1728
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ class_Orderings_Olinorder(X1)
        | ~ c_less(X18,c_0,X1)
        | c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).

fof(f2209,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ class_Orderings_Olinorder(X1)
      | ~ c_less(X18,c_0,X1)
      | c_less(c_plus(X18,X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).

fof(f15808,plain,
    spl0_1727,
    inference(avatar_split_clause,[],[f2208,f15806]) ).

fof(f15806,plain,
    ( spl0_1727
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ class_Orderings_Olinorder(X1)
        | c_less(X18,c_0,X1)
        | ~ c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).

fof(f2208,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ class_Orderings_Olinorder(X1)
      | c_less(X18,c_0,X1)
      | ~ c_less(c_plus(X18,X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).

fof(f15804,plain,
    spl0_1726,
    inference(avatar_split_clause,[],[f2080,f15802]) ).

fof(f15802,plain,
    ( spl0_1726
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X21,tc_nat)
        | ~ c_less(c_0,X15,tc_nat)
        | c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).

fof(f2080,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X21,tc_nat)
      | ~ c_less(c_0,X15,tc_nat)
      | c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).

fof(f15800,plain,
    spl0_1725,
    inference(avatar_split_clause,[],[f2060,f15798]) ).

fof(f15798,plain,
    ( spl0_1725
  <=> ! [X21,X16,X15] :
        ( X15 = X21
        | c_0 = X16
        | c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).

fof(f2060,axiom,
    ! [X21,X16,X15] :
      ( X15 = X21
      | c_0 = X16
      | c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).

fof(f15796,plain,
    spl0_1724,
    inference(avatar_split_clause,[],[f2058,f15794]) ).

fof(f15794,plain,
    ( spl0_1724
  <=> ! [X21,X16,X15] :
        ( X15 = X21
        | c_0 = X16
        | c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).

fof(f2058,axiom,
    ! [X21,X16,X15] :
      ( X15 = X21
      | c_0 = X16
      | c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).

fof(f15792,plain,
    spl0_1723,
    inference(avatar_split_clause,[],[f2037,f15790]) ).

fof(f15790,plain,
    ( spl0_1723
  <=> ! [X16,X59,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).

fof(f15788,plain,
    spl0_1722,
    inference(avatar_split_clause,[],[f2028,f15786]) ).

fof(f15786,plain,
    ( spl0_1722
  <=> ! [X21,X15] :
        ( c_less(c_0,X15,tc_nat)
        | c_less(c_0,X21,tc_nat)
        | ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).

fof(f2028,axiom,
    ! [X21,X15] :
      ( c_less(c_0,X15,tc_nat)
      | c_less(c_0,X21,tc_nat)
      | ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).

fof(f15784,plain,
    spl0_1721,
    inference(avatar_split_clause,[],[f1863,f15782]) ).

fof(f15782,plain,
    ( spl0_1721
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).

fof(f1863,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).

fof(f15780,plain,
    ( spl0_1720
    | ~ spl0_646
    | ~ spl0_943 ),
    inference(avatar_split_clause,[],[f8563,f8223,f6122,f15778]) ).

fof(f15778,plain,
    ( spl0_1720
  <=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).

fof(f8563,plain,
    ( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_943 ),
    inference(superposition,[],[f8224,f6124]) ).

fof(f15776,plain,
    spl0_1719,
    inference(avatar_split_clause,[],[f1860,f15774]) ).

fof(f15774,plain,
    ( spl0_1719
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).

fof(f1860,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).

fof(f15772,plain,
    spl0_1718,
    inference(avatar_split_clause,[],[f1831,f15770]) ).

fof(f15770,plain,
    ( spl0_1718
  <=> ! [X47] :
        ( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
        | c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).

fof(f1831,axiom,
    ! [X47] :
      ( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_0) ).

fof(f15768,plain,
    spl0_1717,
    inference(avatar_split_clause,[],[f1827,f15766]) ).

fof(f15766,plain,
    ( spl0_1717
  <=> ! [X83,X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).

fof(f1827,axiom,
    ! [X83,X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).

fof(f15764,plain,
    spl0_1716,
    inference(avatar_split_clause,[],[f1801,f15762]) ).

fof(f15762,plain,
    ( spl0_1716
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X15,tc_nat)
        | ~ c_less(c_0,X21,tc_nat)
        | c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).

fof(f1801,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X15,tc_nat)
      | ~ c_less(c_0,X21,tc_nat)
      | c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).

fof(f15760,plain,
    spl0_1715,
    inference(avatar_split_clause,[],[f1749,f15758]) ).

fof(f15758,plain,
    ( spl0_1715
  <=> ! [X25,X1,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).

fof(f1749,axiom,
    ! [X1,X25,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).

fof(f15756,plain,
    spl0_1714,
    inference(avatar_split_clause,[],[f1739,f15754]) ).

fof(f1739,axiom,
    ! [X21,X3,X1] :
      ( c_List_Orotate(X21,X3,X1) = X3
      | c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).

fof(f15752,plain,
    spl0_1713,
    inference(avatar_split_clause,[],[f1725,f15750]) ).

fof(f15750,plain,
    ( spl0_1713
  <=> ! [X25,X1,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).

fof(f1725,axiom,
    ! [X1,X25,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).

fof(f15748,plain,
    spl0_1712,
    inference(avatar_split_clause,[],[f1708,f15746]) ).

fof(f1708,axiom,
    ! [X41,X0,X25,X23] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).

fof(f15744,plain,
    spl0_1711,
    inference(avatar_split_clause,[],[f1696,f15742]) ).

fof(f15742,plain,
    ( spl0_1711
  <=> ! [X3,X23,X25,X1] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).

fof(f1696,axiom,
    ! [X3,X1,X25,X23] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).

fof(f15740,plain,
    spl0_1710,
    inference(avatar_split_clause,[],[f1691,f15738]) ).

fof(f15738,plain,
    ( spl0_1710
  <=> ! [X58,X0,X23,X1] :
        ( c_in(X0,c_List_Oset(X23,X1),X1)
        | ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).

fof(f1691,axiom,
    ! [X58,X0,X1,X23] :
      ( c_in(X0,c_List_Oset(X23,X1),X1)
      | ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).

fof(f15736,plain,
    ( spl0_1709
    | ~ spl0_646
    | ~ spl0_940 ),
    inference(avatar_split_clause,[],[f8554,f8211,f6122,f15734]) ).

fof(f15734,plain,
    ( spl0_1709
  <=> ! [X0] :
        ( c_1 != c_IntDef_Oint(X0)
        | c_1 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).

fof(f8211,plain,
    ( spl0_940
  <=> ! [X21,X15] :
        ( X15 = X21
        | c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f8554,plain,
    ( ! [X0] :
        ( c_1 != c_IntDef_Oint(X0)
        | c_1 = X0 )
    | ~ spl0_646
    | ~ spl0_940 ),
    inference(superposition,[],[f8212,f6124]) ).

fof(f8212,plain,
    ( ! [X21,X15] :
        ( c_IntDef_Oint(X21) != c_IntDef_Oint(X15)
        | X15 = X21 )
    | ~ spl0_940 ),
    inference(avatar_component_clause,[],[f8211]) ).

fof(f15732,plain,
    spl0_1708,
    inference(avatar_split_clause,[],[f1690,f15730]) ).

fof(f15730,plain,
    ( spl0_1708
  <=> ! [X3,X0,X23,X1] :
        ( c_in(X0,c_List_Oset(X23,X1),X1)
        | ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).

fof(f1690,axiom,
    ! [X3,X0,X1,X23] :
      ( c_in(X0,c_List_Oset(X23,X1),X1)
      | ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).

fof(f15728,plain,
    spl0_1707,
    inference(avatar_split_clause,[],[f1601,f15726]) ).

fof(f15726,plain,
    ( spl0_1707
  <=> ! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).

fof(f1601,axiom,
    ! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).

fof(f15724,plain,
    spl0_1706,
    inference(avatar_split_clause,[],[f1577,f15722]) ).

fof(f15722,plain,
    ( spl0_1706
  <=> ! [X43,X0,X16,X1] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).

fof(f1577,axiom,
    ! [X0,X1,X16,X43] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).

fof(f15720,plain,
    spl0_1705,
    inference(avatar_split_clause,[],[f1574,f15718]) ).

fof(f15718,plain,
    ( spl0_1705
  <=> ! [X15,X23,X21,X1] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).

fof(f1574,axiom,
    ! [X21,X1,X15,X23] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).

fof(f15716,plain,
    spl0_1704,
    inference(avatar_split_clause,[],[f1554,f15714]) ).

fof(f1554,axiom,
    ! [X41,X0,X23] :
      ( ~ c_List_Odistinct(X23,X41)
      | c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
      | c_in(X0,c_List_Oset(X23,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).

fof(f15712,plain,
    spl0_1703,
    inference(avatar_split_clause,[],[f1547,f15710]) ).

fof(f15710,plain,
    ( spl0_1703
  <=> ! [X50,X1] :
        ( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
        | c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).

fof(f1547,axiom,
    ! [X50,X1] :
      ( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
      | c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).

fof(f15708,plain,
    spl0_1702,
    inference(avatar_split_clause,[],[f1518,f15706]) ).

fof(f15706,plain,
    ( spl0_1702
  <=> ! [X51,X23,X25,X1] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).

fof(f1518,axiom,
    ! [X51,X1,X25,X23] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).

fof(f15704,plain,
    spl0_1701,
    inference(avatar_split_clause,[],[f1508,f15702]) ).

fof(f15702,plain,
    ( spl0_1701
  <=> ! [X50,X1] :
        ( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
        | c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).

fof(f1508,axiom,
    ! [X50,X1] :
      ( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
      | c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).

fof(f15700,plain,
    spl0_1700,
    inference(avatar_split_clause,[],[f1495,f15698]) ).

fof(f15698,plain,
    ( spl0_1700
  <=> ! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).

fof(f1495,axiom,
    ! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).

fof(f15696,plain,
    spl0_1699,
    inference(avatar_split_clause,[],[f1239,f15694]) ).

fof(f15694,plain,
    ( spl0_1699
  <=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).

fof(f1239,axiom,
    ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).

fof(f15692,plain,
    ( spl0_1698
    | ~ spl0_647
    | ~ spl0_920 ),
    inference(avatar_split_clause,[],[f8551,f8128,f6127,f15690]) ).

fof(f15690,plain,
    ( spl0_1698
  <=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).

fof(f8128,plain,
    ( spl0_920
  <=> ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f8551,plain,
    ( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_920 ),
    inference(superposition,[],[f8129,f6129]) ).

fof(f8129,plain,
    ( ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
    | ~ spl0_920 ),
    inference(avatar_component_clause,[],[f8128]) ).

fof(f15688,plain,
    spl0_1697,
    inference(avatar_split_clause,[],[f1237,f15686]) ).

fof(f15686,plain,
    ( spl0_1697
  <=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).

fof(f1237,axiom,
    ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).

fof(f15684,plain,
    spl0_1696,
    inference(avatar_split_clause,[],[f1217,f15682]) ).

fof(f15682,plain,
    ( spl0_1696
  <=> ! [X21,X15] :
        ( ~ c_less(c_1,X21,tc_nat)
        | ~ c_less(c_0,X15,tc_nat)
        | c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).

fof(f1217,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_1,X21,tc_nat)
      | ~ c_less(c_0,X15,tc_nat)
      | c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).

fof(f15680,plain,
    spl0_1695,
    inference(avatar_split_clause,[],[f127,f15678]) ).

fof(f15678,plain,
    ( spl0_1695
  <=> ! [X35,X36,X2,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X35,X2)
        | ~ c_Wellfounded__Recursion_Owf(X36,X1)
        | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).

fof(f127,axiom,
    ! [X2,X36,X1,X35] :
      ( ~ c_Wellfounded__Recursion_Owf(X35,X2)
      | ~ c_Wellfounded__Recursion_Owf(X36,X1)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

fof(f15676,plain,
    spl0_1694,
    inference(avatar_split_clause,[],[f125,f15674]) ).

fof(f15674,plain,
    ( spl0_1694
  <=> ! [X34,X33,X2,X1] :
        ( ~ c_Relation_Otrans(X33,X2)
        | ~ c_Relation_Otrans(X34,X1)
        | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).

fof(f125,axiom,
    ! [X2,X1,X34,X33] :
      ( ~ c_Relation_Otrans(X33,X2)
      | ~ c_Relation_Otrans(X34,X1)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

fof(f15672,plain,
    spl0_1693,
    inference(avatar_split_clause,[],[f80,f15670]) ).

fof(f15670,plain,
    ( spl0_1693
  <=> ! [X12,X1,X4] :
        ( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
        | ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).

fof(f80,axiom,
    ! [X1,X4,X12] :
      ( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
      | ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).

fof(f15619,plain,
    ( spl0_1692
    | ~ spl0_646
    | ~ spl0_920 ),
    inference(avatar_split_clause,[],[f8550,f8128,f6122,f15617]) ).

fof(f15617,plain,
    ( spl0_1692
  <=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).

fof(f8550,plain,
    ( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_920 ),
    inference(superposition,[],[f8129,f6124]) ).

fof(f15540,plain,
    ( spl0_1691
    | ~ spl0_646
    | ~ spl0_920 ),
    inference(avatar_split_clause,[],[f8548,f8128,f6122,f15538]) ).

fof(f15538,plain,
    ( spl0_1691
  <=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).

fof(f8548,plain,
    ( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_920 ),
    inference(superposition,[],[f8129,f6124]) ).

fof(f14630,plain,
    spl0_1690,
    inference(avatar_split_clause,[],[f3386,f14628]) ).

fof(f14628,plain,
    ( spl0_1690
  <=> ! [X1,X3] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_0 = c_Numeral_Onumber__of(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).

fof(f3386,plain,
    ! [X3,X1] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(X3,X1) ),
    inference(forward_demodulation,[],[f3179,f2114]) ).

fof(f3179,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(X3,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1334,f2129]) ).

fof(f1334,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(X3,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).

fof(f14626,plain,
    spl0_1689,
    inference(avatar_split_clause,[],[f3381,f14624]) ).

fof(f14624,plain,
    ( spl0_1689
  <=> ! [X1,X3] :
        ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_0 != c_Numeral_Onumber__of(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).

fof(f3381,plain,
    ! [X3,X1] :
      ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X3,X1) ),
    inference(forward_demodulation,[],[f3175,f2114]) ).

fof(f3175,plain,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X3,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
    inference(definition_unfolding,[],[f1333,f2129]) ).

fof(f1333,axiom,
    ! [X3,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X3,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).

fof(f14622,plain,
    spl0_1688,
    inference(avatar_split_clause,[],[f3269,f14620]) ).

fof(f14620,plain,
    ( spl0_1688
  <=> ! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).

fof(f3269,plain,
    ! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f3074,f2979]) ).

fof(f3074,plain,
    ! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1870,f2544]) ).

fof(f1870,axiom,
    ! [X83] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).

fof(f14618,plain,
    spl0_1687,
    inference(avatar_split_clause,[],[f3184,f14616]) ).

fof(f14616,plain,
    ( spl0_1687
  <=> ! [X21,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_0 = X21
        | c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).

fof(f3184,plain,
    ! [X21,X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_0 = X21
      | c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ),
    inference(definition_unfolding,[],[f1772,f1766]) ).

fof(f1772,axiom,
    ! [X21,X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_0 = X21
      | c_List_Olist_ONil != c_List_Otake(X21,X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).

fof(f14609,plain,
    ( spl0_1686
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1685 ),
    inference(avatar_split_clause,[],[f14583,f14580,f11334,f10936,f7067,f6122,f14607]) ).

fof(f14607,plain,
    ( spl0_1686
  <=> ! [X47] :
        ( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).

fof(f14580,plain,
    ( spl0_1685
  <=> ! [X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).

fof(f14583,plain,
    ( ! [X47] :
        ( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1685 ),
    inference(forward_demodulation,[],[f14581,f12301]) ).

fof(f14581,plain,
    ( ! [X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
    | ~ spl0_1685 ),
    inference(avatar_component_clause,[],[f14580]) ).

fof(f14582,plain,
    spl0_1685,
    inference(avatar_split_clause,[],[f3148,f14580]) ).

fof(f3148,plain,
    ! [X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1822,f2544]) ).

fof(f1822,axiom,
    ! [X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_1 = c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).

fof(f14578,plain,
    spl0_1684,
    inference(avatar_split_clause,[],[f3146,f14576]) ).

fof(f14576,plain,
    ( spl0_1684
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X12,X1)
        | ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).

fof(f3146,plain,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X12,X1)
      | ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
    inference(definition_unfolding,[],[f2606,f2373]) ).

fof(f2606,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X12,X1)
      | ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).

fof(f14574,plain,
    spl0_1683,
    inference(avatar_split_clause,[],[f3145,f14572]) ).

fof(f14572,plain,
    ( spl0_1683
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X13,X1)
        | ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).

fof(f3145,plain,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X13,X1)
      | ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
    inference(definition_unfolding,[],[f2607,f2373]) ).

fof(f2607,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X13,X1)
      | ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).

fof(f14570,plain,
    spl0_1682,
    inference(avatar_split_clause,[],[f3111,f14568]) ).

fof(f14568,plain,
    ( spl0_1682
  <=> ! [X21,X15] :
        ( X15 = X21
        | c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).

fof(f3111,plain,
    ! [X21,X15] :
      ( X15 = X21
      | c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2017,f2544,f2544]) ).

fof(f2017,axiom,
    ! [X21,X15] :
      ( X15 = X21
      | c_Suc(X21) != c_Suc(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).

fof(f14566,plain,
    spl0_1681,
    inference(avatar_split_clause,[],[f3055,f14564]) ).

fof(f14564,plain,
    ( spl0_1681
  <=> ! [X21,X1,X3] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).

fof(f3055,plain,
    ! [X21,X3,X1] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3,
    inference(definition_unfolding,[],[f1535,f1766]) ).

fof(f1535,axiom,
    ! [X21,X3,X1] : c_append(c_List_Otake(X21,X3,X1),c_List_Odrop(X21,X3,X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).

fof(f14562,plain,
    spl0_1680,
    inference(avatar_split_clause,[],[f2950,f14560]) ).

fof(f14560,plain,
    ( spl0_1680
  <=> ! [X102,X12,X114,X91,X22,X86] :
        ( ~ c_Yahalom_OKeyWithNonce(X91,X114,X102)
        | c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(X22,X12,X86),X102,tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).

fof(f2950,axiom,
    ! [X91,X86,X114,X22,X102,X12] :
      ( ~ c_Yahalom_OKeyWithNonce(X91,X114,X102)
      | c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(X22,X12,X86),X102,tc_Event_Oevent)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_3) ).

fof(f14558,plain,
    spl0_1679,
    inference(avatar_split_clause,[],[f2896,f14556]) ).

fof(f14556,plain,
    ( spl0_1679
  <=> ! [X102,X27,X12] :
        ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).

fof(f2896,axiom,
    ! [X27,X12,X102] :
      ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).

fof(f14554,plain,
    spl0_1678,
    inference(avatar_split_clause,[],[f2841,f14552]) ).

fof(f14552,plain,
    ( spl0_1678
  <=> ! [X87,X86,X88] :
        ( c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).

fof(f2841,axiom,
    ! [X88,X86,X87] :
      ( c_in(X87,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_1) ).

fof(f14550,plain,
    spl0_1677,
    inference(avatar_split_clause,[],[f2840,f14548]) ).

fof(f14548,plain,
    ( spl0_1677
  <=> ! [X86,X87,X88] :
        ( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).

fof(f2840,axiom,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_0) ).

fof(f14546,plain,
    spl0_1676,
    inference(avatar_split_clause,[],[f2745,f14544]) ).

fof(f14544,plain,
    ( spl0_1676
  <=> ! [X86,X91,X88] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).

fof(f2745,axiom,
    ! [X91,X88,X86] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).

fof(f14542,plain,
    ( spl0_1675
    | ~ spl0_717
    | ~ spl0_718
    | ~ spl0_720
    | ~ spl0_798
    | ~ spl0_1594 ),
    inference(avatar_split_clause,[],[f14238,f12944,f7554,f7218,f7210,f7205,f14540]) ).

fof(f7210,plain,
    ( spl0_718
  <=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f7218,plain,
    ( spl0_720
  <=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f12944,plain,
    ( spl0_1594
  <=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).

fof(f14238,plain,
    ( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
    | ~ spl0_717
    | ~ spl0_718
    | ~ spl0_720
    | ~ spl0_798
    | ~ spl0_1594 ),
    inference(forward_demodulation,[],[f14237,f7211]) ).

fof(f7211,plain,
    ( ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3
    | ~ spl0_718 ),
    inference(avatar_component_clause,[],[f7210]) ).

fof(f14237,plain,
    ( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
    | ~ spl0_717
    | ~ spl0_720
    | ~ spl0_798
    | ~ spl0_1594 ),
    inference(forward_demodulation,[],[f14236,f7556]) ).

fof(f14236,plain,
    ( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0)
    | ~ spl0_717
    | ~ spl0_720
    | ~ spl0_1594 ),
    inference(forward_demodulation,[],[f14225,f7219]) ).

fof(f7219,plain,
    ( ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11)
    | ~ spl0_720 ),
    inference(avatar_component_clause,[],[f7218]) ).

fof(f14225,plain,
    ( ! [X0] : c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OPls,X0),X0)
    | ~ spl0_717
    | ~ spl0_1594 ),
    inference(superposition,[],[f12945,f7207]) ).

fof(f12945,plain,
    ( ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11)
    | ~ spl0_1594 ),
    inference(avatar_component_clause,[],[f12944]) ).

fof(f14538,plain,
    spl0_1674,
    inference(avatar_split_clause,[],[f2727,f14536]) ).

fof(f14536,plain,
    ( spl0_1674
  <=> ! [X0,X3] :
        ( ~ c_less(X0,X3,tc_nat)
        | c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).

fof(f2727,axiom,
    ! [X3,X0] :
      ( ~ c_less(X0,X3,tc_nat)
      | c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).

fof(f14534,plain,
    spl0_1673,
    inference(avatar_split_clause,[],[f2726,f14532]) ).

fof(f14532,plain,
    ( spl0_1673
  <=> ! [X0,X3] :
        ( c_less(X0,X3,tc_nat)
        | ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).

fof(f2726,axiom,
    ! [X3,X0] :
      ( c_less(X0,X3,tc_nat)
      | ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).

fof(f14530,plain,
    spl0_1672,
    inference(avatar_split_clause,[],[f2683,f14528]) ).

fof(f14528,plain,
    ( spl0_1672
  <=> ! [X18,X12,X27,X1] :
        ( X18 = X27
        | c_in(X18,X12,X1)
        | ~ c_in(X18,c_insert(X27,X12,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).

fof(f2683,axiom,
    ! [X18,X1,X27,X12] :
      ( X18 = X27
      | c_in(X18,X12,X1)
      | ~ c_in(X18,c_insert(X27,X12,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).

fof(f14526,plain,
    spl0_1671,
    inference(avatar_split_clause,[],[f2658,f14524]) ).

fof(f14524,plain,
    ( spl0_1671
  <=> ! [X13,X18,X1] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).

fof(f2658,axiom,
    ! [X18,X1,X13] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).

fof(f14522,plain,
    spl0_1670,
    inference(avatar_split_clause,[],[f2655,f14520]) ).

fof(f14520,plain,
    ( spl0_1670
  <=> ! [X12,X32,X1] :
        ( ~ c_in(X12,c_Union(X32,X1),X1)
        | c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).

fof(f2655,axiom,
    ! [X1,X12,X32] :
      ( ~ c_in(X12,c_Union(X32,X1),X1)
      | c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).

fof(f14518,plain,
    spl0_1669,
    inference(avatar_split_clause,[],[f2621,f14516]) ).

fof(f14516,plain,
    ( spl0_1669
  <=> ! [X12,X32,X1] :
        ( c_in(X12,c_Inter(X32,X1),X1)
        | c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).

fof(f2621,axiom,
    ! [X1,X12,X32] :
      ( c_in(X12,c_Inter(X32,X1),X1)
      | c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).

fof(f14514,plain,
    spl0_1668,
    inference(avatar_split_clause,[],[f2488,f14512]) ).

fof(f14512,plain,
    ( spl0_1668
  <=> ! [X18,X27,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
        | c_0 = X18
        | c_0 = X27
        | c_0 != c_times(X18,X27,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).

fof(f2488,axiom,
    ! [X1,X18,X27] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
      | c_0 = X18
      | c_0 = X27
      | c_0 != c_times(X18,X27,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).

fof(f14510,plain,
    spl0_1667,
    inference(avatar_split_clause,[],[f2472,f14508]) ).

fof(f14508,plain,
    ( spl0_1667
  <=> ! [X4,X27,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_1 = X27
        | c_0 = X4
        | c_times(X27,X4,X1) != X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).

fof(f2472,axiom,
    ! [X1,X27,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_1 = X27
      | c_0 = X4
      | c_times(X27,X4,X1) != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).

fof(f14506,plain,
    spl0_1666,
    inference(avatar_split_clause,[],[f2468,f14504]) ).

fof(f14504,plain,
    ( spl0_1666
  <=> ! [X4,X27,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_1 = X27
        | c_0 = X4
        | c_times(X4,X27,X1) != X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).

fof(f2468,axiom,
    ! [X1,X27,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_1 = X27
      | c_0 = X4
      | c_times(X4,X27,X1) != X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).

fof(f14502,plain,
    spl0_1665,
    inference(avatar_split_clause,[],[f2363,f14500]) ).

fof(f14500,plain,
    ( spl0_1665
  <=> ! [X2,X42,X18,X84,X27,X1] :
        ( X27 = X84
        | c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).

fof(f2363,axiom,
    ! [X2,X18,X1,X27,X84,X42] :
      ( X27 = X84
      | c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).

fof(f14498,plain,
    ( spl0_1664
    | ~ spl0_716
    | ~ spl0_718
    | ~ spl0_743
    | ~ spl0_798
    | ~ spl0_912
    | ~ spl0_1593 ),
    inference(avatar_split_clause,[],[f14219,f12940,f8026,f7554,f7318,f7210,f7200,f14495]) ).

fof(f7200,plain,
    ( spl0_716
  <=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f8026,plain,
    ( spl0_912
  <=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f12940,plain,
    ( spl0_1593
  <=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).

fof(f14219,plain,
    ( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
    | ~ spl0_716
    | ~ spl0_718
    | ~ spl0_743
    | ~ spl0_798
    | ~ spl0_912
    | ~ spl0_1593 ),
    inference(forward_demodulation,[],[f14218,f7202]) ).

fof(f7202,plain,
    ( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
    | ~ spl0_716 ),
    inference(avatar_component_clause,[],[f7200]) ).

fof(f14218,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_718
    | ~ spl0_743
    | ~ spl0_798
    | ~ spl0_912
    | ~ spl0_1593 ),
    inference(forward_demodulation,[],[f14217,f7556]) ).

fof(f14217,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_718
    | ~ spl0_743
    | ~ spl0_912
    | ~ spl0_1593 ),
    inference(forward_demodulation,[],[f14216,f7211]) ).

fof(f14216,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_743
    | ~ spl0_912
    | ~ spl0_1593 ),
    inference(forward_demodulation,[],[f14210,f8027]) ).

fof(f8027,plain,
    ( ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin)
    | ~ spl0_912 ),
    inference(avatar_component_clause,[],[f8026]) ).

fof(f14210,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_743
    | ~ spl0_1593 ),
    inference(superposition,[],[f12941,f7320]) ).

fof(f12941,plain,
    ( ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1)
    | ~ spl0_1593 ),
    inference(avatar_component_clause,[],[f12940]) ).

fof(f14493,plain,
    spl0_1663,
    inference(avatar_split_clause,[],[f2362,f14491]) ).

fof(f14491,plain,
    ( spl0_1663
  <=> ! [X18,X42,X84,X27,X2,X1] :
        ( X18 = X42
        | c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).

fof(f2362,axiom,
    ! [X2,X18,X1,X27,X84,X42] :
      ( X18 = X42
      | c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).

fof(f14489,plain,
    spl0_1662,
    inference(avatar_split_clause,[],[f2349,f14487]) ).

fof(f14487,plain,
    ( spl0_1662
  <=> ! [X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_0,X21,tc_nat)
        | c_0 = c_Nat_Opower(c_0,X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).

fof(f2349,axiom,
    ! [X21,X1] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_0,X21,tc_nat)
      | c_0 = c_Nat_Opower(c_0,X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).

fof(f14485,plain,
    spl0_1661,
    inference(avatar_split_clause,[],[f2348,f14483]) ).

fof(f14483,plain,
    ( spl0_1661
  <=> ! [X18,X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_0,X21,tc_nat)
        | c_0 != c_Nat_Opower(X18,X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).

fof(f2348,axiom,
    ! [X21,X1,X18] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,X21,tc_nat)
      | c_0 != c_Nat_Opower(X18,X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).

fof(f14481,plain,
    spl0_1660,
    inference(avatar_split_clause,[],[f2268,f14479]) ).

fof(f14479,plain,
    ( spl0_1660
  <=> ! [X2,X0,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).

fof(f2268,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).

fof(f14477,plain,
    spl0_1659,
    inference(avatar_split_clause,[],[f2263,f14475]) ).

fof(f14475,plain,
    ( spl0_1659
  <=> ! [X2,X0,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).

fof(f2263,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).

fof(f14473,plain,
    spl0_1658,
    inference(avatar_split_clause,[],[f2246,f14471]) ).

fof(f14471,plain,
    ( spl0_1658
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(X18,X27,X1)
        | c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).

fof(f2246,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(X18,X27,X1)
      | c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).

fof(f14469,plain,
    spl0_1657,
    inference(avatar_split_clause,[],[f2242,f14467]) ).

fof(f14467,plain,
    ( spl0_1657
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(X18,X27,X1)
        | c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).

fof(f2242,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(X18,X27,X1)
      | c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).

fof(f14465,plain,
    spl0_1656,
    inference(avatar_split_clause,[],[f2236,f14463]) ).

fof(f14463,plain,
    ( spl0_1656
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_less(X18,X27,X1)
        | c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).

fof(f2236,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_less(X18,X27,X1)
      | c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).

fof(f14461,plain,
    spl0_1655,
    inference(avatar_split_clause,[],[f2235,f14459]) ).

fof(f14459,plain,
    ( spl0_1655
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_less(X18,X27,X1)
        | ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).

fof(f2235,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_less(X18,X27,X1)
      | ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).

fof(f14457,plain,
    spl0_1654,
    inference(avatar_split_clause,[],[f2232,f14455]) ).

fof(f14455,plain,
    ( spl0_1654
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_lessequals(X18,X27,X1)
        | c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).

fof(f2232,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_lessequals(X18,X27,X1)
      | c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).

fof(f14453,plain,
    ( spl0_1653
    | ~ spl0_672
    | ~ spl0_1575 ),
    inference(avatar_split_clause,[],[f14154,f12825,f7003,f14451]) ).

fof(f14451,plain,
    ( spl0_1653
  <=> ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).

fof(f12825,plain,
    ( spl0_1575
  <=> ! [X20,X88] :
        ( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).

fof(f14154,plain,
    ( ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg))
    | ~ spl0_672
    | ~ spl0_1575 ),
    inference(resolution,[],[f12826,f7004]) ).

fof(f12826,plain,
    ( ! [X88,X20] :
        ( ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
        | c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) )
    | ~ spl0_1575 ),
    inference(avatar_component_clause,[],[f12825]) ).

fof(f14449,plain,
    spl0_1652,
    inference(avatar_split_clause,[],[f2231,f14447]) ).

fof(f14447,plain,
    ( spl0_1652
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_lessequals(X18,X27,X1)
        | ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).

fof(f2231,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_lessequals(X18,X27,X1)
      | ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).

fof(f14445,plain,
    spl0_1651,
    inference(avatar_split_clause,[],[f2195,f14443]) ).

fof(f14443,plain,
    ( spl0_1651
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
        | X4 = X27
        | c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).

fof(f2195,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
      | X4 = X27
      | c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).

fof(f14441,plain,
    spl0_1650,
    inference(avatar_split_clause,[],[f2190,f14439]) ).

fof(f14439,plain,
    ( spl0_1650
  <=> ! [X18,X4,X27,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
        | X4 = X27
        | c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).

fof(f2190,axiom,
    ! [X1,X18,X27,X4] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
      | X4 = X27
      | c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).

fof(f14437,plain,
    spl0_1649,
    inference(avatar_split_clause,[],[f2111,f14435]) ).

fof(f14435,plain,
    ( spl0_1649
  <=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).

fof(f2111,axiom,
    ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).

fof(f14433,plain,
    spl0_1648,
    inference(avatar_split_clause,[],[f2085,f14431]) ).

fof(f14431,plain,
    ( spl0_1648
  <=> ! [X21,X16,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).

fof(f2085,axiom,
    ! [X21,X16,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).

fof(f14429,plain,
    spl0_1647,
    inference(avatar_split_clause,[],[f2084,f14427]) ).

fof(f14427,plain,
    ( spl0_1647
  <=> ! [X21,X16,X15] :
        ( c_less(X15,X21,tc_nat)
        | ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).

fof(f2084,axiom,
    ! [X21,X16,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).

fof(f14425,plain,
    spl0_1646,
    inference(avatar_split_clause,[],[f2083,f14423]) ).

fof(f14423,plain,
    ( spl0_1646
  <=> ! [X21,X16,X15] :
        ( ~ c_lessequals(X15,X21,tc_nat)
        | c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).

fof(f2083,axiom,
    ! [X21,X16,X15] :
      ( ~ c_lessequals(X15,X21,tc_nat)
      | c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).

fof(f14421,plain,
    spl0_1645,
    inference(avatar_split_clause,[],[f2082,f14419]) ).

fof(f14419,plain,
    ( spl0_1645
  <=> ! [X21,X16,X15] :
        ( c_lessequals(X15,X21,tc_nat)
        | ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).

fof(f2082,axiom,
    ! [X21,X16,X15] :
      ( c_lessequals(X15,X21,tc_nat)
      | ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).

fof(f14417,plain,
    spl0_1644,
    inference(avatar_split_clause,[],[f2076,f14415]) ).

fof(f14415,plain,
    ( spl0_1644
  <=> ! [X21,X16,X15] :
        ( c_less(X15,X21,tc_nat)
        | ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).

fof(f2076,axiom,
    ! [X21,X16,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).

fof(f14413,plain,
    spl0_1643,
    inference(avatar_split_clause,[],[f2075,f14411]) ).

fof(f14411,plain,
    ( spl0_1643
  <=> ! [X16,X21,X15] :
        ( c_less(c_0,X16,tc_nat)
        | ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).

fof(f2075,axiom,
    ! [X21,X16,X15] :
      ( c_less(c_0,X16,tc_nat)
      | ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).

fof(f14409,plain,
    ( spl0_1642
    | ~ spl0_672
    | ~ spl0_1573 ),
    inference(avatar_split_clause,[],[f14129,f12817,f7003,f14407]) ).

fof(f14407,plain,
    ( spl0_1642
  <=> ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).

fof(f12817,plain,
    ( spl0_1573
  <=> ! [X20,X88] :
        ( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).

fof(f14129,plain,
    ( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
    | ~ spl0_672
    | ~ spl0_1573 ),
    inference(resolution,[],[f12818,f7004]) ).

fof(f12818,plain,
    ( ! [X88,X20] :
        ( ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
        | c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) )
    | ~ spl0_1573 ),
    inference(avatar_component_clause,[],[f12817]) ).

fof(f14405,plain,
    spl0_1641,
    inference(avatar_split_clause,[],[f2073,f14403]) ).

fof(f14403,plain,
    ( spl0_1641
  <=> ! [X21,X16,X15] :
        ( c_less(X15,X21,tc_nat)
        | ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).

fof(f2073,axiom,
    ! [X21,X16,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).

fof(f14401,plain,
    spl0_1640,
    inference(avatar_split_clause,[],[f2072,f14399]) ).

fof(f14399,plain,
    ( spl0_1640
  <=> ! [X16,X21,X15] :
        ( c_less(c_0,X16,tc_nat)
        | ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).

fof(f2072,axiom,
    ! [X21,X16,X15] :
      ( c_less(c_0,X16,tc_nat)
      | ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).

fof(f14397,plain,
    spl0_1639,
    inference(avatar_split_clause,[],[f2071,f14395]) ).

fof(f14395,plain,
    ( spl0_1639
  <=> ! [X21,X16,X15] :
        ( ~ c_lessequals(X15,X21,tc_nat)
        | c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).

fof(f2071,axiom,
    ! [X21,X16,X15] :
      ( ~ c_lessequals(X15,X21,tc_nat)
      | c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).

fof(f14393,plain,
    spl0_1638,
    inference(avatar_split_clause,[],[f2070,f14391]) ).

fof(f14391,plain,
    ( spl0_1638
  <=> ! [X16,X21,X15] :
        ( c_less(c_0,X16,tc_nat)
        | c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).

fof(f2070,axiom,
    ! [X21,X16,X15] :
      ( c_less(c_0,X16,tc_nat)
      | c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).

fof(f14389,plain,
    spl0_1637,
    inference(avatar_split_clause,[],[f2068,f14387]) ).

fof(f14387,plain,
    ( spl0_1637
  <=> ! [X21,X16,X15] :
        ( ~ c_lessequals(X15,X21,tc_nat)
        | c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).

fof(f2068,axiom,
    ! [X21,X16,X15] :
      ( ~ c_lessequals(X15,X21,tc_nat)
      | c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).

fof(f14385,plain,
    spl0_1636,
    inference(avatar_split_clause,[],[f2067,f14383]) ).

fof(f14383,plain,
    ( spl0_1636
  <=> ! [X16,X21,X15] :
        ( c_less(c_0,X16,tc_nat)
        | c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).

fof(f2067,axiom,
    ! [X21,X16,X15] :
      ( c_less(c_0,X16,tc_nat)
      | c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).

fof(f14381,plain,
    spl0_1635,
    inference(avatar_split_clause,[],[f1927,f14379]) ).

fof(f14379,plain,
    ( spl0_1635
  <=> ! [X2,X27] :
        ( ~ class_HOL_Oone(X2)
        | ~ class_OrderedGroup_Oab__group__add(X2)
        | c_1 != c_uminus(X27,X2)
        | c_uminus(c_1,X2) = X27 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).

fof(f1927,axiom,
    ! [X2,X27] :
      ( ~ class_HOL_Oone(X2)
      | ~ class_OrderedGroup_Oab__group__add(X2)
      | c_1 != c_uminus(X27,X2)
      | c_uminus(c_1,X2) = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).

fof(f14377,plain,
    spl0_1634,
    inference(avatar_split_clause,[],[f1868,f14375]) ).

fof(f14375,plain,
    ( spl0_1634
  <=> ! [X1,X47] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).

fof(f1868,axiom,
    ! [X1,X47] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).

fof(f14373,plain,
    spl0_1633,
    inference(avatar_split_clause,[],[f1820,f14371]) ).

fof(f14371,plain,
    ( spl0_1633
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_less(X15,X21,tc_nat)
        | c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).

fof(f1820,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_less(X15,X21,tc_nat)
      | c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).

fof(f14369,plain,
    spl0_1632,
    inference(avatar_split_clause,[],[f1819,f14367]) ).

fof(f14367,plain,
    ( spl0_1632
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_less(X15,X21,tc_nat)
        | ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).

fof(f1819,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_less(X15,X21,tc_nat)
      | ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).

fof(f14365,plain,
    ( spl0_1631
    | ~ spl0_672
    | ~ spl0_1563 ),
    inference(avatar_split_clause,[],[f14005,f12777,f7003,f14363]) ).

fof(f12777,plain,
    ( spl0_1563
  <=> ! [X20,X88] :
        ( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
        | ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).

fof(f14005,plain,
    ( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
    | ~ spl0_672
    | ~ spl0_1563 ),
    inference(resolution,[],[f12778,f7004]) ).

fof(f12778,plain,
    ( ! [X88,X20] :
        ( ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
        | c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) )
    | ~ spl0_1563 ),
    inference(avatar_component_clause,[],[f12777]) ).

fof(f14361,plain,
    spl0_1630,
    inference(avatar_split_clause,[],[f1817,f14359]) ).

fof(f14359,plain,
    ( spl0_1630
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_lessequals(X15,X21,tc_nat)
        | c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).

fof(f1817,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_lessequals(X15,X21,tc_nat)
      | c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).

fof(f14357,plain,
    spl0_1629,
    inference(avatar_split_clause,[],[f1816,f14355]) ).

fof(f14355,plain,
    ( spl0_1629
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_lessequals(X15,X21,tc_nat)
        | ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).

fof(f1816,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_lessequals(X15,X21,tc_nat)
      | ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).

fof(f14353,plain,
    spl0_1628,
    inference(avatar_split_clause,[],[f1760,f14351]) ).

fof(f14351,plain,
    ( spl0_1628
  <=> ! [X0,X1,X23] :
        ( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
        | c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).

fof(f1760,axiom,
    ! [X0,X1,X23] :
      ( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
      | c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).

fof(f14349,plain,
    spl0_1627,
    inference(avatar_split_clause,[],[f1756,f14347]) ).

fof(f14347,plain,
    ( spl0_1627
  <=> ! [X21,X1,X0] :
        ( c_0 = X21
        | c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).

fof(f1756,axiom,
    ! [X21,X0,X1] :
      ( c_0 = X21
      | c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).

fof(f14345,plain,
    spl0_1626,
    inference(avatar_split_clause,[],[f1710,f14343]) ).

fof(f14343,plain,
    ( spl0_1626
  <=> ! [X41,X0,X3,X25] :
        ( X0 = X3
        | c_List_Oop_Amem(X0,X25,X41)
        | ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).

fof(f1710,axiom,
    ! [X3,X41,X0,X25] :
      ( X0 = X3
      | c_List_Oop_Amem(X0,X25,X41)
      | ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).

fof(f14341,plain,
    spl0_1625,
    inference(avatar_split_clause,[],[f1640,f14339]) ).

fof(f14339,plain,
    ( spl0_1625
  <=> ! [X41,X12,X66] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).

fof(f1640,axiom,
    ! [X41,X66,X12] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).

fof(f14337,plain,
    spl0_1624,
    inference(avatar_split_clause,[],[f1632,f14335]) ).

fof(f1632,axiom,
    ! [X3,X0,X1,X43] :
      ( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
      | c_List_Olist__update(X3,X43,X0,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).

fof(f14333,plain,
    spl0_1623,
    inference(avatar_split_clause,[],[f1612,f14331]) ).

fof(f14331,plain,
    ( spl0_1623
  <=> ! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).

fof(f1612,axiom,
    ! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).

fof(f14329,plain,
    spl0_1622,
    inference(avatar_split_clause,[],[f1600,f14327]) ).

fof(f14327,plain,
    ( spl0_1622
  <=> ! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).

fof(f1600,axiom,
    ! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).

fof(f14325,plain,
    spl0_1621,
    inference(avatar_split_clause,[],[f1596,f14323]) ).

fof(f1596,axiom,
    ! [X59,X43] :
      ( ~ c_less(X43,X59,tc_nat)
      | c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).

fof(f14321,plain,
    spl0_1620,
    inference(avatar_split_clause,[],[f1544,f14319]) ).

fof(f14319,plain,
    ( spl0_1620
  <=> ! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).

fof(f1544,axiom,
    ! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).

fof(f14317,plain,
    spl0_1619,
    inference(avatar_split_clause,[],[f1456,f14315]) ).

fof(f14315,plain,
    ( spl0_1619
  <=> ! [X5,X49] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).

fof(f14313,plain,
    spl0_1618,
    inference(avatar_split_clause,[],[f1431,f14311]) ).

fof(f1431,axiom,
    ! [X48,X11] :
      ( ~ c_less(X11,X48,tc_IntDef_Oint)
      | ~ c_less(c_0,X48,tc_IntDef_Oint)
      | c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).

fof(f14309,plain,
    spl0_1617,
    inference(avatar_split_clause,[],[f1415,f14307]) ).

fof(f1415,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(X11,X48,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).

fof(f14305,plain,
    spl0_1616,
    inference(avatar_split_clause,[],[f1414,f14303]) ).

fof(f14303,plain,
    ( spl0_1616
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(X11,X48,tc_IntDef_Oint)
        | ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).

fof(f1414,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(X11,X48,tc_IntDef_Oint)
      | ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).

fof(f14301,plain,
    spl0_1615,
    inference(avatar_split_clause,[],[f1411,f14299]) ).

fof(f14299,plain,
    ( spl0_1615
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(X11,X48,tc_IntDef_Oint)
        | c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).

fof(f1411,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(X11,X48,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).

fof(f14297,plain,
    spl0_1614,
    inference(avatar_split_clause,[],[f1410,f14295]) ).

fof(f1410,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(X11,X48,tc_IntDef_Oint)
      | ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).

fof(f14293,plain,
    spl0_1613,
    inference(avatar_split_clause,[],[f1281,f14291]) ).

fof(f14291,plain,
    ( spl0_1613
  <=> ! [X13,X1,X46] :
        ( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).

fof(f1281,axiom,
    ! [X46,X1,X13] :
      ( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).

fof(f14289,plain,
    spl0_1612,
    inference(avatar_split_clause,[],[f1198,f14287]) ).

fof(f14287,plain,
    ( spl0_1612
  <=> ! [X9,X7,X8,X10,X2,X1] :
        ( X7 = X8
        | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).

fof(f1198,axiom,
    ! [X2,X10,X1,X8,X9,X7] :
      ( X7 = X8
      | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).

fof(f14285,plain,
    spl0_1611,
    inference(avatar_split_clause,[],[f1197,f14283]) ).

fof(f14283,plain,
    ( spl0_1611
  <=> ! [X7,X10,X8,X9,X2,X1] :
        ( X9 = X10
        | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).

fof(f1197,axiom,
    ! [X2,X10,X1,X8,X9,X7] :
      ( X9 = X10
      | c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).

fof(f14281,plain,
    spl0_1610,
    inference(avatar_split_clause,[],[f99,f14279]) ).

fof(f14279,plain,
    ( spl0_1610
  <=> ! [X12,X32,X1] :
        ( ~ c_in(X12,c_Union(X32,X1),X1)
        | c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).

fof(f99,axiom,
    ! [X1,X12,X32] :
      ( ~ c_in(X12,c_Union(X32,X1),X1)
      | c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).

fof(f14277,plain,
    spl0_1609,
    inference(avatar_split_clause,[],[f96,f14275]) ).

fof(f14275,plain,
    ( spl0_1609
  <=> ! [X12,X32,X1] :
        ( c_in(X12,c_Inter(X32,X1),X1)
        | c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).

fof(f96,axiom,
    ! [X1,X12,X32] :
      ( c_in(X12,c_Inter(X32,X1),X1)
      | c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).

fof(f14273,plain,
    spl0_1608,
    inference(avatar_split_clause,[],[f59,f14271]) ).

fof(f14271,plain,
    ( spl0_1608
  <=> ! [X0,X12,X1,X26] :
        ( c_in(X0,X12,X1)
        | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).

fof(f59,axiom,
    ! [X0,X1,X26,X12] :
      ( c_in(X0,X12,X1)
      | ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

fof(f14269,plain,
    spl0_1607,
    inference(avatar_split_clause,[],[f48,f14267]) ).

fof(f14267,plain,
    ( spl0_1607
  <=> ! [X12,X1,X23] :
        ( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
        | c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).

fof(f48,axiom,
    ! [X1,X12,X23] :
      ( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
      | c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

fof(f14265,plain,
    spl0_1606,
    inference(avatar_split_clause,[],[f43,f14263]) ).

fof(f43,axiom,
    ! [X17,X15] :
      ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
      | c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

fof(f14261,plain,
    spl0_1605,
    inference(avatar_split_clause,[],[f27,f14259]) ).

fof(f27,axiom,
    ! [X17,X15] :
      ( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
      | c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).

fof(f14166,plain,
    ( spl0_1604
    | ~ spl0_120
    | ~ spl0_1558 ),
    inference(avatar_split_clause,[],[f13918,f12754,f4018,f14164]) ).

fof(f14164,plain,
    ( spl0_1604
  <=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).

fof(f12754,plain,
    ( spl0_1558
  <=> ! [X18,X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
        | ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).

fof(f13918,plain,
    ( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
    | ~ spl0_120
    | ~ spl0_1558 ),
    inference(resolution,[],[f12755,f4019]) ).

fof(f12755,plain,
    ( ! [X18,X1,X5] :
        ( ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1))
        | ~ c_Wellfounded__Recursion_Owf(X5,X1) )
    | ~ spl0_1558 ),
    inference(avatar_component_clause,[],[f12754]) ).

fof(f14044,plain,
    ( spl0_1603
    | ~ spl0_1197
    | ~ spl0_1558 ),
    inference(avatar_split_clause,[],[f13912,f12754,f9595,f14042]) ).

fof(f14042,plain,
    ( spl0_1603
  <=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).

fof(f9595,plain,
    ( spl0_1197
  <=> ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).

fof(f13912,plain,
    ( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
    | ~ spl0_1197
    | ~ spl0_1558 ),
    inference(resolution,[],[f12755,f9596]) ).

fof(f9596,plain,
    ( ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1))
    | ~ spl0_1197 ),
    inference(avatar_component_clause,[],[f9595]) ).

fof(f13902,plain,
    ( ~ spl0_44
    | ~ spl0_1602
    | ~ spl0_1380
    | spl0_1487 ),
    inference(avatar_split_clause,[],[f13075,f12449,f10968,f13899,f3649]) ).

fof(f3649,plain,
    ( spl0_44
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f13899,plain,
    ( spl0_1602
  <=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).

fof(f10968,plain,
    ( spl0_1380
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_lessequals(X18,c_0,X1)
        | c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).

fof(f12449,plain,
    ( spl0_1487
  <=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).

fof(f13075,plain,
    ( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
    | ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
    | ~ spl0_1380
    | spl0_1487 ),
    inference(resolution,[],[f12451,f10969]) ).

fof(f10969,plain,
    ( ! [X18,X1] :
        ( c_lessequals(c_0,c_uminus(X18,X1),X1)
        | ~ c_lessequals(X18,c_0,X1)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
    | ~ spl0_1380 ),
    inference(avatar_component_clause,[],[f10968]) ).

fof(f12451,plain,
    ( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | spl0_1487 ),
    inference(avatar_component_clause,[],[f12449]) ).

fof(f13800,plain,
    ( spl0_1601
    | ~ spl0_912
    | ~ spl0_1365 ),
    inference(avatar_split_clause,[],[f12539,f10903,f8026,f13797]) ).

fof(f13797,plain,
    ( spl0_1601
  <=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).

fof(f10903,plain,
    ( spl0_1365
  <=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).

fof(f12539,plain,
    ( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
    | ~ spl0_912
    | ~ spl0_1365 ),
    inference(superposition,[],[f10905,f8027]) ).

fof(f10905,plain,
    ( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
    | ~ spl0_1365 ),
    inference(avatar_component_clause,[],[f10903]) ).

fof(f13599,plain,
    ( ~ spl0_1600
    | spl0_104
    | ~ spl0_835
    | ~ spl0_1178
    | ~ spl0_1285 ),
    inference(avatar_split_clause,[],[f12406,f10180,f9519,f7704,f3946,f13596]) ).

fof(f13596,plain,
    ( spl0_1600
  <=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).

fof(f3946,plain,
    ( spl0_104
  <=> c_0 = c_1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f7704,plain,
    ( spl0_835
  <=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f9519,plain,
    ( spl0_1178
  <=> ! [X47] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f10180,plain,
    ( spl0_1285
  <=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).

fof(f12406,plain,
    ( c_0 = c_1
    | ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
    | ~ spl0_835
    | ~ spl0_1178
    | ~ spl0_1285 ),
    inference(forward_demodulation,[],[f12400,f7706]) ).

fof(f7706,plain,
    ( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
    | ~ spl0_835 ),
    inference(avatar_component_clause,[],[f7704]) ).

fof(f12400,plain,
    ( ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
    | c_0 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
    | ~ spl0_1178
    | ~ spl0_1285 ),
    inference(superposition,[],[f9520,f10182]) ).

fof(f10182,plain,
    ( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
    | ~ spl0_1285 ),
    inference(avatar_component_clause,[],[f10180]) ).

fof(f9520,plain,
    ( ! [X47] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_Numeral_Onumber__of(X47,tc_nat) )
    | ~ spl0_1178 ),
    inference(avatar_component_clause,[],[f9519]) ).

fof(f13297,plain,
    ( spl0_1599
    | ~ spl0_780
    | ~ spl0_1494 ),
    inference(avatar_split_clause,[],[f13171,f12478,f7482,f13295]) ).

fof(f13295,plain,
    ( spl0_1599
  <=> ! [X0,X1] :
        ( ~ c_List_Onull(X0,X1)
        | c_List_Olist_ONil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).

fof(f7482,plain,
    ( spl0_780
  <=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f13171,plain,
    ( ! [X0,X1] :
        ( ~ c_List_Onull(X0,X1)
        | c_List_Olist_ONil = X0 )
    | ~ spl0_780
    | ~ spl0_1494 ),
    inference(superposition,[],[f7483,f12479]) ).

fof(f7483,plain,
    ( ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41)
    | ~ spl0_780 ),
    inference(avatar_component_clause,[],[f7482]) ).

fof(f13165,plain,
    ( spl0_1598
    | ~ spl0_1044
    | ~ spl0_1252 ),
    inference(avatar_split_clause,[],[f12117,f10047,f8763,f13163]) ).

fof(f13163,plain,
    ( spl0_1598
  <=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).

fof(f10047,plain,
    ( spl0_1252
  <=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).

fof(f12117,plain,
    ( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1044
    | ~ spl0_1252 ),
    inference(superposition,[],[f8764,f10048]) ).

fof(f10048,plain,
    ( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
    | ~ spl0_1252 ),
    inference(avatar_component_clause,[],[f10047]) ).

fof(f12958,plain,
    spl0_1597,
    inference(avatar_split_clause,[],[f3338,f12956]) ).

fof(f12956,plain,
    ( spl0_1597
  <=> ! [X83] :
        ( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).

fof(f3338,plain,
    ! [X83] :
      ( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3149,f2979]) ).

fof(f3149,plain,
    ! [X83] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1871,f2544,f2544]) ).

fof(f1871,axiom,
    ! [X83] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).

fof(f12954,plain,
    spl0_1596,
    inference(avatar_split_clause,[],[f3322,f12952]) ).

fof(f12952,plain,
    ( spl0_1596
  <=> ! [X21,X43] :
        ( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
        | ~ c_less(c_0,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).

fof(f3322,plain,
    ! [X21,X43] :
      ( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
      | ~ c_less(c_0,X21,tc_nat) ),
    inference(forward_demodulation,[],[f3127,f3051]) ).

fof(f3127,plain,
    ! [X21,X43] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_less(c_minus(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X43,tc_nat),tc_nat),tc_nat),X21,tc_nat) ),
    inference(definition_unfolding,[],[f2036,f2544]) ).

fof(f2036,axiom,
    ! [X21,X43] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_less(c_minus(X21,c_Suc(X43),tc_nat),X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).

fof(f12950,plain,
    spl0_1595,
    inference(avatar_split_clause,[],[f3273,f12948]) ).

fof(f3273,plain,
    ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3,
    inference(forward_demodulation,[],[f3272,f2156]) ).

fof(f3272,plain,
    ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X3,
    inference(forward_demodulation,[],[f3271,f2154]) ).

fof(f3271,plain,
    ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
    inference(forward_demodulation,[],[f1883,f2156]) ).

fof(f1883,axiom,
    ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).

fof(f12946,plain,
    spl0_1594,
    inference(avatar_split_clause,[],[f3259,f12944]) ).

fof(f3259,plain,
    ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11),
    inference(forward_demodulation,[],[f2128,f2127]) ).

fof(f2127,axiom,
    ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).

fof(f2128,axiom,
    ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).

fof(f12942,plain,
    spl0_1593,
    inference(avatar_split_clause,[],[f3255,f12940]) ).

fof(f3255,plain,
    ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1),
    inference(forward_demodulation,[],[f3040,f3005]) ).

fof(f3005,plain,
    ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
    inference(definition_unfolding,[],[f2112,f2113]) ).

fof(f2113,axiom,
    ! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).

fof(f2112,axiom,
    ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__pred(X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).

fof(f3040,plain,
    ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_OMin),c_Numeral_Obit_OB1),
    inference(definition_unfolding,[],[f2124,f2129,f2113,f2129]) ).

fof(f2124,axiom,
    ! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).

fof(f12938,plain,
    spl0_1592,
    inference(avatar_split_clause,[],[f3159,f12936]) ).

fof(f12936,plain,
    ( spl0_1592
  <=> ! [X47] :
        ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).

fof(f3159,plain,
    ! [X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(definition_unfolding,[],[f1853,f2129]) ).

fof(f1853,axiom,
    ! [X47] :
      ( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).

fof(f12934,plain,
    spl0_1591,
    inference(avatar_split_clause,[],[f3157,f12932]) ).

fof(f12932,plain,
    ( spl0_1591
  <=> ! [X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
        | c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).

fof(f3157,plain,
    ! [X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1854,f2129]) ).

fof(f1854,axiom,
    ! [X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint)
      | c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).

fof(f12903,plain,
    ( spl0_1590
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1589 ),
    inference(avatar_split_clause,[],[f12893,f12890,f11334,f10936,f7067,f6122,f12901]) ).

fof(f12890,plain,
    ( spl0_1589
  <=> ! [X59,X43] :
        ( c_lessequals(X43,X59,tc_nat)
        | c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).

fof(f12893,plain,
    ( ! [X59,X43] :
        ( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
        | c_lessequals(X43,X59,tc_nat) )
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1589 ),
    inference(forward_demodulation,[],[f12891,f12301]) ).

fof(f12891,plain,
    ( ! [X59,X43] :
        ( c_lessequals(X43,X59,tc_nat)
        | c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
    | ~ spl0_1589 ),
    inference(avatar_component_clause,[],[f12890]) ).

fof(f12892,plain,
    spl0_1589,
    inference(avatar_split_clause,[],[f3143,f12890]) ).

fof(f3143,plain,
    ! [X59,X43] :
      ( c_lessequals(X43,X59,tc_nat)
      | c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
    inference(definition_unfolding,[],[f1783,f2544]) ).

fof(f1783,axiom,
    ! [X59,X43] :
      ( c_lessequals(X43,X59,tc_nat)
      | c_List_Olist_ONil = c_List_Oupt(X43,c_Suc(X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).

fof(f12888,plain,
    spl0_1588,
    inference(avatar_split_clause,[],[f3101,f12886]) ).

fof(f3101,plain,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ),
    inference(definition_unfolding,[],[f2117,f2129]) ).

fof(f2117,axiom,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).

fof(f12880,plain,
    ( spl0_1587
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1586 ),
    inference(avatar_split_clause,[],[f12876,f12873,f11334,f10936,f7067,f6122,f12878]) ).

fof(f12873,plain,
    ( spl0_1586
  <=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).

fof(f12876,plain,
    ( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1586 ),
    inference(forward_demodulation,[],[f12874,f12301]) ).

fof(f12874,plain,
    ( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat)
    | ~ spl0_1586 ),
    inference(avatar_component_clause,[],[f12873]) ).

fof(f12875,plain,
    spl0_1586,
    inference(avatar_split_clause,[],[f3041,f12873]) ).

fof(f3041,plain,
    ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2527,f2544]) ).

fof(f2527,axiom,
    ! [X15] : c_SetInterval_OatLeastLessThan(X15,c_Suc(X15),tc_nat) = c_insert(X15,c_emptyset,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).

fof(f12871,plain,
    spl0_1585,
    inference(avatar_split_clause,[],[f3037,f12869]) ).

fof(f3037,plain,
    ! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1),
    inference(definition_unfolding,[],[f2589,f2373]) ).

fof(f2589,axiom,
    ! [X1,X12,X13] : c_emptyset = c_inter(X12,c_minus(X13,X12,tc_set(X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).

fof(f12867,plain,
    spl0_1584,
    inference(avatar_split_clause,[],[f3024,f12865]) ).

fof(f3024,plain,
    ! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
    inference(definition_unfolding,[],[f2706,f2716]) ).

fof(f2706,axiom,
    ! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).

fof(f12863,plain,
    spl0_1583,
    inference(avatar_split_clause,[],[f3023,f12861]) ).

fof(f3023,plain,
    ! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
    inference(definition_unfolding,[],[f2707,f2716]) ).

fof(f2707,axiom,
    ! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).

fof(f12856,plain,
    ( spl0_1582
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1581 ),
    inference(avatar_split_clause,[],[f12852,f12849,f11334,f10936,f7067,f6122,f12854]) ).

fof(f12854,plain,
    ( spl0_1582
  <=> ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).

fof(f12849,plain,
    ( spl0_1581
  <=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).

fof(f12852,plain,
    ( ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21)
    | ~ spl0_646
    | ~ spl0_687
    | ~ spl0_1373
    | ~ spl0_1461
    | ~ spl0_1581 ),
    inference(forward_demodulation,[],[f12850,f12301]) ).

fof(f12850,plain,
    ( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21)
    | ~ spl0_1581 ),
    inference(avatar_component_clause,[],[f12849]) ).

fof(f12851,plain,
    spl0_1581,
    inference(avatar_split_clause,[],[f3018,f12849]) ).

fof(f3018,plain,
    ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21),
    inference(definition_unfolding,[],[f1163,f2544,f2544]) ).

fof(f1163,axiom,
    ! [X21] : c_Suc(X21) = c_Binomial_Obinomial(c_Suc(X21),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).

fof(f12847,plain,
    spl0_1580,
    inference(avatar_split_clause,[],[f2946,f12845]) ).

fof(f12845,plain,
    ( spl0_1580
  <=> ! [X102,X12,X114,X91,X86] :
        ( ~ c_Yahalom_OKeyWithNonce(X91,X114,X102)
        | c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).

fof(f2946,axiom,
    ! [X91,X86,X114,X102,X12] :
      ( ~ c_Yahalom_OKeyWithNonce(X91,X114,X102)
      | c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Notes_1) ).

fof(f12843,plain,
    spl0_1579,
    inference(avatar_split_clause,[],[f2945,f12841]) ).

fof(f12841,plain,
    ( spl0_1579
  <=> ! [X102,X12,X114,X91,X86] :
        ( c_Yahalom_OKeyWithNonce(X91,X114,X102)
        | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).

fof(f2945,axiom,
    ! [X91,X86,X114,X102,X12] :
      ( c_Yahalom_OKeyWithNonce(X91,X114,X102)
      | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Notes_0) ).

fof(f12839,plain,
    spl0_1578,
    inference(avatar_split_clause,[],[f2944,f12837]) ).

fof(f12837,plain,
    ( spl0_1578
  <=> ! [X102,X12,X114,X91,X86] :
        ( ~ c_Yahalom_OKeyWithNonce(X91,X114,X102)
        | c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).

fof(f2944,axiom,
    ! [X91,X86,X114,X102,X12] :
      ( ~ c_Yahalom_OKeyWithNonce(X91,X114,X102)
      | c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Gets_1) ).

fof(f12835,plain,
    spl0_1577,
    inference(avatar_split_clause,[],[f2943,f12833]) ).

fof(f12833,plain,
    ( spl0_1577
  <=> ! [X102,X12,X114,X91,X86] :
        ( c_Yahalom_OKeyWithNonce(X91,X114,X102)
        | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).

fof(f2943,axiom,
    ! [X91,X86,X114,X102,X12] :
      ( c_Yahalom_OKeyWithNonce(X91,X114,X102)
      | ~ c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Gets_0) ).

fof(f12831,plain,
    spl0_1576,
    inference(avatar_split_clause,[],[f2889,f12829]) ).

fof(f12829,plain,
    ( spl0_1576
  <=> ! [X20,X88] :
        ( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
        | c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).

fof(f2889,axiom,
    ! [X88,X20] :
      ( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_1) ).

fof(f12827,plain,
    spl0_1575,
    inference(avatar_split_clause,[],[f2888,f12825]) ).

fof(f2888,axiom,
    ! [X88,X20] :
      ( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
      | ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_0) ).

fof(f12823,plain,
    spl0_1574,
    inference(avatar_split_clause,[],[f2882,f12821]) ).

fof(f12821,plain,
    ( spl0_1574
  <=> ! [X20,X88] :
        ( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
        | c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).

fof(f2882,axiom,
    ! [X88,X20] :
      ( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).

fof(f12819,plain,
    spl0_1573,
    inference(avatar_split_clause,[],[f2881,f12817]) ).

fof(f2881,axiom,
    ! [X88,X20] :
      ( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
      | ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).

fof(f12815,plain,
    spl0_1572,
    inference(avatar_split_clause,[],[f2879,f12813]) ).

fof(f2879,axiom,
    ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).

fof(f12811,plain,
    ( ~ spl0_1570
    | spl0_1571
    | ~ spl0_118
    | ~ spl0_1379 ),
    inference(avatar_split_clause,[],[f11665,f10964,f4010,f12809,f12805]) ).

fof(f12805,plain,
    ( spl0_1570
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).

fof(f12809,plain,
    ( spl0_1571
  <=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).

fof(f10964,plain,
    ( spl0_1379
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_lessequals(X18,c_0,X1)
        | ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).

fof(f11665,plain,
    ( ! [X0] :
        ( c_lessequals(X0,c_0,tc_nat)
        | ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
    | ~ spl0_118
    | ~ spl0_1379 ),
    inference(resolution,[],[f10965,f4011]) ).

fof(f10965,plain,
    ( ! [X18,X1] :
        ( ~ c_lessequals(c_0,c_uminus(X18,X1),X1)
        | c_lessequals(X18,c_0,X1)
        | ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
    | ~ spl0_1379 ),
    inference(avatar_component_clause,[],[f10964]) ).

fof(f12803,plain,
    spl0_1569,
    inference(avatar_split_clause,[],[f2878,f12801]) ).

fof(f2878,axiom,
    ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).

fof(f12799,plain,
    spl0_1568,
    inference(avatar_split_clause,[],[f2876,f12797]) ).

fof(f2876,axiom,
    ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).

fof(f12795,plain,
    spl0_1567,
    inference(avatar_split_clause,[],[f2875,f12793]) ).

fof(f2875,axiom,
    ! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).

fof(f12791,plain,
    spl0_1566,
    inference(avatar_split_clause,[],[f2872,f12789]) ).

fof(f2872,axiom,
    ! [X88,X110] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oparts(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).

fof(f12787,plain,
    spl0_1565,
    inference(avatar_split_clause,[],[f2870,f12785]) ).

fof(f2870,axiom,
    ! [X88,X86] :
      ( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
      | c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).

fof(f12783,plain,
    spl0_1564,
    inference(avatar_split_clause,[],[f2864,f12781]) ).

fof(f12781,plain,
    ( spl0_1564
  <=> ! [X20,X88] :
        ( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
        | c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).

fof(f2864,axiom,
    ! [X88,X20] :
      ( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
      | c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_1) ).

fof(f12779,plain,
    spl0_1563,
    inference(avatar_split_clause,[],[f2863,f12777]) ).

fof(f2863,axiom,
    ! [X88,X20] :
      ( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
      | ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).

fof(f12775,plain,
    spl0_1562,
    inference(avatar_split_clause,[],[f2861,f12773]) ).

fof(f2861,axiom,
    ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).

fof(f12771,plain,
    spl0_1561,
    inference(avatar_split_clause,[],[f2860,f12769]) ).

fof(f2860,axiom,
    ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).

fof(f12767,plain,
    spl0_1560,
    inference(avatar_split_clause,[],[f2857,f12765]) ).

fof(f2857,axiom,
    ! [X88,X86] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).

fof(f12760,plain,
    spl0_1559,
    inference(avatar_split_clause,[],[f2855,f12758]) ).

fof(f2855,axiom,
    ! [X88,X110] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X110),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X110),c_Message_Oanalz(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).

fof(f12756,plain,
    spl0_1558,
    inference(avatar_split_clause,[],[f2725,f12754]) ).

fof(f2725,axiom,
    ! [X1,X18,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).

fof(f12752,plain,
    spl0_1557,
    inference(avatar_split_clause,[],[f2689,f12750]) ).

fof(f2689,axiom,
    ! [X0,X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).

fof(f12748,plain,
    spl0_1556,
    inference(avatar_split_clause,[],[f2656,f12746]) ).

fof(f12746,plain,
    ( spl0_1556
  <=> ! [X12,X32,X1] :
        ( ~ c_in(X12,c_Union(X32,X1),X1)
        | c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).

fof(f2656,axiom,
    ! [X1,X12,X32] :
      ( ~ c_in(X12,c_Union(X32,X1),X1)
      | c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).

fof(f12744,plain,
    spl0_1555,
    inference(avatar_split_clause,[],[f2652,f12742]) ).

fof(f12742,plain,
    ( spl0_1555
  <=> ! [X12,X1,X24] :
        ( c_emptyset = X24
        | c_emptyset != c_Union(X12,X1)
        | ~ c_in(X24,X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).

fof(f2652,axiom,
    ! [X1,X24,X12] :
      ( c_emptyset = X24
      | c_emptyset != c_Union(X12,X1)
      | ~ c_in(X24,X12,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).

fof(f12740,plain,
    spl0_1554,
    inference(avatar_split_clause,[],[f2646,f12738]) ).

fof(f2646,axiom,
    ! [X1,X12,X32,X13] :
      ( c_lessequals(X13,X32,tc_set(X1))
      | ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).

fof(f12736,plain,
    spl0_1553,
    inference(avatar_split_clause,[],[f2645,f12734]) ).

fof(f2645,axiom,
    ! [X1,X12,X32,X13] :
      ( c_lessequals(X12,X32,tc_set(X1))
      | ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).

fof(f12732,plain,
    spl0_1552,
    inference(avatar_split_clause,[],[f2631,f12730]) ).

fof(f2631,axiom,
    ! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).

fof(f12728,plain,
    spl0_1551,
    inference(avatar_split_clause,[],[f2630,f12726]) ).

fof(f2630,axiom,
    ! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).

fof(f12724,plain,
    spl0_1550,
    inference(avatar_split_clause,[],[f2622,f12722]) ).

fof(f12722,plain,
    ( spl0_1550
  <=> ! [X12,X32,X1] :
        ( c_in(X12,c_Inter(X32,X1),X1)
        | ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).

fof(f2622,axiom,
    ! [X1,X12,X32] :
      ( c_in(X12,c_Inter(X32,X1),X1)
      | ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).

fof(f12720,plain,
    spl0_1549,
    inference(avatar_split_clause,[],[f2616,f12718]) ).

fof(f12718,plain,
    ( spl0_1549
  <=> ! [X12,X1,X24] :
        ( c_UNIV = X24
        | c_UNIV != c_Inter(X12,X1)
        | ~ c_in(X24,X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).

fof(f2616,axiom,
    ! [X1,X24,X12] :
      ( c_UNIV = X24
      | c_UNIV != c_Inter(X12,X1)
      | ~ c_in(X24,X12,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).

fof(f12716,plain,
    spl0_1548,
    inference(avatar_split_clause,[],[f2555,f12714]) ).

fof(f12714,plain,
    ( spl0_1548
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X43,X14,X1)
        | ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).

fof(f2555,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X43,X14,X1)
      | ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).

fof(f12712,plain,
    spl0_1547,
    inference(avatar_split_clause,[],[f2554,f12710]) ).

fof(f12710,plain,
    ( spl0_1547
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X26,X43,X1)
        | ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).

fof(f2554,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X26,X43,X1)
      | ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).

fof(f12708,plain,
    spl0_1546,
    inference(avatar_split_clause,[],[f2552,f12706]) ).

fof(f12706,plain,
    ( spl0_1546
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X43,X14,X1)
        | ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).

fof(f2552,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X43,X14,X1)
      | ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).

fof(f12704,plain,
    spl0_1545,
    inference(avatar_split_clause,[],[f2551,f12702]) ).

fof(f12702,plain,
    ( spl0_1545
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X26,X43,X1)
        | ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).

fof(f2551,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X26,X43,X1)
      | ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).

fof(f12700,plain,
    spl0_1544,
    inference(avatar_split_clause,[],[f2525,f12698]) ).

fof(f12698,plain,
    ( spl0_1544
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X43,X14,X1)
        | ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).

fof(f2525,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X43,X14,X1)
      | ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).

fof(f12696,plain,
    spl0_1543,
    inference(avatar_split_clause,[],[f2524,f12694]) ).

fof(f12694,plain,
    ( spl0_1543
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X26,X43,X1)
        | ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).

fof(f2524,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X26,X43,X1)
      | ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).

fof(f12692,plain,
    spl0_1542,
    inference(avatar_split_clause,[],[f2520,f12690]) ).

fof(f12690,plain,
    ( spl0_1542
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X43,X14,X1)
        | ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).

fof(f2520,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X43,X14,X1)
      | ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).

fof(f12688,plain,
    spl0_1541,
    inference(avatar_split_clause,[],[f2519,f12686]) ).

fof(f12686,plain,
    ( spl0_1541
  <=> ! [X43,X14,X1,X26] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X26,X43,X1)
        | ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).

fof(f2519,axiom,
    ! [X1,X26,X14,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X26,X43,X1)
      | ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).

fof(f12684,plain,
    spl0_1540,
    inference(avatar_split_clause,[],[f2387,f12682]) ).

fof(f12682,plain,
    ( spl0_1540
  <=> ! [X18,X27,X1] :
        ( X18 = X27
        | ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).

fof(f2387,axiom,
    ! [X18,X1,X27] :
      ( X18 = X27
      | ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).

fof(f12680,plain,
    ( ~ spl0_1538
    | spl0_1539
    | ~ spl0_118
    | ~ spl0_1341 ),
    inference(avatar_split_clause,[],[f11448,f10805,f4010,f12678,f12674]) ).

fof(f12674,plain,
    ( spl0_1538
  <=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).

fof(f12678,plain,
    ( spl0_1539
  <=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).

fof(f10805,plain,
    ( spl0_1341
  <=> ! [X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_0,X48,tc_IntDef_Oint)
        | ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).

fof(f11448,plain,
    ( ! [X0] :
        ( c_lessequals(c_0,X0,tc_IntDef_Oint)
        | ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
    | ~ spl0_118
    | ~ spl0_1341 ),
    inference(resolution,[],[f10806,f4011]) ).

fof(f10806,plain,
    ( ! [X48,X1] :
        ( ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1)
        | c_lessequals(c_0,X48,tc_IntDef_Oint)
        | ~ class_Ring__and__Field_Oordered__idom(X1) )
    | ~ spl0_1341 ),
    inference(avatar_component_clause,[],[f10805]) ).

fof(f12672,plain,
    spl0_1537,
    inference(avatar_split_clause,[],[f2367,f12670]) ).

fof(f2367,axiom,
    ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).

fof(f12668,plain,
    spl0_1536,
    inference(avatar_split_clause,[],[f2365,f12666]) ).

fof(f2365,axiom,
    ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).

fof(f12664,plain,
    spl0_1535,
    inference(avatar_split_clause,[],[f2361,f12662]) ).

fof(f12662,plain,
    ( spl0_1535
  <=> ! [X18,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).

fof(f2361,axiom,
    ! [X1,X18] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).

fof(f12660,plain,
    spl0_1534,
    inference(avatar_split_clause,[],[f2358,f12658]) ).

fof(f12658,plain,
    ( spl0_1534
  <=> ! [X18,X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).

fof(f2358,axiom,
    ! [X21,X1,X18] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).

fof(f12656,plain,
    spl0_1533,
    inference(avatar_split_clause,[],[f2347,f12654]) ).

fof(f12654,plain,
    ( spl0_1533
  <=> ! [X18,X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = X18
        | c_0 != c_Nat_Opower(X18,X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).

fof(f2347,axiom,
    ! [X21,X1,X18] :
      ( ~ class_Power_Orecpower(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = X18
      | c_0 != c_Nat_Opower(X18,X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).

fof(f12652,plain,
    spl0_1532,
    inference(avatar_split_clause,[],[f2339,f12650]) ).

fof(f12650,plain,
    ( spl0_1532
  <=> ! [X0,X11] :
        ( ~ c_less(c_0,X0,tc_nat)
        | c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).

fof(f2339,axiom,
    ! [X0,X11] :
      ( ~ c_less(c_0,X0,tc_nat)
      | c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).

fof(f12648,plain,
    spl0_1531,
    inference(avatar_split_clause,[],[f2295,f12646]) ).

fof(f12646,plain,
    ( spl0_1531
  <=> ! [X0,X21] :
        ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
        | ~ c_less(c_0,X21,tc_nat)
        | c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).

fof(f2295,axiom,
    ! [X21,X0] :
      ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
      | ~ c_less(c_0,X21,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).

fof(f12644,plain,
    spl0_1530,
    inference(avatar_split_clause,[],[f2282,f12642]) ).

fof(f12642,plain,
    ( spl0_1530
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X0,tc_nat)
        | ~ c_less(c_0,X3,tc_nat)
        | c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).

fof(f2282,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X0,tc_nat)
      | ~ c_less(c_0,X3,tc_nat)
      | c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).

fof(f12640,plain,
    spl0_1529,
    inference(avatar_split_clause,[],[f2265,f12638]) ).

fof(f12638,plain,
    ( spl0_1529
  <=> ! [X2,X48,X0,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_lessequals(X3,X48,X2)
        | ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).

fof(f2265,axiom,
    ! [X2,X3,X48,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_lessequals(X3,X48,X2)
      | ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).

fof(f12636,plain,
    spl0_1528,
    inference(avatar_split_clause,[],[f2264,f12634]) ).

fof(f12634,plain,
    ( spl0_1528
  <=> ! [X48,X0,X3,X2] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_lessequals(X0,X48,X2)
        | ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).

fof(f2264,axiom,
    ! [X2,X3,X48,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_lessequals(X0,X48,X2)
      | ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).

fof(f12627,plain,
    spl0_1527,
    inference(avatar_split_clause,[],[f2260,f12625]) ).

fof(f12625,plain,
    ( spl0_1527
  <=> ! [X48,X0,X3,X2] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_lessequals(X0,X48,X2)
        | ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).

fof(f2260,axiom,
    ! [X2,X3,X48,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_lessequals(X0,X48,X2)
      | ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).

fof(f12623,plain,
    spl0_1526,
    inference(avatar_split_clause,[],[f2259,f12621]) ).

fof(f12621,plain,
    ( spl0_1526
  <=> ! [X48,X0,X3,X2] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_lessequals(X0,X3,X2)
        | ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).

fof(f2259,axiom,
    ! [X2,X3,X48,X0] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_lessequals(X0,X3,X2)
      | ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).

fof(f12619,plain,
    spl0_1525,
    inference(avatar_split_clause,[],[f2257,f12617]) ).

fof(f12617,plain,
    ( spl0_1525
  <=> ! [X48,X0,X3,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_less(X48,X3,X1)
        | ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).

fof(f2257,axiom,
    ! [X3,X48,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_less(X48,X3,X1)
      | ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).

fof(f12615,plain,
    spl0_1524,
    inference(avatar_split_clause,[],[f2256,f12613]) ).

fof(f12613,plain,
    ( spl0_1524
  <=> ! [X48,X0,X3,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_less(X48,X0,X1)
        | ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).

fof(f2256,axiom,
    ! [X3,X48,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_less(X48,X0,X1)
      | ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).

fof(f12611,plain,
    spl0_1523,
    inference(avatar_split_clause,[],[f2254,f12609]) ).

fof(f12609,plain,
    ( spl0_1523
  <=> ! [X48,X1,X0,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_less(X3,X48,X1)
        | ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).

fof(f2254,axiom,
    ! [X3,X48,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_less(X3,X48,X1)
      | ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).

fof(f12607,plain,
    spl0_1522,
    inference(avatar_split_clause,[],[f2253,f12605]) ).

fof(f12605,plain,
    ( spl0_1522
  <=> ! [X48,X0,X3,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_less(X0,X48,X1)
        | ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).

fof(f2253,axiom,
    ! [X3,X48,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_less(X0,X48,X1)
      | ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).

fof(f12603,plain,
    spl0_1521,
    inference(avatar_split_clause,[],[f2249,f12601]) ).

fof(f12601,plain,
    ( spl0_1521
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(c_0,X18,X1)
        | c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).

fof(f2249,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(c_0,X18,X1)
      | c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).

fof(f12599,plain,
    spl0_1520,
    inference(avatar_split_clause,[],[f2248,f12597]) ).

fof(f12597,plain,
    ( spl0_1520
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_lessequals(c_0,X18,X1)
        | ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).

fof(f2248,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_lessequals(c_0,X18,X1)
      | ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).

fof(f12595,plain,
    spl0_1519,
    inference(avatar_split_clause,[],[f2215,f12593]) ).

fof(f12593,plain,
    ( spl0_1519
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).

fof(f2215,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).

fof(f12591,plain,
    spl0_1518,
    inference(avatar_split_clause,[],[f2212,f12589]) ).

fof(f12589,plain,
    ( spl0_1518
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = X18
        | c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).

fof(f2212,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_0 = X18
      | c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).

fof(f12583,plain,
    spl0_1517,
    inference(avatar_split_clause,[],[f2210,f12581]) ).

fof(f12581,plain,
    ( spl0_1517
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = X18
        | c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).

fof(f2210,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_0 = X18
      | c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).

fof(f12579,plain,
    spl0_1516,
    inference(avatar_split_clause,[],[f2207,f12577]) ).

fof(f12577,plain,
    ( spl0_1516
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(X18,c_0,X1)
        | c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).

fof(f2207,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(X18,c_0,X1)
      | c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).

fof(f12575,plain,
    spl0_1515,
    inference(avatar_split_clause,[],[f2206,f12573]) ).

fof(f12573,plain,
    ( spl0_1515
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_lessequals(X18,c_0,X1)
        | ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).

fof(f2206,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_lessequals(X18,c_0,X1)
      | ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).

fof(f12571,plain,
    spl0_1514,
    inference(avatar_split_clause,[],[f2204,f12569]) ).

fof(f12569,plain,
    ( spl0_1514
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).

fof(f2204,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).

fof(f12567,plain,
    spl0_1513,
    inference(avatar_split_clause,[],[f2203,f12565]) ).

fof(f12565,plain,
    ( spl0_1513
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_less(X18,X27,X1)
        | c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).

fof(f2203,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_less(X18,X27,X1)
      | c_less(c_minus(X18,X27,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).

fof(f12563,plain,
    spl0_1512,
    inference(avatar_split_clause,[],[f2202,f12561]) ).

fof(f12561,plain,
    ( spl0_1512
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_less(X18,X27,X1)
        | ~ c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).

fof(f2202,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_less(X18,X27,X1)
      | ~ c_less(c_minus(X18,X27,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).

fof(f12559,plain,
    spl0_1511,
    inference(avatar_split_clause,[],[f2201,f12557]) ).

fof(f12557,plain,
    ( spl0_1511
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_lessequals(X18,X27,X1)
        | c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).

fof(f2201,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_lessequals(X18,X27,X1)
      | c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).

fof(f12555,plain,
    spl0_1510,
    inference(avatar_split_clause,[],[f2200,f12553]) ).

fof(f12553,plain,
    ( spl0_1510
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_lessequals(X18,X27,X1)
        | ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).

fof(f2200,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_lessequals(X18,X27,X1)
      | ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).

fof(f12551,plain,
    spl0_1509,
    inference(avatar_split_clause,[],[f2184,f12549]) ).

fof(f12549,plain,
    ( spl0_1509
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | ~ c_lessequals(X18,c_0,X1)
        | c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).

fof(f2184,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | ~ c_lessequals(X18,c_0,X1)
      | c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).

fof(f12547,plain,
    spl0_1508,
    inference(avatar_split_clause,[],[f2110,f12545]) ).

fof(f12545,plain,
    ( spl0_1508
  <=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).

fof(f2110,axiom,
    ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).

fof(f12538,plain,
    spl0_1507,
    inference(avatar_split_clause,[],[f2109,f12536]) ).

fof(f12536,plain,
    ( spl0_1507
  <=> ! [X11,X3,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).

fof(f2109,axiom,
    ! [X3,X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).

fof(f12534,plain,
    spl0_1506,
    inference(avatar_split_clause,[],[f2045,f12532]) ).

fof(f12532,plain,
    ( spl0_1506
  <=> ! [X21,X3] :
        ( ~ c_lessequals(X21,X3,tc_nat)
        | c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).

fof(f2045,axiom,
    ! [X21,X3] :
      ( ~ c_lessequals(X21,X3,tc_nat)
      | c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).

fof(f12530,plain,
    spl0_1505,
    inference(avatar_split_clause,[],[f2044,f12528]) ).

fof(f12528,plain,
    ( spl0_1505
  <=> ! [X21,X3] :
        ( ~ c_lessequals(X21,X3,tc_nat)
        | c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).

fof(f2044,axiom,
    ! [X21,X3] :
      ( ~ c_lessequals(X21,X3,tc_nat)
      | c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).

fof(f12526,plain,
    spl0_1504,
    inference(avatar_split_clause,[],[f1852,f12524]) ).

fof(f12524,plain,
    ( spl0_1504
  <=> ! [X47] :
        ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).

fof(f1852,axiom,
    ! [X47] :
      ( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).

fof(f12522,plain,
    spl0_1503,
    inference(avatar_split_clause,[],[f1799,f12520]) ).

fof(f12520,plain,
    ( spl0_1503
  <=> ! [X21,X3] :
        ( ~ c_lessequals(X3,X21,tc_nat)
        | c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).

fof(f1799,axiom,
    ! [X21,X3] :
      ( ~ c_lessequals(X3,X21,tc_nat)
      | c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).

fof(f12518,plain,
    spl0_1502,
    inference(avatar_split_clause,[],[f1765,f12516]) ).

fof(f12516,plain,
    ( spl0_1502
  <=> ! [X0,X12,X1] :
        ( c_in(c_0,X12,tc_nat)
        | c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).

fof(f1765,axiom,
    ! [X0,X1,X12] :
      ( c_in(c_0,X12,tc_nat)
      | c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).

fof(f12514,plain,
    spl0_1501,
    inference(avatar_split_clause,[],[f1748,f12512]) ).

fof(f1748,axiom,
    ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).

fof(f12510,plain,
    spl0_1500,
    inference(avatar_split_clause,[],[f1742,f12508]) ).

fof(f12508,plain,
    ( spl0_1500
  <=> ! [X21,X1,X3] :
        ( c_List_Orotate(X21,X3,X1) = X3
        | ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).

fof(f1742,axiom,
    ! [X21,X3,X1] :
      ( c_List_Orotate(X21,X3,X1) = X3
      | ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).

fof(f12506,plain,
    spl0_1499,
    inference(avatar_split_clause,[],[f1702,f12504]) ).

fof(f12504,plain,
    ( spl0_1499
  <=> ! [X43,X3,X21,X1] :
        ( ~ c_less(X43,X21,tc_nat)
        | c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).

fof(f1702,axiom,
    ! [X21,X3,X1,X43] :
      ( ~ c_less(X43,X21,tc_nat)
      | c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).

fof(f12502,plain,
    spl0_1498,
    inference(avatar_split_clause,[],[f1604,f12500]) ).

fof(f12500,plain,
    ( spl0_1498
  <=> ! [X43,X0,X23,X1] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).

fof(f1604,axiom,
    ! [X0,X1,X23,X43] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).

fof(f12492,plain,
    spl0_1497,
    inference(avatar_split_clause,[],[f1591,f12490]) ).

fof(f12490,plain,
    ( spl0_1497
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X25
        | c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).

fof(f1591,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X25
      | c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).

fof(f12488,plain,
    spl0_1496,
    inference(avatar_split_clause,[],[f1589,f12486]) ).

fof(f12486,plain,
    ( spl0_1496
  <=> ! [X0,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).

fof(f1589,axiom,
    ! [X0,X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).

fof(f12484,plain,
    spl0_1495,
    inference(avatar_split_clause,[],[f1581,f12482]) ).

fof(f12482,plain,
    ( spl0_1495
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).

fof(f1581,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).

fof(f12480,plain,
    spl0_1494,
    inference(avatar_split_clause,[],[f1580,f12478]) ).

fof(f1580,axiom,
    ! [X3,X1] :
      ( c_List_Olist_ONil = X3
      | c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).

fof(f12476,plain,
    spl0_1493,
    inference(avatar_split_clause,[],[f1578,f12474]) ).

fof(f12474,plain,
    ( spl0_1493
  <=> ! [X59,X43,X15] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).

fof(f1578,axiom,
    ! [X59,X15,X43] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).

fof(f12472,plain,
    spl0_1492,
    inference(avatar_split_clause,[],[f1576,f12470]) ).

fof(f1576,axiom,
    ! [X21,X1,X23] :
      ( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
      | ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).

fof(f12468,plain,
    spl0_1491,
    inference(avatar_split_clause,[],[f1575,f12466]) ).

fof(f12466,plain,
    ( spl0_1491
  <=> ! [X21,X1,X23] :
        ( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
        | c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).

fof(f1575,axiom,
    ! [X21,X1,X23] :
      ( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
      | c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).

fof(f12464,plain,
    spl0_1490,
    inference(avatar_split_clause,[],[f1475,f12462]) ).

fof(f12462,plain,
    ( spl0_1490
  <=> ! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).

fof(f1475,axiom,
    ! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).

fof(f12460,plain,
    spl0_1489,
    inference(avatar_split_clause,[],[f1416,f12458]) ).

fof(f12458,plain,
    ( spl0_1489
  <=> ! [X48,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).

fof(f1416,axiom,
    ! [X48,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).

fof(f12456,plain,
    spl0_1488,
    inference(avatar_split_clause,[],[f1305,f12454]) ).

fof(f12454,plain,
    ( spl0_1488
  <=> ! [X21,X16,X15] :
        ( c_Divides_Oop_Advd(X16,X21,tc_nat)
        | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).

fof(f1305,axiom,
    ! [X21,X16,X15] :
      ( c_Divides_Oop_Advd(X16,X21,tc_nat)
      | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).

fof(f12452,plain,
    ( ~ spl0_1487
    | ~ spl0_647
    | ~ spl0_1129
    | ~ spl0_1314 ),
    inference(avatar_split_clause,[],[f10315,f10309,f9201,f6127,f12449]) ).

fof(f10309,plain,
    ( spl0_1314
  <=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).

fof(f10315,plain,
    ( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_1129
    | ~ spl0_1314 ),
    inference(forward_demodulation,[],[f10314,f9202]) ).

fof(f10314,plain,
    ( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_1314 ),
    inference(superposition,[],[f10310,f6129]) ).

fof(f10310,plain,
    ( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1314 ),
    inference(avatar_component_clause,[],[f10309]) ).

fof(f12447,plain,
    spl0_1486,
    inference(avatar_split_clause,[],[f1304,f12445]) ).

fof(f1304,axiom,
    ! [X21,X16,X15] :
      ( c_Divides_Oop_Advd(X16,X15,tc_nat)
      | ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).

fof(f12443,plain,
    spl0_1485,
    inference(avatar_split_clause,[],[f1291,f12441]) ).

fof(f12441,plain,
    ( spl0_1485
  <=> ! [X12,X1,X18] :
        ( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).

fof(f1291,axiom,
    ! [X1,X18,X12] :
      ( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).

fof(f12439,plain,
    spl0_1484,
    inference(avatar_split_clause,[],[f1287,f12437]) ).

fof(f12437,plain,
    ( spl0_1484
  <=> ! [X20,X1,X19] :
        ( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).

fof(f1287,axiom,
    ! [X1,X19,X20] :
      ( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).

fof(f12435,plain,
    spl0_1483,
    inference(avatar_split_clause,[],[f1286,f12433]) ).

fof(f12433,plain,
    ( spl0_1483
  <=> ! [X20,X1,X19] :
        ( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).

fof(f1286,axiom,
    ! [X1,X19,X20] :
      ( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).

fof(f12431,plain,
    spl0_1482,
    inference(avatar_split_clause,[],[f1285,f12429]) ).

fof(f12429,plain,
    ( spl0_1482
  <=> ! [X12,X1] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).

fof(f1285,axiom,
    ! [X1,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).

fof(f12427,plain,
    spl0_1481,
    inference(avatar_split_clause,[],[f1284,f12425]) ).

fof(f12425,plain,
    ( spl0_1481
  <=> ! [X12,X1] :
        ( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).

fof(f1284,axiom,
    ! [X1,X12] :
      ( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).

fof(f12423,plain,
    spl0_1480,
    inference(avatar_split_clause,[],[f1276,f12421]) ).

fof(f12421,plain,
    ( spl0_1480
  <=> ! [X12,X1] :
        ( c_emptyset = X12
        | c_0 != c_Finite__Set_Ocard(X12,X1)
        | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).

fof(f1276,axiom,
    ! [X1,X12] :
      ( c_emptyset = X12
      | c_0 != c_Finite__Set_Ocard(X12,X1)
      | ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).

fof(f12419,plain,
    spl0_1479,
    inference(avatar_split_clause,[],[f1223,f12417]) ).

fof(f12417,plain,
    ( spl0_1479
  <=> ! [X21,X3] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).

fof(f1223,axiom,
    ! [X21,X3] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).

fof(f12415,plain,
    spl0_1478,
    inference(avatar_split_clause,[],[f1221,f12413]) ).

fof(f12413,plain,
    ( spl0_1478
  <=> ! [X21,X3] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).

fof(f1221,axiom,
    ! [X21,X3] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).

fof(f12411,plain,
    spl0_1477,
    inference(avatar_split_clause,[],[f111,f12409]) ).

fof(f111,axiom,
    ! [X1,X12,X13] :
      ( X12 = X13
      | ~ c_lessequals(X12,X13,tc_set(X1))
      | ~ c_lessequals(X13,X12,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

fof(f12396,plain,
    spl0_1476,
    inference(avatar_split_clause,[],[f108,f12394]) ).

fof(f12394,plain,
    ( spl0_1476
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X12,X1)
        | c_in(X4,X13,X1)
        | ~ c_lessequals(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).

fof(f108,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X12,X1)
      | c_in(X4,X13,X1)
      | ~ c_lessequals(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

fof(f12392,plain,
    spl0_1475,
    inference(avatar_split_clause,[],[f104,f12390]) ).

fof(f104,axiom,
    ! [X1,X12,X13] :
      ( X12 = X13
      | ~ c_lessequals(X12,X13,tc_set(X1))
      | c_less(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).

fof(f12388,plain,
    spl0_1474,
    inference(avatar_split_clause,[],[f100,f12386]) ).

fof(f12386,plain,
    ( spl0_1474
  <=> ! [X12,X32,X1] :
        ( ~ c_in(X12,c_Union(X32,X1),X1)
        | c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).

fof(f100,axiom,
    ! [X1,X12,X32] :
      ( ~ c_in(X12,c_Union(X32,X1),X1)
      | c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).

fof(f12384,plain,
    spl0_1473,
    inference(avatar_split_clause,[],[f97,f12382]) ).

fof(f12382,plain,
    ( spl0_1473
  <=> ! [X12,X32,X1] :
        ( c_in(X12,c_Inter(X32,X1),X1)
        | ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).

fof(f97,axiom,
    ! [X1,X12,X32] :
      ( c_in(X12,c_Inter(X32,X1),X1)
      | ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).

fof(f12380,plain,
    spl0_1472,
    inference(avatar_split_clause,[],[f29,f12378]) ).

fof(f12378,plain,
    ( spl0_1472
  <=> ! [X12,X1,X18] :
        ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).

fof(f29,axiom,
    ! [X1,X18,X12] :
      ( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).

fof(f11919,plain,
    ( spl0_1471
    | ~ spl0_659
    | ~ spl0_815
    | ~ spl0_1216 ),
    inference(avatar_split_clause,[],[f9979,f9671,f7623,f6180,f11916]) ).

fof(f11916,plain,
    ( spl0_1471
  <=> c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).

fof(f6180,plain,
    ( spl0_659
  <=> c_emptyset = c_Message_Oparts(c_emptyset) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f7623,plain,
    ( spl0_815
  <=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f9671,plain,
    ( spl0_1216
  <=> ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).

fof(f9979,plain,
    ( c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
    | ~ spl0_659
    | ~ spl0_815
    | ~ spl0_1216 ),
    inference(forward_demodulation,[],[f9974,f7624]) ).

fof(f7624,plain,
    ( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
    | ~ spl0_815 ),
    inference(avatar_component_clause,[],[f7623]) ).

fof(f9974,plain,
    ( c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
    | ~ spl0_659
    | ~ spl0_1216 ),
    inference(superposition,[],[f9672,f6182]) ).

fof(f6182,plain,
    ( c_emptyset = c_Message_Oparts(c_emptyset)
    | ~ spl0_659 ),
    inference(avatar_component_clause,[],[f6180]) ).

fof(f9672,plain,
    ( ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg)
    | ~ spl0_1216 ),
    inference(avatar_component_clause,[],[f9671]) ).

fof(f11822,plain,
    ( spl0_1470
    | ~ spl0_662
    | ~ spl0_815
    | ~ spl0_1215 ),
    inference(avatar_split_clause,[],[f9973,f9667,f7623,f6195,f11819]) ).

fof(f11819,plain,
    ( spl0_1470
  <=> c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).

fof(f6195,plain,
    ( spl0_662
  <=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f9667,plain,
    ( spl0_1215
  <=> ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).

fof(f9973,plain,
    ( c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset))
    | ~ spl0_662
    | ~ spl0_815
    | ~ spl0_1215 ),
    inference(forward_demodulation,[],[f9968,f7624]) ).

fof(f9968,plain,
    ( c_Message_Oanalz(c_Message_Osynth(c_emptyset)) = c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg)
    | ~ spl0_662
    | ~ spl0_1215 ),
    inference(superposition,[],[f9668,f6197]) ).

fof(f6197,plain,
    ( c_emptyset = c_Message_Oanalz(c_emptyset)
    | ~ spl0_662 ),
    inference(avatar_component_clause,[],[f6195]) ).

fof(f9668,plain,
    ( ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg)
    | ~ spl0_1215 ),
    inference(avatar_component_clause,[],[f9667]) ).

fof(f11612,plain,
    ( spl0_1469
    | ~ spl0_726
    | ~ spl0_1196 ),
    inference(avatar_split_clause,[],[f9940,f9591,f7244,f11610]) ).

fof(f11610,plain,
    ( spl0_1469
  <=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).

fof(f7244,plain,
    ( spl0_726
  <=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f9591,plain,
    ( spl0_1196
  <=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).

fof(f9940,plain,
    ( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
    | ~ spl0_726
    | ~ spl0_1196 ),
    inference(superposition,[],[f9592,f7245]) ).

fof(f7245,plain,
    ( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
    | ~ spl0_726 ),
    inference(avatar_component_clause,[],[f7244]) ).

fof(f9592,plain,
    ( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
    | ~ spl0_1196 ),
    inference(avatar_component_clause,[],[f9591]) ).

fof(f11424,plain,
    ( spl0_1468
    | ~ spl0_1081
    | ~ spl0_1330 ),
    inference(avatar_split_clause,[],[f11387,f10761,f8912,f11422]) ).

fof(f8912,plain,
    ( spl0_1081
  <=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f10761,plain,
    ( spl0_1330
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).

fof(f11387,plain,
    ( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
    | ~ spl0_1081
    | ~ spl0_1330 ),
    inference(resolution,[],[f10762,f8913]) ).

fof(f8913,plain,
    ( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
    | ~ spl0_1081 ),
    inference(avatar_component_clause,[],[f8912]) ).

fof(f10762,plain,
    ( ! [X1,X12,X13] :
        ( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
        | c_lessequals(X12,X13,tc_set(X1)) )
    | ~ spl0_1330 ),
    inference(avatar_component_clause,[],[f10761]) ).

fof(f11360,plain,
    spl0_1467,
    inference(avatar_split_clause,[],[f3385,f11358]) ).

fof(f11358,plain,
    ( spl0_1467
  <=> ! [X0,X1] :
        ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_0 = c_Numeral_Onumber__of(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).

fof(f3385,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(X0,X1) ),
    inference(forward_demodulation,[],[f3384,f2115]) ).

fof(f3384,plain,
    ! [X0,X1] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(X0,X1) ),
    inference(forward_demodulation,[],[f3178,f2978]) ).

fof(f3178,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(X0,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
    inference(definition_unfolding,[],[f1338,f2129]) ).

fof(f1338,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(X0,X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).

fof(f11356,plain,
    spl0_1466,
    inference(avatar_split_clause,[],[f3313,f11354]) ).

fof(f11354,plain,
    ( spl0_1466
  <=> ! [X1] :
        ( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
        | ~ class_Power_Orecpower(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).

fof(f3313,plain,
    ! [X1] :
      ( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
      | ~ class_Power_Orecpower(X1) ),
    inference(forward_demodulation,[],[f3312,f2156]) ).

fof(f3312,plain,
    ! [X1] :
      ( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X1)
      | ~ class_Power_Orecpower(X1) ),
    inference(forward_demodulation,[],[f3311,f2154]) ).

fof(f3311,plain,
    ! [X1] :
      ( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X1)
      | ~ class_Power_Orecpower(X1) ),
    inference(forward_demodulation,[],[f1878,f2156]) ).

fof(f1878,axiom,
    ! [X1] :
      ( ~ class_Power_Orecpower(X1)
      | c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).

fof(f11352,plain,
    spl0_1465,
    inference(avatar_split_clause,[],[f3306,f11350]) ).

fof(f3306,plain,
    ! [X1] :
      ( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f3305,f2156]) ).

fof(f3305,plain,
    ! [X1] :
      ( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f3304,f2154]) ).

fof(f3304,plain,
    ! [X1] :
      ( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f1328,f2156]) ).

fof(f1328,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).

fof(f11348,plain,
    spl0_1464,
    inference(avatar_split_clause,[],[f3117,f11346]) ).

fof(f11346,plain,
    ( spl0_1464
  <=> ! [X13,X12,X1] :
        ( c_UNIV = X12
        | c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).

fof(f3117,plain,
    ! [X1,X12,X13] :
      ( c_UNIV = X12
      | c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
    inference(definition_unfolding,[],[f2598,f2373]) ).

fof(f2598,axiom,
    ! [X1,X12,X13] :
      ( c_UNIV = X12
      | c_UNIV != c_inter(X12,X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).

fof(f11344,plain,
    spl0_1463,
    inference(avatar_split_clause,[],[f3116,f11342]) ).

fof(f11342,plain,
    ( spl0_1463
  <=> ! [X13,X12,X1] :
        ( c_UNIV = X13
        | c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).

fof(f3116,plain,
    ! [X1,X12,X13] :
      ( c_UNIV = X13
      | c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
    inference(definition_unfolding,[],[f2599,f2373]) ).

fof(f2599,axiom,
    ! [X1,X12,X13] :
      ( c_UNIV = X13
      | c_UNIV != c_inter(X12,X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).

fof(f11340,plain,
    spl0_1462,
    inference(avatar_split_clause,[],[f3107,f11338]) ).

fof(f11338,plain,
    ( spl0_1462
  <=> ! [X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).

fof(f3107,plain,
    ! [X21,X1] :
      ( ~ class_Power_Orecpower(X1)
      | c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
    inference(definition_unfolding,[],[f2346,f2544]) ).

fof(f2346,axiom,
    ! [X21,X1] :
      ( ~ class_Power_Orecpower(X1)
      | c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).

fof(f11336,plain,
    spl0_1461,
    inference(avatar_split_clause,[],[f3031,f11334]) ).

fof(f3031,plain,
    ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)),
    inference(definition_unfolding,[],[f1372,f2544]) ).

fof(f1372,axiom,
    ! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).

fof(f11332,plain,
    spl0_1460,
    inference(avatar_split_clause,[],[f3028,f11330]) ).

fof(f11330,plain,
    ( spl0_1460
  <=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).

fof(f3028,plain,
    ! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1),
    inference(definition_unfolding,[],[f2578,f2373]) ).

fof(f2578,axiom,
    ! [X1,X12] : c_emptyset = c_inter(c_uminus(X12,tc_set(X1)),X12,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).

fof(f11328,plain,
    spl0_1459,
    inference(avatar_split_clause,[],[f3027,f11326]) ).

fof(f11326,plain,
    ( spl0_1459
  <=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).

fof(f3027,plain,
    ! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1),
    inference(definition_unfolding,[],[f2579,f2373]) ).

fof(f2579,axiom,
    ! [X1,X12] : c_emptyset = c_inter(X12,c_uminus(X12,tc_set(X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).

fof(f11324,plain,
    spl0_1458,
    inference(avatar_split_clause,[],[f2935,f11322]) ).

fof(f11322,plain,
    ( spl0_1458
  <=> ! [X86,X91,X88] :
        ( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).

fof(f2935,axiom,
    ! [X91,X88,X86] :
      ( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).

fof(f11320,plain,
    ( spl0_1457
    | ~ spl0_650
    | ~ spl0_1166 ),
    inference(avatar_split_clause,[],[f9857,f9471,f6141,f11318]) ).

fof(f11318,plain,
    ( spl0_1457
  <=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).

fof(f6141,plain,
    ( spl0_650
  <=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f9471,plain,
    ( spl0_1166
  <=> ! [X48,X11] :
        ( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).

fof(f9857,plain,
    ( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_650
    | ~ spl0_1166 ),
    inference(resolution,[],[f9472,f6142]) ).

fof(f6142,plain,
    ( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
    | ~ spl0_650 ),
    inference(avatar_component_clause,[],[f6141]) ).

fof(f9472,plain,
    ( ! [X48,X11] :
        ( ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint)
        | c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
    | ~ spl0_1166 ),
    inference(avatar_component_clause,[],[f9471]) ).

fof(f11316,plain,
    spl0_1456,
    inference(avatar_split_clause,[],[f2897,f11314]) ).

fof(f11314,plain,
    ( spl0_1456
  <=> ! [X102,X12] :
        ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
        | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).

fof(f2897,axiom,
    ! [X12,X102] :
      ( ~ c_in(X12,c_Event_Obad,tc_Message_Oagent)
      | c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).

fof(f11312,plain,
    spl0_1455,
    inference(avatar_split_clause,[],[f2893,f11310]) ).

fof(f11310,plain,
    ( spl0_1455
  <=> ! [X86,X87,X88] :
        ( c_in(X86,c_Event_Oused(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).

fof(f2893,axiom,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Event_Oused(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).

fof(f11308,plain,
    spl0_1454,
    inference(avatar_split_clause,[],[f2892,f11306]) ).

fof(f11306,plain,
    ( spl0_1454
  <=> ! [X87,X86,X88] :
        ( c_in(X87,c_Event_Oused(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).

fof(f2892,axiom,
    ! [X88,X86,X87] :
      ( c_in(X87,c_Event_Oused(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Event_Oused(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).

fof(f11304,plain,
    spl0_1453,
    inference(avatar_split_clause,[],[f2851,f11302]) ).

fof(f11302,plain,
    ( spl0_1453
  <=> ! [X20,X88] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X88,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).

fof(f2851,axiom,
    ! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Oanalz(X20),X88,tc_Message_Omsg)) = c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).

fof(f11300,plain,
    spl0_1452,
    inference(avatar_split_clause,[],[f2834,f11298]) ).

fof(f2834,axiom,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).

fof(f11296,plain,
    spl0_1451,
    inference(avatar_split_clause,[],[f2833,f11294]) ).

fof(f2833,axiom,
    ! [X88,X86,X87] :
      ( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).

fof(f11292,plain,
    spl0_1450,
    inference(avatar_split_clause,[],[f2796,f11290]) ).

fof(f11290,plain,
    ( spl0_1450
  <=> ! [X102,X86,X12] : c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).

fof(f2796,axiom,
    ! [X86,X102,X12] : c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Gets_0) ).

fof(f11288,plain,
    spl0_1449,
    inference(avatar_split_clause,[],[f2794,f11286]) ).

fof(f11286,plain,
    ( spl0_1449
  <=> ! [X24,X88] :
        ( ~ c_in(c_Message_Omsg_OKey(X24),X88,tc_Message_Omsg)
        | c_in(c_Message_OinvKey(X24),c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).

fof(f2794,axiom,
    ! [X88,X24] :
      ( ~ c_in(c_Message_Omsg_OKey(X24),X88,tc_Message_Omsg)
      | c_in(c_Message_OinvKey(X24),c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_3) ).

fof(f11284,plain,
    spl0_1448,
    inference(avatar_split_clause,[],[f2783,f11282]) ).

fof(f11282,plain,
    ( spl0_1448
  <=> ! [X105,X106,X97,X104,X103,X96] :
        ( X96 = X97
        | c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).

fof(f2783,axiom,
    ! [X106,X96,X97,X104,X105,X103] :
      ( X96 = X97
      | c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_2) ).

fof(f11280,plain,
    spl0_1447,
    inference(avatar_split_clause,[],[f2782,f11278]) ).

fof(f11278,plain,
    ( spl0_1447
  <=> ! [X105,X106,X97,X104,X103,X96] :
        ( X104 = X106
        | c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).

fof(f2782,axiom,
    ! [X106,X96,X97,X104,X105,X103] :
      ( X104 = X106
      | c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_1) ).

fof(f11276,plain,
    ( spl0_1446
    | ~ spl0_650
    | ~ spl0_1163 ),
    inference(avatar_split_clause,[],[f9847,f9458,f6141,f11274]) ).

fof(f11274,plain,
    ( spl0_1446
  <=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).

fof(f9458,plain,
    ( spl0_1163
  <=> ! [X48,X11] :
        ( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
        | ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f9847,plain,
    ( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
    | ~ spl0_650
    | ~ spl0_1163 ),
    inference(resolution,[],[f9459,f6142]) ).

fof(f9459,plain,
    ( ! [X48,X11] :
        ( ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
    | ~ spl0_1163 ),
    inference(avatar_component_clause,[],[f9458]) ).

fof(f11272,plain,
    spl0_1445,
    inference(avatar_split_clause,[],[f2781,f11270]) ).

fof(f11270,plain,
    ( spl0_1445
  <=> ! [X105,X106,X97,X104,X96,X103] :
        ( X103 = X105
        | c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).

fof(f2781,axiom,
    ! [X106,X96,X97,X104,X105,X103] :
      ( X103 = X105
      | c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OSays(X105,X106,X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_0) ).

fof(f11268,plain,
    spl0_1444,
    inference(avatar_split_clause,[],[f2774,f11266]) ).

fof(f2774,axiom,
    ! [X4,X102] :
      ( c_in(X4,c_Event_Oused(X102),tc_Message_Omsg)
      | ~ c_in(X4,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).

fof(f11264,plain,
    spl0_1443,
    inference(avatar_split_clause,[],[f2771,f11262]) ).

fof(f11262,plain,
    ( spl0_1443
  <=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).

fof(f2771,axiom,
    ! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).

fof(f11260,plain,
    spl0_1442,
    inference(avatar_split_clause,[],[f2768,f11258]) ).

fof(f11258,plain,
    ( spl0_1442
  <=> ! [X20,X88] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).

fof(f2768,axiom,
    ! [X88,X20] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).

fof(f11256,plain,
    spl0_1441,
    inference(avatar_split_clause,[],[f2742,f11254]) ).

fof(f11254,plain,
    ( spl0_1441
  <=> ! [X93,X88] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).

fof(f2742,axiom,
    ! [X88,X93] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).

fof(f11252,plain,
    spl0_1440,
    inference(avatar_split_clause,[],[f2729,f11250]) ).

fof(f11250,plain,
    ( spl0_1440
  <=> ! [X86,X87,X88] :
        ( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).

fof(f2729,axiom,
    ! [X88,X86,X87] :
      ( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).

fof(f11248,plain,
    spl0_1439,
    inference(avatar_split_clause,[],[f2728,f11246]) ).

fof(f11246,plain,
    ( spl0_1439
  <=> ! [X87,X86,X88] :
        ( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).

fof(f2728,axiom,
    ! [X88,X86,X87] :
      ( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).

fof(f11244,plain,
    spl0_1438,
    inference(avatar_split_clause,[],[f2703,f11242]) ).

fof(f11242,plain,
    ( spl0_1438
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).

fof(f2703,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).

fof(f11240,plain,
    spl0_1437,
    inference(avatar_split_clause,[],[f2701,f11238]) ).

fof(f11238,plain,
    ( spl0_1437
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).

fof(f2701,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).

fof(f11236,plain,
    spl0_1436,
    inference(avatar_split_clause,[],[f2692,f11234]) ).

fof(f11234,plain,
    ( spl0_1436
  <=> ! [X18,X12,X27,X1] :
        ( X18 = X27
        | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).

fof(f2692,axiom,
    ! [X18,X1,X27,X12] :
      ( X18 = X27
      | c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).

fof(f11219,plain,
    spl0_1435,
    inference(avatar_split_clause,[],[f2688,f11217]) ).

fof(f11217,plain,
    ( spl0_1435
  <=> ! [X13,X0,X12,X1] :
        ( c_in(X0,X13,X1)
        | ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).

fof(f2688,axiom,
    ! [X0,X1,X12,X13] :
      ( c_in(X0,X13,X1)
      | ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).

fof(f11215,plain,
    spl0_1434,
    inference(avatar_split_clause,[],[f2676,f11213]) ).

fof(f11213,plain,
    ( spl0_1434
  <=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).

fof(f2676,axiom,
    ! [X0,X1,X12] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).

fof(f11211,plain,
    spl0_1433,
    inference(avatar_split_clause,[],[f2670,f11209]) ).

fof(f11209,plain,
    ( spl0_1433
  <=> ! [X12,X1] :
        ( c_emptyset = c_Union(X12,X1)
        | c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).

fof(f2670,axiom,
    ! [X1,X12] :
      ( c_emptyset = c_Union(X12,X1)
      | c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).

fof(f11207,plain,
    spl0_1432,
    inference(avatar_split_clause,[],[f2653,f11205]) ).

fof(f11205,plain,
    ( spl0_1432
  <=> ! [X12,X1] :
        ( c_emptyset = c_Union(X12,X1)
        | c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).

fof(f2653,axiom,
    ! [X1,X12] :
      ( c_emptyset = c_Union(X12,X1)
      | c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).

fof(f11203,plain,
    spl0_1431,
    inference(avatar_split_clause,[],[f2628,f11201]) ).

fof(f11201,plain,
    ( spl0_1431
  <=> ! [X13,X12,X1] :
        ( ~ c_lessequals(X12,X13,tc_set(X1))
        | c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).

fof(f2628,axiom,
    ! [X1,X12,X13] :
      ( ~ c_lessequals(X12,X13,tc_set(X1))
      | c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).

fof(f11199,plain,
    spl0_1430,
    inference(avatar_split_clause,[],[f2627,f11197]) ).

fof(f11197,plain,
    ( spl0_1430
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).

fof(f2627,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).

fof(f11195,plain,
    spl0_1429,
    inference(avatar_split_clause,[],[f2617,f11193]) ).

fof(f11193,plain,
    ( spl0_1429
  <=> ! [X12,X1] :
        ( c_UNIV = c_Inter(X12,X1)
        | c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).

fof(f2617,axiom,
    ! [X1,X12] :
      ( c_UNIV = c_Inter(X12,X1)
      | c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).

fof(f11191,plain,
    spl0_1428,
    inference(avatar_split_clause,[],[f2614,f11189]) ).

fof(f11189,plain,
    ( spl0_1428
  <=> ! [X12,X1] :
        ( c_UNIV = c_Inter(X12,X1)
        | c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).

fof(f2614,axiom,
    ! [X1,X12] :
      ( c_UNIV = c_Inter(X12,X1)
      | c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).

fof(f11187,plain,
    spl0_1427,
    inference(avatar_split_clause,[],[f2595,f11185]) ).

fof(f2595,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X13,X1)
      | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).

fof(f11183,plain,
    spl0_1426,
    inference(avatar_split_clause,[],[f2594,f11181]) ).

fof(f11181,plain,
    ( spl0_1426
  <=> ! [X4,X13,X12,X1] :
        ( c_in(X4,X12,X1)
        | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).

fof(f2594,axiom,
    ! [X1,X4,X12,X13] :
      ( c_in(X4,X12,X1)
      | ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).

fof(f11173,plain,
    spl0_1425,
    inference(avatar_split_clause,[],[f2592,f11171]) ).

fof(f11171,plain,
    ( spl0_1425
  <=> ! [X13,X12,X1] :
        ( ~ c_lessequals(X12,X13,tc_set(X1))
        | c_emptyset = c_minus(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).

fof(f2592,axiom,
    ! [X1,X12,X13] :
      ( ~ c_lessequals(X12,X13,tc_set(X1))
      | c_emptyset = c_minus(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).

fof(f11169,plain,
    spl0_1424,
    inference(avatar_split_clause,[],[f2591,f11167]) ).

fof(f2591,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | c_emptyset != c_minus(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).

fof(f11165,plain,
    spl0_1423,
    inference(avatar_split_clause,[],[f2581,f11163]) ).

fof(f11163,plain,
    ( spl0_1423
  <=> ! [X13,X12,X1] :
        ( X12 = X13
        | c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).

fof(f2581,axiom,
    ! [X1,X12,X13] :
      ( X12 = X13
      | c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).

fof(f11161,plain,
    spl0_1422,
    inference(avatar_split_clause,[],[f2570,f11159]) ).

fof(f11159,plain,
    ( spl0_1422
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_less(X43,X16,X1)
        | c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).

fof(f2570,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_less(X43,X16,X1)
      | c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).

fof(f11157,plain,
    spl0_1421,
    inference(avatar_split_clause,[],[f2569,f11155]) ).

fof(f11155,plain,
    ( spl0_1421
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X43,X16,X1)
        | ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).

fof(f2569,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X43,X16,X1)
      | ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).

fof(f11153,plain,
    spl0_1420,
    inference(avatar_split_clause,[],[f2568,f11151]) ).

fof(f11151,plain,
    ( spl0_1420
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).

fof(f2568,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).

fof(f11149,plain,
    spl0_1419,
    inference(avatar_split_clause,[],[f2559,f11147]) ).

fof(f11147,plain,
    ( spl0_1419
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_less(X16,X43,X1)
        | c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).

fof(f2559,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_less(X16,X43,X1)
      | c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).

fof(f11145,plain,
    spl0_1418,
    inference(avatar_split_clause,[],[f2558,f11143]) ).

fof(f11143,plain,
    ( spl0_1418
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | c_less(X16,X43,X1)
        | ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).

fof(f2558,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_less(X16,X43,X1)
      | ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).

fof(f11141,plain,
    spl0_1417,
    inference(avatar_split_clause,[],[f2557,f11139]) ).

fof(f11139,plain,
    ( spl0_1417
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).

fof(f2557,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).

fof(f11137,plain,
    spl0_1416,
    inference(avatar_split_clause,[],[f2550,f11135]) ).

fof(f2550,axiom,
    ! [X1,X26,X16] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_lessequals(X26,X16,X1)
      | c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).

fof(f11120,plain,
    spl0_1415,
    inference(avatar_split_clause,[],[f2546,f11118]) ).

fof(f11118,plain,
    ( spl0_1415
  <=> ! [X14,X26] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).

fof(f2546,axiom,
    ! [X26,X14] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).

fof(f11116,plain,
    spl0_1414,
    inference(avatar_split_clause,[],[f2543,f11114]) ).

fof(f11114,plain,
    ( spl0_1414
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).

fof(f2543,axiom,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).

fof(f11112,plain,
    spl0_1413,
    inference(avatar_split_clause,[],[f2537,f11110]) ).

fof(f11110,plain,
    ( spl0_1413
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_lessequals(X43,X16,X1)
        | c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).

fof(f2537,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_lessequals(X43,X16,X1)
      | c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).

fof(f11108,plain,
    spl0_1412,
    inference(avatar_split_clause,[],[f2536,f11106]) ).

fof(f11106,plain,
    ( spl0_1412
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X43,X16,X1)
        | ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).

fof(f2536,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X43,X16,X1)
      | ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).

fof(f11104,plain,
    spl0_1411,
    inference(avatar_split_clause,[],[f2535,f11102]) ).

fof(f11102,plain,
    ( spl0_1411
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).

fof(f2535,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).

fof(f11100,plain,
    spl0_1410,
    inference(avatar_split_clause,[],[f2531,f11098]) ).

fof(f11098,plain,
    ( spl0_1410
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | ~ c_lessequals(X16,X43,X1)
        | c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).

fof(f2531,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | ~ c_lessequals(X16,X43,X1)
      | c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).

fof(f11096,plain,
    spl0_1409,
    inference(avatar_split_clause,[],[f2530,f11094]) ).

fof(f11094,plain,
    ( spl0_1409
  <=> ! [X16,X1,X43] :
        ( ~ class_Orderings_Oord(X1)
        | c_lessequals(X16,X43,X1)
        | ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).

fof(f2530,axiom,
    ! [X1,X16,X43] :
      ( ~ class_Orderings_Oord(X1)
      | c_lessequals(X16,X43,X1)
      | ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).

fof(f11092,plain,
    spl0_1408,
    inference(avatar_split_clause,[],[f2529,f11090]) ).

fof(f11090,plain,
    ( spl0_1408
  <=> ! [X0,X1,X3] :
        ( ~ class_Orderings_Olinorder(X1)
        | X0 = X3
        | c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).

fof(f2529,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | X0 = X3
      | c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).

fof(f11088,plain,
    spl0_1407,
    inference(avatar_split_clause,[],[f2523,f11086]) ).

fof(f2523,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_lessequals(X21,X15,X1)
      | c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).

fof(f11084,plain,
    spl0_1406,
    inference(avatar_split_clause,[],[f2518,f11082]) ).

fof(f2518,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_less(X21,X15,X1)
      | c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).

fof(f11074,plain,
    spl0_1405,
    inference(avatar_split_clause,[],[f2517,f11072]) ).

fof(f11072,plain,
    ( spl0_1405
  <=> ! [X16,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).

fof(f2517,axiom,
    ! [X1,X16] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).

fof(f11070,plain,
    spl0_1404,
    inference(avatar_split_clause,[],[f2516,f11068]) ).

fof(f11068,plain,
    ( spl0_1404
  <=> ! [X16,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).

fof(f2516,axiom,
    ! [X1,X16] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).

fof(f11066,plain,
    spl0_1403,
    inference(avatar_split_clause,[],[f2515,f11064]) ).

fof(f11064,plain,
    ( spl0_1403
  <=> ! [X16,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).

fof(f2515,axiom,
    ! [X1,X16] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).

fof(f11062,plain,
    spl0_1402,
    inference(avatar_split_clause,[],[f2514,f11060]) ).

fof(f11060,plain,
    ( spl0_1402
  <=> ! [X16,X1] :
        ( ~ class_Orderings_Olinorder(X1)
        | c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).

fof(f2514,axiom,
    ! [X1,X16] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).

fof(f11058,plain,
    spl0_1401,
    inference(avatar_split_clause,[],[f2302,f11056]) ).

fof(f11056,plain,
    ( spl0_1401
  <=> ! [X0,X3] :
        ( c_Parity_Oeven(X3,tc_IntDef_Oint)
        | c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).

fof(f2302,axiom,
    ! [X3,X0] :
      ( c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).

fof(f11054,plain,
    spl0_1400,
    inference(avatar_split_clause,[],[f2301,f11052]) ).

fof(f11052,plain,
    ( spl0_1400
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).

fof(f2301,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).

fof(f11050,plain,
    spl0_1399,
    inference(avatar_split_clause,[],[f2300,f11048]) ).

fof(f11048,plain,
    ( spl0_1399
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(X3,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).

fof(f2300,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).

fof(f11046,plain,
    spl0_1398,
    inference(avatar_split_clause,[],[f2299,f11044]) ).

fof(f11044,plain,
    ( spl0_1398
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
        | c_Parity_Oeven(X0,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).

fof(f2299,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(X0,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).

fof(f11042,plain,
    spl0_1397,
    inference(avatar_split_clause,[],[f2296,f11040]) ).

fof(f11040,plain,
    ( spl0_1397
  <=> ! [X0,X3] :
        ( c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(X3,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).

fof(f2296,axiom,
    ! [X3,X0] :
      ( c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).

fof(f11038,plain,
    spl0_1396,
    inference(avatar_split_clause,[],[f2289,f11036]) ).

fof(f11036,plain,
    ( spl0_1396
  <=> ! [X0,X3] :
        ( c_Parity_Oeven(X3,tc_nat)
        | c_Parity_Oeven(X0,tc_nat)
        | c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).

fof(f2289,axiom,
    ! [X3,X0] :
      ( c_Parity_Oeven(X3,tc_nat)
      | c_Parity_Oeven(X0,tc_nat)
      | c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).

fof(f11031,plain,
    spl0_1395,
    inference(avatar_split_clause,[],[f2288,f11029]) ).

fof(f11029,plain,
    ( spl0_1395
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_nat)
        | ~ c_Parity_Oeven(X0,tc_nat)
        | c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).

fof(f2288,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_nat)
      | ~ c_Parity_Oeven(X0,tc_nat)
      | c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).

fof(f11027,plain,
    spl0_1394,
    inference(avatar_split_clause,[],[f2287,f11025]) ).

fof(f11025,plain,
    ( spl0_1394
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X0,tc_nat)
        | c_Parity_Oeven(X3,tc_nat)
        | ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).

fof(f2287,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X0,tc_nat)
      | c_Parity_Oeven(X3,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).

fof(f11023,plain,
    spl0_1393,
    inference(avatar_split_clause,[],[f2286,f11021]) ).

fof(f11021,plain,
    ( spl0_1393
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_nat)
        | c_Parity_Oeven(X0,tc_nat)
        | ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).

fof(f2286,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_nat)
      | c_Parity_Oeven(X0,tc_nat)
      | ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).

fof(f11019,plain,
    spl0_1392,
    inference(avatar_split_clause,[],[f2283,f11017]) ).

fof(f11017,plain,
    ( spl0_1392
  <=> ! [X0,X3] :
        ( c_Parity_Oeven(X0,tc_nat)
        | c_Parity_Oeven(X3,tc_nat)
        | ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).

fof(f2283,axiom,
    ! [X3,X0] :
      ( c_Parity_Oeven(X0,tc_nat)
      | c_Parity_Oeven(X3,tc_nat)
      | ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).

fof(f11015,plain,
    spl0_1391,
    inference(avatar_split_clause,[],[f2277,f11013]) ).

fof(f11013,plain,
    ( spl0_1391
  <=> ! [X0,X3] :
        ( c_Parity_Oeven(X3,tc_IntDef_Oint)
        | c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).

fof(f2277,axiom,
    ! [X3,X0] :
      ( c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).

fof(f11011,plain,
    spl0_1390,
    inference(avatar_split_clause,[],[f2276,f11009]) ).

fof(f11009,plain,
    ( spl0_1390
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).

fof(f2276,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).

fof(f11007,plain,
    spl0_1389,
    inference(avatar_split_clause,[],[f2275,f11005]) ).

fof(f11005,plain,
    ( spl0_1389
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(X3,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).

fof(f2275,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(X3,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).

fof(f11003,plain,
    spl0_1388,
    inference(avatar_split_clause,[],[f2274,f11001]) ).

fof(f11001,plain,
    ( spl0_1388
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
        | c_Parity_Oeven(X0,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).

fof(f2274,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(X0,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).

fof(f10999,plain,
    spl0_1387,
    inference(avatar_split_clause,[],[f2234,f10997]) ).

fof(f10997,plain,
    ( spl0_1387
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_less(c_0,X18,X1)
        | c_less(c_uminus(X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).

fof(f2234,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_less(c_0,X18,X1)
      | c_less(c_uminus(X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).

fof(f10995,plain,
    spl0_1386,
    inference(avatar_split_clause,[],[f2233,f10993]) ).

fof(f10993,plain,
    ( spl0_1386
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_less(c_0,X18,X1)
        | ~ c_less(c_uminus(X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).

fof(f2233,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_less(c_0,X18,X1)
      | ~ c_less(c_uminus(X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).

fof(f10990,plain,
    spl0_1385,
    inference(avatar_split_clause,[],[f2230,f10988]) ).

fof(f10988,plain,
    ( spl0_1385
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_lessequals(c_0,X18,X1)
        | c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).

fof(f2230,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_lessequals(c_0,X18,X1)
      | c_lessequals(c_uminus(X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).

fof(f10986,plain,
    spl0_1384,
    inference(avatar_split_clause,[],[f2229,f10984]) ).

fof(f10984,plain,
    ( spl0_1384
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_lessequals(c_0,X18,X1)
        | ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).

fof(f2229,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_lessequals(c_0,X18,X1)
      | ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).

fof(f10982,plain,
    spl0_1383,
    inference(avatar_split_clause,[],[f2227,f10980]) ).

fof(f10980,plain,
    ( spl0_1383
  <=> ! [X18,X27,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | X18 = X27
        | c_uminus(X18,X1) != c_uminus(X27,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).

fof(f2227,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | X18 = X27
      | c_uminus(X18,X1) != c_uminus(X27,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).

fof(f10978,plain,
    spl0_1382,
    inference(avatar_split_clause,[],[f2224,f10976]) ).

fof(f10976,plain,
    ( spl0_1382
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | ~ c_less(X18,c_0,X1)
        | c_less(c_0,c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).

fof(f2224,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_less(X18,c_0,X1)
      | c_less(c_0,c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).

fof(f10974,plain,
    spl0_1381,
    inference(avatar_split_clause,[],[f2223,f10972]) ).

fof(f10972,plain,
    ( spl0_1381
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
        | c_less(X18,c_0,X1)
        | ~ c_less(c_0,c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).

fof(f2223,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_less(X18,c_0,X1)
      | ~ c_less(c_0,c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).

fof(f10970,plain,
    spl0_1380,
    inference(avatar_split_clause,[],[f2222,f10968]) ).

fof(f2222,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | ~ c_lessequals(X18,c_0,X1)
      | c_lessequals(c_0,c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).

fof(f10966,plain,
    spl0_1379,
    inference(avatar_split_clause,[],[f2221,f10964]) ).

fof(f2221,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_lessequals(X18,c_0,X1)
      | ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).

fof(f10962,plain,
    spl0_1378,
    inference(avatar_split_clause,[],[f2167,f10960]) ).

fof(f10960,plain,
    ( spl0_1378
  <=> ! [X48,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).

fof(f2167,axiom,
    ! [X48,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).

fof(f10958,plain,
    spl0_1377,
    inference(avatar_split_clause,[],[f2166,f10956]) ).

fof(f10956,plain,
    ( spl0_1377
  <=> ! [X48,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).

fof(f2166,axiom,
    ! [X48,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).

fof(f10954,plain,
    spl0_1376,
    inference(avatar_split_clause,[],[f2086,f10952]) ).

fof(f10952,plain,
    ( spl0_1376
  <=> ! [X21,X16,X15] :
        ( X15 = X21
        | c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).

fof(f2086,axiom,
    ! [X21,X16,X15] :
      ( X15 = X21
      | c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).

fof(f10946,plain,
    spl0_1375,
    inference(avatar_split_clause,[],[f2081,f10944]) ).

fof(f10944,plain,
    ( spl0_1375
  <=> ! [X21,X16,X15] :
        ( X15 = X21
        | c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).

fof(f2081,axiom,
    ! [X21,X16,X15] :
      ( X15 = X21
      | c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).

fof(f10942,plain,
    spl0_1374,
    inference(avatar_split_clause,[],[f2065,f10940]) ).

fof(f10940,plain,
    ( spl0_1374
  <=> ! [X21,X15] :
        ( c_0 = X15
        | c_0 = X21
        | c_0 != c_times(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).

fof(f2065,axiom,
    ! [X21,X15] :
      ( c_0 = X15
      | c_0 = X21
      | c_0 != c_times(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).

fof(f10938,plain,
    spl0_1373,
    inference(avatar_split_clause,[],[f1850,f10936]) ).

fof(f1850,axiom,
    ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).

fof(f10934,plain,
    spl0_1372,
    inference(avatar_split_clause,[],[f1813,f10932]) ).

fof(f10932,plain,
    ( spl0_1372
  <=> ! [X21,X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | X15 = X21
        | c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).

fof(f1813,axiom,
    ! [X21,X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | X15 = X21
      | c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).

fof(f10930,plain,
    spl0_1371,
    inference(avatar_split_clause,[],[f1807,f10928]) ).

fof(f10928,plain,
    ( spl0_1371
  <=> ! [X21,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_less(c_0,X21,tc_nat)
        | c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).

fof(f1807,axiom,
    ! [X21,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_less(c_0,X21,tc_nat)
      | c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).

fof(f10926,plain,
    spl0_1370,
    inference(avatar_split_clause,[],[f1806,f10924]) ).

fof(f10924,plain,
    ( spl0_1370
  <=> ! [X21,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_less(c_0,X21,tc_nat)
        | ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).

fof(f1806,axiom,
    ! [X21,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_less(c_0,X21,tc_nat)
      | ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).

fof(f10922,plain,
    spl0_1369,
    inference(avatar_split_clause,[],[f1784,f10920]) ).

fof(f10920,plain,
    ( spl0_1369
  <=> ! [X59,X43] :
        ( c_0 = X59
        | c_lessequals(X59,X43,tc_nat)
        | c_List_Olist_ONil != c_List_Oupt(X43,X59) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).

fof(f1784,axiom,
    ! [X59,X43] :
      ( c_0 = X59
      | c_lessequals(X59,X43,tc_nat)
      | c_List_Olist_ONil != c_List_Oupt(X43,X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).

fof(f10918,plain,
    spl0_1368,
    inference(avatar_split_clause,[],[f1743,f10916]) ).

fof(f10916,plain,
    ( spl0_1368
  <=> ! [X51,X23,X25,X1] :
        ( X25 = X51
        | c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).

fof(f1743,axiom,
    ! [X51,X1,X25,X23] :
      ( X25 = X51
      | c_append(X23,X25,X1) != c_append(X23,X51,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).

fof(f10914,plain,
    spl0_1367,
    inference(avatar_split_clause,[],[f1737,f10912]) ).

fof(f10912,plain,
    ( spl0_1367
  <=> ! [X1,X3] :
        ( c_List_Orotate1(X3,X1) = X3
        | ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).

fof(f1737,axiom,
    ! [X3,X1] :
      ( c_List_Orotate1(X3,X1) = X3
      | ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).

fof(f10910,plain,
    spl0_1366,
    inference(avatar_split_clause,[],[f1626,f10908]) ).

fof(f10908,plain,
    ( spl0_1366
  <=> ! [X18,X42,X64,X63,X1] :
        ( X63 = X64
        | c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).

fof(f1626,axiom,
    ! [X1,X18,X63,X42,X64] :
      ( X63 = X64
      | c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).

fof(f10906,plain,
    ( spl0_1365
    | ~ spl0_717
    | ~ spl0_798
    | ~ spl0_1120 ),
    inference(avatar_split_clause,[],[f9324,f9068,f7554,f7205,f10903]) ).

fof(f9068,plain,
    ( spl0_1120
  <=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f9324,plain,
    ( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
    | ~ spl0_717
    | ~ spl0_798
    | ~ spl0_1120 ),
    inference(forward_demodulation,[],[f9321,f7207]) ).

fof(f9321,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_798
    | ~ spl0_1120 ),
    inference(superposition,[],[f9069,f7556]) ).

fof(f9069,plain,
    ( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin)
    | ~ spl0_1120 ),
    inference(avatar_component_clause,[],[f9068]) ).

fof(f10901,plain,
    spl0_1364,
    inference(avatar_split_clause,[],[f1625,f10899]) ).

fof(f10899,plain,
    ( spl0_1364
  <=> ! [X18,X42,X64,X63,X1] :
        ( X18 = X42
        | c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).

fof(f1625,axiom,
    ! [X18,X1,X63,X42,X64] :
      ( X18 = X42
      | c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).

fof(f10897,plain,
    spl0_1363,
    inference(avatar_split_clause,[],[f1610,f10895]) ).

fof(f10895,plain,
    ( spl0_1363
  <=> ! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).

fof(f1610,axiom,
    ! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).

fof(f10893,plain,
    spl0_1362,
    inference(avatar_split_clause,[],[f1552,f10891]) ).

fof(f10891,plain,
    ( spl0_1362
  <=> ! [X41,X0,X23] :
        ( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
        | ~ c_in(X0,c_List_Oset(X23,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).

fof(f1552,axiom,
    ! [X41,X0,X23] :
      ( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
      | ~ c_in(X0,c_List_Oset(X23,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).

fof(f10889,plain,
    spl0_1361,
    inference(avatar_split_clause,[],[f1530,f10887]) ).

fof(f10887,plain,
    ( spl0_1361
  <=> ! [X51,X23,X25,X1] :
        ( X25 = X51
        | c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).

fof(f1530,axiom,
    ! [X51,X1,X25,X23] :
      ( X25 = X51
      | c_append(X25,X23,X1) != c_append(X51,X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).

fof(f10885,plain,
    spl0_1360,
    inference(avatar_split_clause,[],[f1493,f10883]) ).

fof(f10883,plain,
    ( spl0_1360
  <=> ! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).

fof(f1493,axiom,
    ! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).

fof(f10881,plain,
    spl0_1359,
    inference(avatar_split_clause,[],[f1492,f10879]) ).

fof(f10879,plain,
    ( spl0_1359
  <=> ! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).

fof(f1492,axiom,
    ! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).

fof(f10877,plain,
    spl0_1358,
    inference(avatar_split_clause,[],[f1485,f10875]) ).

fof(f10875,plain,
    ( spl0_1358
  <=> ! [X0,X21] :
        ( c_0 = X0
        | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).

fof(f1485,axiom,
    ! [X21,X0] :
      ( c_0 = X0
      | c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).

fof(f10872,plain,
    ( spl0_1357
    | ~ spl0_917
    | ~ spl0_1356 ),
    inference(avatar_split_clause,[],[f10868,f10865,f8106,f10870]) ).

fof(f10870,plain,
    ( spl0_1357
  <=> ! [X21] :
        ( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = X21 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).

fof(f8106,plain,
    ( spl0_917
  <=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).

fof(f10865,plain,
    ( spl0_1356
  <=> ! [X21] :
        ( c_0 = X21
        | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).

fof(f10868,plain,
    ( ! [X21] :
        ( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = X21 )
    | ~ spl0_917
    | ~ spl0_1356 ),
    inference(forward_demodulation,[],[f10866,f8108]) ).

fof(f8108,plain,
    ( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
    | ~ spl0_917 ),
    inference(avatar_component_clause,[],[f8106]) ).

fof(f10866,plain,
    ( ! [X21] :
        ( c_0 = X21
        | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) )
    | ~ spl0_1356 ),
    inference(avatar_component_clause,[],[f10865]) ).

fof(f10867,plain,
    spl0_1356,
    inference(avatar_split_clause,[],[f1484,f10865]) ).

fof(f1484,axiom,
    ! [X21] :
      ( c_0 = X21
      | ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).

fof(f10863,plain,
    spl0_1355,
    inference(avatar_split_clause,[],[f1477,f10861]) ).

fof(f10861,plain,
    ( spl0_1355
  <=> ! [X27,X3] :
        ( c_0 = X27
        | c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).

fof(f1477,axiom,
    ! [X3,X27] :
      ( c_0 = X27
      | c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).

fof(f10859,plain,
    spl0_1354,
    inference(avatar_split_clause,[],[f1476,f10857]) ).

fof(f10857,plain,
    ( spl0_1354
  <=> ! [X27,X3] :
        ( c_0 = X27
        | c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).

fof(f1476,axiom,
    ! [X3,X27] :
      ( c_0 = X27
      | c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).

fof(f10855,plain,
    spl0_1353,
    inference(avatar_split_clause,[],[f1457,f10853]) ).

fof(f10853,plain,
    ( spl0_1353
  <=> ! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).

fof(f1457,axiom,
    ! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).

fof(f10851,plain,
    spl0_1352,
    inference(avatar_split_clause,[],[f1442,f10849]) ).

fof(f10849,plain,
    ( spl0_1352
  <=> ! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).

fof(f1442,axiom,
    ! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).

fof(f10847,plain,
    spl0_1351,
    inference(avatar_split_clause,[],[f1413,f10845]) ).

fof(f10845,plain,
    ( spl0_1351
  <=> ! [X11,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(X11,c_0,tc_IntDef_Oint)
        | c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).

fof(f1413,axiom,
    ! [X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(X11,c_0,tc_IntDef_Oint)
      | c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).

fof(f10843,plain,
    spl0_1350,
    inference(avatar_split_clause,[],[f1412,f10841]) ).

fof(f10841,plain,
    ( spl0_1350
  <=> ! [X11,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(X11,c_0,tc_IntDef_Oint)
        | ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).

fof(f1412,axiom,
    ! [X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(X11,c_0,tc_IntDef_Oint)
      | ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).

fof(f10839,plain,
    spl0_1349,
    inference(avatar_split_clause,[],[f1409,f10837]) ).

fof(f10837,plain,
    ( spl0_1349
  <=> ! [X11,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
        | c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).

fof(f1409,axiom,
    ! [X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
      | c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).

fof(f10835,plain,
    spl0_1348,
    inference(avatar_split_clause,[],[f1408,f10833]) ).

fof(f10833,plain,
    ( spl0_1348
  <=> ! [X11,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_lessequals(X11,c_0,tc_IntDef_Oint)
        | ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).

fof(f1408,axiom,
    ! [X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(X11,c_0,tc_IntDef_Oint)
      | ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).

fof(f10831,plain,
    spl0_1347,
    inference(avatar_split_clause,[],[f1406,f10829]) ).

fof(f10829,plain,
    ( spl0_1347
  <=> ! [X11,X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | X11 = X48
        | c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).

fof(f1406,axiom,
    ! [X48,X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | X11 = X48
      | c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).

fof(f10827,plain,
    spl0_1346,
    inference(avatar_split_clause,[],[f1400,f10825]) ).

fof(f10825,plain,
    ( spl0_1346
  <=> ! [X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_less(c_0,X48,tc_IntDef_Oint)
        | c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).

fof(f1400,axiom,
    ! [X48,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_less(c_0,X48,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).

fof(f10823,plain,
    ( spl0_1344
    | ~ spl0_1345
    | ~ spl0_800
    | ~ spl0_1079 ),
    inference(avatar_split_clause,[],[f9259,f8904,f7563,f10820,f10817]) ).

fof(f10817,plain,
    ( spl0_1344
  <=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).

fof(f10820,plain,
    ( spl0_1345
  <=> c_Parity_Oeven(c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).

fof(f7563,plain,
    ( spl0_800
  <=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f8904,plain,
    ( spl0_1079
  <=> ! [X0,X3] :
        ( c_Parity_Oeven(X0,tc_nat)
        | ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f9259,plain,
    ( ! [X0] :
        ( ~ c_Parity_Oeven(c_1,tc_nat)
        | c_Parity_Oeven(X0,tc_nat) )
    | ~ spl0_800
    | ~ spl0_1079 ),
    inference(superposition,[],[f8905,f7564]) ).

fof(f7564,plain,
    ( ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat)
    | ~ spl0_800 ),
    inference(avatar_component_clause,[],[f7563]) ).

fof(f8905,plain,
    ( ! [X3,X0] :
        ( ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat)
        | c_Parity_Oeven(X0,tc_nat) )
    | ~ spl0_1079 ),
    inference(avatar_component_clause,[],[f8904]) ).

fof(f10815,plain,
    spl0_1343,
    inference(avatar_split_clause,[],[f1399,f10813]) ).

fof(f10813,plain,
    ( spl0_1343
  <=> ! [X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_less(c_0,X48,tc_IntDef_Oint)
        | ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).

fof(f1399,axiom,
    ! [X48,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_less(c_0,X48,tc_IntDef_Oint)
      | ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).

fof(f10811,plain,
    spl0_1342,
    inference(avatar_split_clause,[],[f1398,f10809]) ).

fof(f10809,plain,
    ( spl0_1342
  <=> ! [X48,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
        | c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).

fof(f1398,axiom,
    ! [X48,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
      | c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).

fof(f10807,plain,
    spl0_1341,
    inference(avatar_split_clause,[],[f1397,f10805]) ).

fof(f1397,axiom,
    ! [X48,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_lessequals(c_0,X48,tc_IntDef_Oint)
      | ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).

fof(f10803,plain,
    spl0_1340,
    inference(avatar_split_clause,[],[f1361,f10801]) ).

fof(f10801,plain,
    ( spl0_1340
  <=> ! [X18,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_in(X18,c_IntDef_OInts,X1)
        | c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).

fof(f1361,axiom,
    ! [X1,X18] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | ~ c_in(X18,c_IntDef_OInts,X1)
      | c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).

fof(f10799,plain,
    spl0_1339,
    inference(avatar_split_clause,[],[f1356,f10797]) ).

fof(f10797,plain,
    ( spl0_1339
  <=> ! [X3] :
        ( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
        | ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).

fof(f1356,axiom,
    ! [X3] :
      ( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
      | ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).

fof(f10795,plain,
    spl0_1338,
    inference(avatar_split_clause,[],[f1342,f10793]) ).

fof(f10793,plain,
    ( spl0_1338
  <=> ! [X15,X47] :
        ( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
        | c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).

fof(f1342,axiom,
    ! [X47,X15] :
      ( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).

fof(f10791,plain,
    spl0_1337,
    inference(avatar_split_clause,[],[f1341,f10789]) ).

fof(f10789,plain,
    ( spl0_1337
  <=> ! [X15,X47] :
        ( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
        | c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).

fof(f1341,axiom,
    ! [X47,X15] :
      ( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
      | c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).

fof(f10787,plain,
    spl0_1336,
    inference(avatar_split_clause,[],[f1243,f10785]) ).

fof(f10785,plain,
    ( spl0_1336
  <=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).

fof(f1243,axiom,
    ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).

fof(f10783,plain,
    spl0_1335,
    inference(avatar_split_clause,[],[f1233,f10781]) ).

fof(f10781,plain,
    ( spl0_1335
  <=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).

fof(f1233,axiom,
    ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).

fof(f10779,plain,
    spl0_1334,
    inference(avatar_split_clause,[],[f1232,f10777]) ).

fof(f10777,plain,
    ( spl0_1334
  <=> ! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).

fof(f1232,axiom,
    ! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).

fof(f10775,plain,
    spl0_1333,
    inference(avatar_split_clause,[],[f1191,f10773]) ).

fof(f10773,plain,
    ( spl0_1333
  <=> ! [X7,X9,X2,X1] :
        ( X7 = X9
        | c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).

fof(f1191,axiom,
    ! [X2,X1,X9,X7] :
      ( X7 = X9
      | c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).

fof(f10771,plain,
    spl0_1332,
    inference(avatar_split_clause,[],[f1189,f10769]) ).

fof(f10769,plain,
    ( spl0_1332
  <=> ! [X7,X9,X2,X1] :
        ( X7 = X9
        | c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).

fof(f1189,axiom,
    ! [X2,X1,X9,X7] :
      ( X7 = X9
      | c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).

fof(f10767,plain,
    spl0_1331,
    inference(avatar_split_clause,[],[f1185,f10765]) ).

fof(f10765,plain,
    ( spl0_1331
  <=> ! [X2,X18,X27,X1] :
        ( X18 = X27
        | c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).

fof(f1185,axiom,
    ! [X2,X18,X1,X27] :
      ( X18 = X27
      | c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).

fof(f10763,plain,
    spl0_1330,
    inference(avatar_split_clause,[],[f110,f10761]) ).

fof(f110,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

fof(f10759,plain,
    spl0_1329,
    inference(avatar_split_clause,[],[f109,f10757]) ).

fof(f10757,plain,
    ( spl0_1329
  <=> ! [X13,X12,X1] :
        ( c_lessequals(X12,X13,tc_set(X1))
        | c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).

fof(f109,axiom,
    ! [X1,X12,X13] :
      ( c_lessequals(X12,X13,tc_set(X1))
      | c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

fof(f10755,plain,
    spl0_1328,
    inference(avatar_split_clause,[],[f49,f10753]) ).

fof(f49,axiom,
    ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).

fof(f10751,plain,
    spl0_1327,
    inference(avatar_split_clause,[],[f2,f10749]) ).

fof(f10749,plain,
    ( spl0_1327
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).

fof(f10747,plain,
    spl0_1326,
    inference(avatar_split_clause,[],[f1,f10745]) ).

fof(f10745,plain,
    ( spl0_1326
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X3
        | c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X3
      | c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).

fof(f10659,plain,
    ( ~ spl0_1324
    | spl0_1325
    | ~ spl0_788
    | ~ spl0_1290 ),
    inference(avatar_split_clause,[],[f10561,f10201,f7514,f10657,f10653]) ).

fof(f10653,plain,
    ( spl0_1324
  <=> class_OrderedGroup_Oab__group__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).

fof(f10657,plain,
    ( spl0_1325
  <=> ! [X0] : c_0 = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).

fof(f10561,plain,
    ( ! [X0] :
        ( c_0 = X0
        | ~ class_OrderedGroup_Oab__group__add(tc_nat) )
    | ~ spl0_788
    | ~ spl0_1290 ),
    inference(trivial_inequality_removal,[],[f10554]) ).

fof(f10554,plain,
    ( ! [X0] :
        ( c_0 != c_0
        | c_0 = X0
        | ~ class_OrderedGroup_Oab__group__add(tc_nat) )
    | ~ spl0_788
    | ~ spl0_1290 ),
    inference(superposition,[],[f10202,f7515]) ).

fof(f10536,plain,
    ( spl0_1323
    | ~ spl0_766
    | ~ spl0_1042 ),
    inference(avatar_split_clause,[],[f9165,f8755,f7426,f10534]) ).

fof(f10534,plain,
    ( spl0_1323
  <=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).

fof(f7426,plain,
    ( spl0_766
  <=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f8755,plain,
    ( spl0_1042
  <=> ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f9165,plain,
    ( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
    | ~ spl0_766
    | ~ spl0_1042 ),
    inference(superposition,[],[f8756,f7427]) ).

fof(f7427,plain,
    ( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
    | ~ spl0_766 ),
    inference(avatar_component_clause,[],[f7426]) ).

fof(f8756,plain,
    ( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
    | ~ spl0_1042 ),
    inference(avatar_component_clause,[],[f8755]) ).

fof(f10383,plain,
    ( spl0_1322
    | ~ spl0_57
    | ~ spl0_1074
    | ~ spl0_1248 ),
    inference(avatar_split_clause,[],[f10033,f10030,f8884,f3714,f10381]) ).

fof(f10381,plain,
    ( spl0_1322
  <=> ! [X1] :
        ( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).

fof(f10030,plain,
    ( spl0_1248
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).

fof(f10033,plain,
    ( ! [X1] :
        ( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
        | ~ class_Numeral_Onumber__ring(X1) )
    | ~ spl0_57
    | ~ spl0_1074
    | ~ spl0_1248 ),
    inference(forward_demodulation,[],[f10031,f9250]) ).

fof(f10031,plain,
    ( ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) )
    | ~ spl0_1248 ),
    inference(avatar_component_clause,[],[f10030]) ).

fof(f10349,plain,
    spl0_1321,
    inference(avatar_split_clause,[],[f3330,f10347]) ).

fof(f10347,plain,
    ( spl0_1321
  <=> ! [X21,X15] :
        ( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
        | c_lessequals(c_1,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).

fof(f3330,plain,
    ! [X21,X15] :
      ( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
      | c_lessequals(c_1,X21,tc_nat) ),
    inference(forward_demodulation,[],[f3140,f2979]) ).

fof(f3140,plain,
    ! [X21,X15] :
      ( c_lessequals(c_1,X21,tc_nat)
      | ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2096,f2544]) ).

fof(f2096,axiom,
    ! [X21,X15] :
      ( c_lessequals(c_1,X21,tc_nat)
      | ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).

fof(f10345,plain,
    spl0_1320,
    inference(avatar_split_clause,[],[f3329,f10343]) ).

fof(f3329,plain,
    ! [X21,X15] :
      ( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
      | c_lessequals(c_1,X15,tc_nat) ),
    inference(forward_demodulation,[],[f3139,f2979]) ).

fof(f3139,plain,
    ! [X21,X15] :
      ( c_lessequals(c_1,X15,tc_nat)
      | ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2095,f2544]) ).

fof(f2095,axiom,
    ! [X21,X15] :
      ( c_lessequals(c_1,X15,tc_nat)
      | ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).

fof(f10341,plain,
    spl0_1319,
    inference(avatar_split_clause,[],[f3319,f10339]) ).

fof(f10339,plain,
    ( spl0_1319
  <=> ! [X21,X43] :
        ( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
        | ~ c_lessequals(c_1,X43,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).

fof(f3319,plain,
    ! [X21,X43] :
      ( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
      | ~ c_lessequals(c_1,X43,tc_nat) ),
    inference(forward_demodulation,[],[f3124,f2979]) ).

fof(f3124,plain,
    ! [X21,X43] :
      ( ~ c_lessequals(c_1,X43,tc_nat)
      | c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2340,f2544]) ).

fof(f2340,axiom,
    ! [X21,X43] :
      ( ~ c_lessequals(c_1,X43,tc_nat)
      | c_lessequals(c_Suc(c_0),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).

fof(f10337,plain,
    spl0_1318,
    inference(avatar_split_clause,[],[f3258,f10335]) ).

fof(f3258,plain,
    ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
    inference(forward_demodulation,[],[f3049,f2979]) ).

fof(f3049,plain,
    ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2764,f2544]) ).

fof(f2764,axiom,
    ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__5_0) ).

fof(f10333,plain,
    spl0_1317,
    inference(avatar_split_clause,[],[f3254,f10331]) ).

fof(f3254,plain,
    ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
    inference(forward_demodulation,[],[f3035,f3031]) ).

fof(f3035,plain,
    ! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
    inference(definition_unfolding,[],[f38,f2544]) ).

fof(f38,axiom,
    ! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).

fof(f10329,plain,
    spl0_1316,
    inference(avatar_split_clause,[],[f3250,f10327]) ).

fof(f10327,plain,
    ( spl0_1316
  <=> ! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).

fof(f3250,plain,
    ! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
    inference(forward_demodulation,[],[f3033,f3005]) ).

fof(f3033,plain,
    ! [X11] : c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1),
    inference(definition_unfolding,[],[f2131,f2113,f2113]) ).

fof(f2131,axiom,
    ! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).

fof(f10325,plain,
    spl0_1315,
    inference(avatar_split_clause,[],[f3034,f10323]) ).

fof(f10323,plain,
    ( spl0_1315
  <=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).

fof(f3034,plain,
    ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0),
    inference(definition_unfolding,[],[f2123,f2129,f2129]) ).

fof(f2123,axiom,
    ! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X11),c_Numeral_Obit_OB0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).

fof(f10311,plain,
    ( spl0_1314
    | ~ spl0_1313 ),
    inference(avatar_split_clause,[],[f10307,f10304,f10309]) ).

fof(f10304,plain,
    ( spl0_1313
  <=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).

fof(f10307,plain,
    ( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1313 ),
    inference(forward_demodulation,[],[f10305,f3031]) ).

fof(f10305,plain,
    ( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1313 ),
    inference(avatar_component_clause,[],[f10304]) ).

fof(f10306,plain,
    spl0_1313,
    inference(avatar_split_clause,[],[f3022,f10304]) ).

fof(f3022,plain,
    ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(definition_unfolding,[],[f1394,f2544]) ).

fof(f1394,axiom,
    ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).

fof(f10302,plain,
    spl0_1312,
    inference(avatar_split_clause,[],[f2890,f10300]) ).

fof(f10300,plain,
    ( spl0_1312
  <=> ! [X86,X88] :
        ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
        | ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).

fof(f2890,axiom,
    ! [X88,X86] :
      ( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
      | ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).

fof(f10298,plain,
    spl0_1311,
    inference(avatar_split_clause,[],[f2885,f10296]) ).

fof(f10296,plain,
    ( spl0_1311
  <=> ! [X86,X88] :
        ( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
        | c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).

fof(f2885,axiom,
    ! [X88,X86] :
      ( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
      | c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).

fof(f10294,plain,
    spl0_1310,
    inference(avatar_split_clause,[],[f2843,f10292]) ).

fof(f10292,plain,
    ( spl0_1310
  <=> ! [X88,X7] :
        ( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).

fof(f2843,axiom,
    ! [X88,X7] :
      ( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).

fof(f10290,plain,
    spl0_1309,
    inference(avatar_split_clause,[],[f2831,f10288]) ).

fof(f10288,plain,
    ( spl0_1309
  <=> ! [X91,X88] :
        ( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
        | ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).

fof(f2831,axiom,
    ! [X91,X88] :
      ( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
      | ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).

fof(f10286,plain,
    spl0_1308,
    inference(avatar_split_clause,[],[f2793,f10284]) ).

fof(f10284,plain,
    ( spl0_1308
  <=> ! [X91,X88] :
        ( ~ c_in(X91,c_Message_OkeysFor(X88),tc_nat)
        | c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).

fof(f2793,axiom,
    ! [X91,X88] :
      ( ~ c_in(X91,c_Message_OkeysFor(X88),tc_nat)
      | c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_2) ).

fof(f10282,plain,
    spl0_1307,
    inference(avatar_split_clause,[],[f2715,f10280]) ).

fof(f10280,plain,
    ( spl0_1307
  <=> ! [X5,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).

fof(f2715,axiom,
    ! [X1,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).

fof(f10278,plain,
    spl0_1306,
    inference(avatar_split_clause,[],[f2713,f10276]) ).

fof(f10276,plain,
    ( spl0_1306
  <=> ! [X5,X1] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).

fof(f2713,axiom,
    ! [X1,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).

fof(f10268,plain,
    spl0_1305,
    inference(avatar_split_clause,[],[f2685,f10266]) ).

fof(f10266,plain,
    ( spl0_1305
  <=> ! [X18,X12,X27,X1] :
        ( ~ c_in(X18,X12,X1)
        | c_in(X18,c_insert(X27,X12,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).

fof(f2685,axiom,
    ! [X18,X1,X27,X12] :
      ( ~ c_in(X18,X12,X1)
      | c_in(X18,c_insert(X27,X12,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).

fof(f10264,plain,
    spl0_1304,
    inference(avatar_split_clause,[],[f2642,f10262]) ).

fof(f10262,plain,
    ( spl0_1304
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X13,X1)
        | c_in(X4,c_union(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).

fof(f2642,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X13,X1)
      | c_in(X4,c_union(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).

fof(f10260,plain,
    spl0_1303,
    inference(avatar_split_clause,[],[f2641,f10258]) ).

fof(f10258,plain,
    ( spl0_1303
  <=> ! [X4,X13,X12,X1] :
        ( ~ c_in(X4,X12,X1)
        | c_in(X4,c_union(X12,X13,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).

fof(f2641,axiom,
    ! [X1,X4,X12,X13] :
      ( ~ c_in(X4,X12,X1)
      | c_in(X4,c_union(X12,X13,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).

fof(f10256,plain,
    spl0_1302,
    inference(avatar_split_clause,[],[f2583,f10254]) ).

fof(f10254,plain,
    ( spl0_1302
  <=> ! [X12,X1,X4] :
        ( c_in(X4,X12,X1)
        | c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).

fof(f2583,axiom,
    ! [X1,X4,X12] :
      ( c_in(X4,X12,X1)
      | c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).

fof(f10252,plain,
    spl0_1301,
    inference(avatar_split_clause,[],[f2582,f10250]) ).

fof(f10250,plain,
    ( spl0_1301
  <=> ! [X12,X1,X4] :
        ( ~ c_in(X4,X12,X1)
        | ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).

fof(f2582,axiom,
    ! [X1,X4,X12] :
      ( ~ c_in(X4,X12,X1)
      | ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).

fof(f10248,plain,
    spl0_1300,
    inference(avatar_split_clause,[],[f2545,f10246]) ).

fof(f10246,plain,
    ( spl0_1300
  <=> ! [X14,X26] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).

fof(f2545,axiom,
    ! [X26,X14] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).

fof(f10244,plain,
    spl0_1299,
    inference(avatar_split_clause,[],[f2542,f10242]) ).

fof(f10242,plain,
    ( spl0_1299
  <=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).

fof(f2542,axiom,
    ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).

fof(f10240,plain,
    spl0_1298,
    inference(avatar_split_clause,[],[f2522,f10238]) ).

fof(f10238,plain,
    ( spl0_1298
  <=> ! [X18,X1] :
        ( ~ class_Orderings_Oorder(X1)
        | c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).

fof(f2522,axiom,
    ! [X1,X18] :
      ( ~ class_Orderings_Oorder(X1)
      | c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).

fof(f10236,plain,
    spl0_1297,
    inference(avatar_split_clause,[],[f2271,f10234]) ).

fof(f10234,plain,
    ( spl0_1297
  <=> ! [X47] :
        ( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
        | ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).

fof(f2271,axiom,
    ! [X47] :
      ( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
      | ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
    file('/export/starexec/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(f10232,plain,
    spl0_1296,
    inference(avatar_split_clause,[],[f2270,f10230]) ).

fof(f10230,plain,
    ( spl0_1296
  <=> ! [X47] :
        ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
        | c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).

fof(f2270,axiom,
    ! [X47] :
      ( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
      | c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
    file('/export/starexec/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(f10223,plain,
    spl0_1295,
    inference(avatar_split_clause,[],[f2252,f10221]) ).

fof(f10221,plain,
    ( spl0_1295
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_0 = X18
        | c_less(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).

fof(f2252,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_0 = X18
      | c_less(c_0,c_HOL_Oabs(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).

fof(f10219,plain,
    spl0_1294,
    inference(avatar_split_clause,[],[f2245,f10217]) ).

fof(f10217,plain,
    ( spl0_1294
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(c_0,X3,X1)
        | c_OrderedGroup_Opprt(X3,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).

fof(f2245,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(c_0,X3,X1)
      | c_OrderedGroup_Opprt(X3,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).

fof(f10215,plain,
    spl0_1293,
    inference(avatar_split_clause,[],[f2244,f10213]) ).

fof(f10213,plain,
    ( spl0_1293
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(X0,c_0,X1)
        | c_0 = c_OrderedGroup_Opprt(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).

fof(f2244,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(X0,c_0,X1)
      | c_0 = c_OrderedGroup_Opprt(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).

fof(f10211,plain,
    spl0_1292,
    inference(avatar_split_clause,[],[f2240,f10209]) ).

fof(f10209,plain,
    ( spl0_1292
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | ~ c_lessequals(X3,c_0,X1)
        | c_OrderedGroup_Onprt(X3,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).

fof(f2240,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(X3,c_0,X1)
      | c_OrderedGroup_Onprt(X3,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).

fof(f10207,plain,
    spl0_1291,
    inference(avatar_split_clause,[],[f2239,f10205]) ).

fof(f2239,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | ~ c_lessequals(c_0,X0,X1)
      | c_0 = c_OrderedGroup_Onprt(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).

fof(f10203,plain,
    spl0_1290,
    inference(avatar_split_clause,[],[f2199,f10201]) ).

fof(f2199,axiom,
    ! [X1,X18,X27] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | X18 = X27
      | c_0 != c_minus(X18,X27,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).

fof(f10199,plain,
    spl0_1289,
    inference(avatar_split_clause,[],[f2183,f10197]) ).

fof(f2183,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | ~ c_lessequals(c_0,X3,X1)
      | c_HOL_Oabs(X3,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).

fof(f10195,plain,
    spl0_1288,
    inference(avatar_split_clause,[],[f2181,f10193]) ).

fof(f10193,plain,
    ( spl0_1288
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).

fof(f2181,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).

fof(f10191,plain,
    spl0_1287,
    inference(avatar_split_clause,[],[f2179,f10189]) ).

fof(f10189,plain,
    ( spl0_1287
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_0 = X18
        | ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).

fof(f2179,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_0 = X18
      | ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).

fof(f10187,plain,
    spl0_1286,
    inference(avatar_split_clause,[],[f2178,f10185]) ).

fof(f10185,plain,
    ( spl0_1286
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).

fof(f2178,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).

fof(f10183,plain,
    ( spl0_1285
    | ~ spl0_57
    | ~ spl0_1022 ),
    inference(avatar_split_clause,[],[f8680,f8545,f3714,f10180]) ).

fof(f8545,plain,
    ( spl0_1022
  <=> ! [X1] :
        ( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
        | ~ class_Numeral_Onumber__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f8680,plain,
    ( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
    | ~ spl0_57
    | ~ spl0_1022 ),
    inference(resolution,[],[f8546,f3716]) ).

fof(f8546,plain,
    ( ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
    | ~ spl0_1022 ),
    inference(avatar_component_clause,[],[f8545]) ).

fof(f10178,plain,
    spl0_1284,
    inference(avatar_split_clause,[],[f2147,f10176]) ).

fof(f10176,plain,
    ( spl0_1284
  <=> ! [X11,X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).

fof(f2147,axiom,
    ! [X11,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).

fof(f10174,plain,
    spl0_1283,
    inference(avatar_split_clause,[],[f2127,f10172]) ).

fof(f10170,plain,
    spl0_1282,
    inference(avatar_split_clause,[],[f2104,f10168]) ).

fof(f10168,plain,
    ( spl0_1282
  <=> ! [X21,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).

fof(f2104,axiom,
    ! [X21,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).

fof(f10166,plain,
    spl0_1281,
    inference(avatar_split_clause,[],[f2103,f10164]) ).

fof(f10164,plain,
    ( spl0_1281
  <=> ! [X21,X15] :
        ( c_less(X15,X21,tc_nat)
        | ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).

fof(f2103,axiom,
    ! [X21,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).

fof(f10162,plain,
    spl0_1280,
    inference(avatar_split_clause,[],[f2079,f10160]) ).

fof(f10160,plain,
    ( spl0_1280
  <=> ! [X21,X15] :
        ( c_less(c_0,X21,tc_nat)
        | ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).

fof(f2079,axiom,
    ! [X21,X15] :
      ( c_less(c_0,X21,tc_nat)
      | ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).

fof(f10158,plain,
    spl0_1279,
    inference(avatar_split_clause,[],[f2078,f10156]) ).

fof(f10156,plain,
    ( spl0_1279
  <=> ! [X21,X15] :
        ( c_less(c_0,X15,tc_nat)
        | ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).

fof(f2078,axiom,
    ! [X21,X15] :
      ( c_less(c_0,X15,tc_nat)
      | ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).

fof(f10154,plain,
    spl0_1278,
    inference(avatar_split_clause,[],[f2030,f10152]) ).

fof(f10152,plain,
    ( spl0_1278
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).

fof(f2030,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).

fof(f10150,plain,
    spl0_1277,
    inference(avatar_split_clause,[],[f2029,f10148]) ).

fof(f10148,plain,
    ( spl0_1277
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X15,tc_nat)
        | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).

fof(f2029,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X15,tc_nat)
      | c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).

fof(f10146,plain,
    spl0_1276,
    inference(avatar_split_clause,[],[f1851,f10144]) ).

fof(f10144,plain,
    ( spl0_1276
  <=> ! [X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).

fof(f1851,axiom,
    ! [X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).

fof(f10142,plain,
    spl0_1275,
    inference(avatar_split_clause,[],[f1814,f10140]) ).

fof(f10140,plain,
    ( spl0_1275
  <=> ! [X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_0 = X15
        | ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).

fof(f1814,axiom,
    ! [X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_0 = X15
      | ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).

fof(f10138,plain,
    ( spl0_1274
    | ~ spl0_895
    | ~ spl0_997 ),
    inference(avatar_split_clause,[],[f8654,f8441,f7956,f10135]) ).

fof(f10135,plain,
    ( spl0_1274
  <=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).

fof(f8654,plain,
    ( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
    | ~ spl0_895
    | ~ spl0_997 ),
    inference(superposition,[],[f7957,f8443]) ).

fof(f10133,plain,
    spl0_1273,
    inference(avatar_split_clause,[],[f1761,f10131]) ).

fof(f10131,plain,
    ( spl0_1273
  <=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).

fof(f1761,axiom,
    ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_1) ).

fof(f10129,plain,
    spl0_1272,
    inference(avatar_split_clause,[],[f1731,f10127]) ).

fof(f10127,plain,
    ( spl0_1272
  <=> ! [X0,X1,X21] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).

fof(f1731,axiom,
    ! [X21,X0,X1] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).

fof(f10125,plain,
    spl0_1271,
    inference(avatar_split_clause,[],[f1712,f10123]) ).

fof(f10123,plain,
    ( spl0_1271
  <=> ! [X41,X0,X3,X25] :
        ( ~ c_List_Oop_Amem(X0,X25,X41)
        | c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).

fof(f1712,axiom,
    ! [X41,X3,X0,X25] :
      ( ~ c_List_Oop_Amem(X0,X25,X41)
      | c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).

fof(f10121,plain,
    spl0_1270,
    inference(avatar_split_clause,[],[f1613,f10119]) ).

fof(f10119,plain,
    ( spl0_1270
  <=> ! [X43,X59] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).

fof(f1613,axiom,
    ! [X59,X43] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).

fof(f10117,plain,
    spl0_1269,
    inference(avatar_split_clause,[],[f1609,f10115]) ).

fof(f10115,plain,
    ( spl0_1269
  <=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).

fof(f1609,axiom,
    ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).

fof(f10113,plain,
    spl0_1268,
    inference(avatar_split_clause,[],[f1608,f10111]) ).

fof(f10111,plain,
    ( spl0_1268
  <=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).

fof(f1608,axiom,
    ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).

fof(f10109,plain,
    spl0_1267,
    inference(avatar_split_clause,[],[f1595,f10107]) ).

fof(f10107,plain,
    ( spl0_1267
  <=> ! [X1,X23,X3] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).

fof(f1595,axiom,
    ! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).

fof(f10105,plain,
    spl0_1266,
    inference(avatar_split_clause,[],[f1594,f10103]) ).

fof(f10103,plain,
    ( spl0_1266
  <=> ! [X21,X1,X3] :
        ( c_0 = X21
        | c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).

fof(f1594,axiom,
    ! [X21,X3,X1] :
      ( c_0 = X21
      | c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).

fof(f10101,plain,
    spl0_1265,
    inference(avatar_split_clause,[],[f1593,f10099]) ).

fof(f10099,plain,
    ( spl0_1265
  <=> ! [X60,X1] :
        ( c_List_Olist_ONil = X60
        | c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).

fof(f1593,axiom,
    ! [X1,X60] :
      ( c_List_Olist_ONil = X60
      | c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).

fof(f10097,plain,
    spl0_1264,
    inference(avatar_split_clause,[],[f1584,f10095]) ).

fof(f1584,axiom,
    ! [X3,X59] :
      ( ~ c_less(X3,X59,tc_nat)
      | c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).

fof(f10093,plain,
    ( spl0_1263
    | ~ spl0_92
    | ~ spl0_984 ),
    inference(avatar_split_clause,[],[f8640,f8388,f3889,f10091]) ).

fof(f10091,plain,
    ( spl0_1263
  <=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).

fof(f3889,plain,
    ( spl0_92
  <=> class_Power_Orecpower(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f8388,plain,
    ( spl0_984
  <=> ! [X1,X3] :
        ( ~ class_Power_Orecpower(X1)
        | c_Nat_Opower(X3,c_1,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).

fof(f8640,plain,
    ( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
    | ~ spl0_92
    | ~ spl0_984 ),
    inference(resolution,[],[f8389,f3891]) ).

fof(f3891,plain,
    ( class_Power_Orecpower(tc_nat)
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f3889]) ).

fof(f8389,plain,
    ( ! [X3,X1] :
        ( ~ class_Power_Orecpower(X1)
        | c_Nat_Opower(X3,c_1,X1) = X3 )
    | ~ spl0_984 ),
    inference(avatar_component_clause,[],[f8388]) ).

fof(f10089,plain,
    spl0_1262,
    inference(avatar_split_clause,[],[f1583,f10087]) ).

fof(f10087,plain,
    ( spl0_1262
  <=> ! [X21,X1,X3] :
        ( c_0 = X21
        | c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).

fof(f1583,axiom,
    ! [X21,X3,X1] :
      ( c_0 = X21
      | c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).

fof(f10085,plain,
    spl0_1261,
    inference(avatar_split_clause,[],[f1582,f10083]) ).

fof(f10083,plain,
    ( spl0_1261
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).

fof(f1582,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).

fof(f10081,plain,
    spl0_1260,
    inference(avatar_split_clause,[],[f1539,f10079]) ).

fof(f10079,plain,
    ( spl0_1260
  <=> ! [X0,X1,X3] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).

fof(f1539,axiom,
    ! [X3,X0,X1] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).

fof(f10077,plain,
    spl0_1259,
    inference(avatar_split_clause,[],[f1463,f10075]) ).

fof(f10075,plain,
    ( spl0_1259
  <=> ! [X18,X27] :
        ( ~ c_less(c_0,X27,tc_IntDef_Oint)
        | c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).

fof(f1463,axiom,
    ! [X18,X27] :
      ( ~ c_less(c_0,X27,tc_IntDef_Oint)
      | c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).

fof(f10073,plain,
    spl0_1258,
    inference(avatar_split_clause,[],[f1462,f10071]) ).

fof(f10071,plain,
    ( spl0_1258
  <=> ! [X18,X27] :
        ( ~ c_less(c_0,X27,tc_IntDef_Oint)
        | c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).

fof(f1462,axiom,
    ! [X18,X27] :
      ( ~ c_less(c_0,X27,tc_IntDef_Oint)
      | c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).

fof(f10069,plain,
    spl0_1257,
    inference(avatar_split_clause,[],[f1455,f10067]) ).

fof(f10067,plain,
    ( spl0_1257
  <=> ! [X18,X27] :
        ( ~ c_less(X27,c_0,tc_IntDef_Oint)
        | c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).

fof(f1455,axiom,
    ! [X18,X27] :
      ( ~ c_less(X27,c_0,tc_IntDef_Oint)
      | c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).

fof(f10065,plain,
    spl0_1256,
    inference(avatar_split_clause,[],[f1454,f10063]) ).

fof(f10063,plain,
    ( spl0_1256
  <=> ! [X18,X27] :
        ( ~ c_less(X27,c_0,tc_IntDef_Oint)
        | c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).

fof(f1454,axiom,
    ! [X18,X27] :
      ( ~ c_less(X27,c_0,tc_IntDef_Oint)
      | c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).

fof(f10061,plain,
    spl0_1255,
    inference(avatar_split_clause,[],[f1418,f10059]) ).

fof(f10059,plain,
    ( spl0_1255
  <=> ! [X21,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).

fof(f1418,axiom,
    ! [X21,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).

fof(f10057,plain,
    spl0_1254,
    inference(avatar_split_clause,[],[f1354,f10055]) ).

fof(f10055,plain,
    ( spl0_1254
  <=> ! [X48,X11] :
        ( ~ c_less(X11,X48,tc_IntDef_Oint)
        | c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).

fof(f1354,axiom,
    ! [X48,X11] :
      ( ~ c_less(X11,X48,tc_IntDef_Oint)
      | c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).

fof(f10053,plain,
    spl0_1253,
    inference(avatar_split_clause,[],[f1353,f10051]) ).

fof(f10051,plain,
    ( spl0_1253
  <=> ! [X48,X11] :
        ( c_less(X11,X48,tc_IntDef_Oint)
        | ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).

fof(f1353,axiom,
    ! [X48,X11] :
      ( c_less(X11,X48,tc_IntDef_Oint)
      | ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).

fof(f10049,plain,
    ( spl0_1252
    | ~ spl0_58
    | ~ spl0_984 ),
    inference(avatar_split_clause,[],[f8639,f8388,f3719,f10047]) ).

fof(f3719,plain,
    ( spl0_58
  <=> class_Power_Orecpower(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f8639,plain,
    ( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
    | ~ spl0_58
    | ~ spl0_984 ),
    inference(resolution,[],[f8389,f3721]) ).

fof(f3721,plain,
    ( class_Power_Orecpower(tc_IntDef_Oint)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f3719]) ).

fof(f10045,plain,
    spl0_1251,
    inference(avatar_split_clause,[],[f1352,f10043]) ).

fof(f10043,plain,
    ( spl0_1251
  <=> ! [X48,X11] :
        ( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
        | c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).

fof(f1352,axiom,
    ! [X48,X11] :
      ( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
      | c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).

fof(f10041,plain,
    spl0_1250,
    inference(avatar_split_clause,[],[f1351,f10039]) ).

fof(f10039,plain,
    ( spl0_1250
  <=> ! [X48,X11] :
        ( c_lessequals(X11,X48,tc_IntDef_Oint)
        | ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).

fof(f1351,axiom,
    ! [X48,X11] :
      ( c_lessequals(X11,X48,tc_IntDef_Oint)
      | ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).

fof(f10037,plain,
    spl0_1249,
    inference(avatar_split_clause,[],[f1348,f10035]) ).

fof(f1348,axiom,
    ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).

fof(f10032,plain,
    spl0_1248,
    inference(avatar_split_clause,[],[f1345,f10030]) ).

fof(f1345,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).

fof(f10028,plain,
    spl0_1247,
    inference(avatar_split_clause,[],[f1310,f10026]) ).

fof(f10026,plain,
    ( spl0_1247
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).

fof(f1310,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).

fof(f10024,plain,
    spl0_1246,
    inference(avatar_split_clause,[],[f1307,f10022]) ).

fof(f10022,plain,
    ( spl0_1246
  <=> ! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).

fof(f1307,axiom,
    ! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).

fof(f10020,plain,
    spl0_1245,
    inference(avatar_split_clause,[],[f1236,f10018]) ).

fof(f10018,plain,
    ( spl0_1245
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).

fof(f1236,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).

fof(f10016,plain,
    spl0_1244,
    inference(avatar_split_clause,[],[f1234,f10014]) ).

fof(f10014,plain,
    ( spl0_1244
  <=> ! [X21,X15] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).

fof(f1234,axiom,
    ! [X21,X15] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).

fof(f10012,plain,
    spl0_1243,
    inference(avatar_split_clause,[],[f1178,f10010]) ).

fof(f1178,axiom,
    ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).

fof(f10008,plain,
    spl0_1242,
    inference(avatar_split_clause,[],[f1166,f10006]) ).

fof(f10006,plain,
    ( spl0_1242
  <=> ! [X0,X1,X40] :
        ( c_Datatype_Ooption_OSome(X0,X1) = X40
        | ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).

fof(f1166,axiom,
    ! [X40,X0,X1] :
      ( c_Datatype_Ooption_OSome(X0,X1) = X40
      | ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).

fof(f10004,plain,
    ( spl0_1241
    | ~ spl0_92
    | ~ spl0_983 ),
    inference(avatar_split_clause,[],[f8638,f8384,f3889,f10002]) ).

fof(f10002,plain,
    ( spl0_1241
  <=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).

fof(f8384,plain,
    ( spl0_983
  <=> ! [X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).

fof(f8638,plain,
    ( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
    | ~ spl0_92
    | ~ spl0_983 ),
    inference(resolution,[],[f8385,f3891]) ).

fof(f8385,plain,
    ( ! [X21,X1] :
        ( ~ class_Power_Orecpower(X1)
        | c_1 = c_Nat_Opower(c_1,X21,X1) )
    | ~ spl0_983 ),
    inference(avatar_component_clause,[],[f8384]) ).

fof(f9985,plain,
    ( spl0_1240
    | ~ spl0_58
    | ~ spl0_983 ),
    inference(avatar_split_clause,[],[f8637,f8384,f3719,f9983]) ).

fof(f9983,plain,
    ( spl0_1240
  <=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).

fof(f8637,plain,
    ( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
    | ~ spl0_58
    | ~ spl0_983 ),
    inference(resolution,[],[f8385,f3721]) ).

fof(f9955,plain,
    ( spl0_1239
    | ~ spl0_96
    | ~ spl0_980 ),
    inference(avatar_split_clause,[],[f8632,f8372,f3909,f9953]) ).

fof(f9953,plain,
    ( spl0_1239
  <=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).

fof(f8372,plain,
    ( spl0_980
  <=> ! [X2,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Orderings_Omax(X3,X3,X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).

fof(f8632,plain,
    ( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
    | ~ spl0_96
    | ~ spl0_980 ),
    inference(resolution,[],[f8373,f3911]) ).

fof(f8373,plain,
    ( ! [X2,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Orderings_Omax(X3,X3,X2) = X3 )
    | ~ spl0_980 ),
    inference(avatar_component_clause,[],[f8372]) ).

fof(f9947,plain,
    ( spl0_1238
    | ~ spl0_32
    | ~ spl0_980 ),
    inference(avatar_split_clause,[],[f8631,f8372,f3589,f9945]) ).

fof(f9945,plain,
    ( spl0_1238
  <=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).

fof(f8631,plain,
    ( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
    | ~ spl0_32
    | ~ spl0_980 ),
    inference(resolution,[],[f8373,f3591]) ).

fof(f9921,plain,
    ( spl0_1237
    | ~ spl0_96
    | ~ spl0_979 ),
    inference(avatar_split_clause,[],[f8630,f8368,f3909,f9919]) ).

fof(f9919,plain,
    ( spl0_1237
  <=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).

fof(f8368,plain,
    ( spl0_979
  <=> ! [X2,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Orderings_Omin(X3,X3,X2) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).

fof(f8630,plain,
    ( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
    | ~ spl0_96
    | ~ spl0_979 ),
    inference(resolution,[],[f8369,f3911]) ).

fof(f8369,plain,
    ( ! [X2,X3] :
        ( ~ class_Orderings_Olinorder(X2)
        | c_Orderings_Omin(X3,X3,X2) = X3 )
    | ~ spl0_979 ),
    inference(avatar_component_clause,[],[f8368]) ).

fof(f9881,plain,
    ( spl0_1236
    | ~ spl0_32
    | ~ spl0_979 ),
    inference(avatar_split_clause,[],[f8629,f8368,f3589,f9879]) ).

fof(f9879,plain,
    ( spl0_1236
  <=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).

fof(f8629,plain,
    ( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
    | ~ spl0_32
    | ~ spl0_979 ),
    inference(resolution,[],[f8369,f3591]) ).

fof(f9856,plain,
    ( spl0_1235
    | ~ spl0_57
    | ~ spl0_1074
    | ~ spl0_1165 ),
    inference(avatar_split_clause,[],[f9469,f9466,f8884,f3714,f9854]) ).

fof(f9854,plain,
    ( spl0_1235
  <=> ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).

fof(f9466,plain,
    ( spl0_1165
  <=> ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).

fof(f9469,plain,
    ( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_57
    | ~ spl0_1074
    | ~ spl0_1165 ),
    inference(forward_demodulation,[],[f9467,f9250]) ).

fof(f9467,plain,
    ( ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint)
    | ~ spl0_1165 ),
    inference(avatar_component_clause,[],[f9466]) ).

fof(f9800,plain,
    ( spl0_1234
    | spl0_685
    | ~ spl0_1151 ),
    inference(avatar_split_clause,[],[f9793,f9410,f7058,f9797]) ).

fof(f9797,plain,
    ( spl0_1234
  <=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).

fof(f7058,plain,
    ( spl0_685
  <=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f9410,plain,
    ( spl0_1151
  <=> ! [X12,X1] :
        ( c_0 = c_Finite__Set_Ocard(X12,X1)
        | c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f9793,plain,
    ( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
    | spl0_685
    | ~ spl0_1151 ),
    inference(resolution,[],[f9411,f7060]) ).

fof(f7060,plain,
    ( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
    | spl0_685 ),
    inference(avatar_component_clause,[],[f7058]) ).

fof(f9411,plain,
    ( ! [X1,X12] :
        ( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
        | c_0 = c_Finite__Set_Ocard(X12,X1) )
    | ~ spl0_1151 ),
    inference(avatar_component_clause,[],[f9410]) ).

fof(f9747,plain,
    spl0_1233,
    inference(avatar_split_clause,[],[f3380,f9745]) ).

fof(f9745,plain,
    ( spl0_1233
  <=> ! [X0,X1] :
        ( c_IntDef_Oiszero(c_0,X1)
        | ~ class_Numeral_Onumber__ring(X1)
        | c_0 != c_Numeral_Onumber__of(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).

fof(f3380,plain,
    ! [X0,X1] :
      ( c_IntDef_Oiszero(c_0,X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X0,X1) ),
    inference(inner_rewriting,[],[f3379]) ).

fof(f3379,plain,
    ! [X0,X1] :
      ( c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X0,X1) ),
    inference(forward_demodulation,[],[f3378,f2115]) ).

fof(f3378,plain,
    ! [X0,X1] :
      ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
      | ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X0,X1) ),
    inference(forward_demodulation,[],[f3174,f2978]) ).

fof(f3174,plain,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X0,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
    inference(definition_unfolding,[],[f1337,f2129]) ).

fof(f1337,axiom,
    ! [X0,X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 != c_Numeral_Onumber__of(X0,X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).

fof(f9743,plain,
    ( spl0_1232
    | ~ spl0_647
    | ~ spl0_1129
    | ~ spl0_1225 ),
    inference(avatar_split_clause,[],[f9714,f9709,f9201,f6127,f9740]) ).

fof(f9740,plain,
    ( spl0_1232
  <=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).

fof(f9714,plain,
    ( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_1129
    | ~ spl0_1225 ),
    inference(forward_demodulation,[],[f9713,f9202]) ).

fof(f9713,plain,
    ( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_1225 ),
    inference(superposition,[],[f9710,f6129]) ).

fof(f9738,plain,
    spl0_1231,
    inference(avatar_split_clause,[],[f3261,f9736]) ).

fof(f9736,plain,
    ( spl0_1231
  <=> ! [X96,X90] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).

fof(f3261,plain,
    ! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
    inference(forward_demodulation,[],[f3260,f3258]) ).

fof(f3260,plain,
    ! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
    inference(forward_demodulation,[],[f3063,f2979]) ).

fof(f3063,plain,
    ! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2766,f2544]) ).

fof(f2766,axiom,
    ! [X90,X96] : c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__7_0) ).

fof(f9734,plain,
    spl0_1230,
    inference(avatar_split_clause,[],[f3257,f9732]) ).

fof(f9732,plain,
    ( spl0_1230
  <=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).

fof(f3257,plain,
    ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
    inference(forward_demodulation,[],[f3043,f2979]) ).

fof(f3043,plain,
    ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1210,f2544]) ).

fof(f1210,axiom,
    ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).

fof(f9730,plain,
    spl0_1229,
    inference(avatar_split_clause,[],[f3256,f9728]) ).

fof(f9728,plain,
    ( spl0_1229
  <=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).

fof(f3256,plain,
    ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
    inference(forward_demodulation,[],[f3042,f2979]) ).

fof(f3042,plain,
    ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
    inference(definition_unfolding,[],[f1209,f2544]) ).

fof(f1209,axiom,
    ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).

fof(f9726,plain,
    spl0_1228,
    inference(avatar_split_clause,[],[f3123,f9724]) ).

fof(f9724,plain,
    ( spl0_1228
  <=> ! [X0] :
        ( c_Parity_Oeven(X0,tc_nat)
        | c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).

fof(f3123,plain,
    ! [X0] :
      ( c_Parity_Oeven(X0,tc_nat)
      | c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2279,f2544]) ).

fof(f2279,axiom,
    ! [X0] :
      ( c_Parity_Oeven(X0,tc_nat)
      | c_Parity_Oeven(c_Suc(X0),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).

fof(f9722,plain,
    spl0_1227,
    inference(avatar_split_clause,[],[f3109,f9720]) ).

fof(f9720,plain,
    ( spl0_1227
  <=> ! [X0] :
        ( ~ c_Parity_Oeven(X0,tc_nat)
        | ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).

fof(f3109,plain,
    ! [X0] :
      ( ~ c_Parity_Oeven(X0,tc_nat)
      | ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2278,f2544]) ).

fof(f2278,axiom,
    ! [X0] :
      ( ~ c_Parity_Oeven(X0,tc_nat)
      | ~ c_Parity_Oeven(c_Suc(X0),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).

fof(f9718,plain,
    spl0_1226,
    inference(avatar_split_clause,[],[f3036,f9716]) ).

fof(f9716,plain,
    ( spl0_1226
  <=> ! [X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(X12,c_List_Olist_ONil),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).

fof(f3036,plain,
    ! [X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oknows(X12,c_List_Olist_ONil),tc_Message_Omsg),
    inference(definition_unfolding,[],[f2913,f2795]) ).

fof(f2795,axiom,
    ! [X12] : c_Event_Oknows(X12,c_List_Olist_ONil) = c_Event_OinitState(X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows_Oknows__Nil_0) ).

fof(f2913,axiom,
    ! [X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_OinitState(X12),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).

fof(f9711,plain,
    ( spl0_1225
    | ~ spl0_1224 ),
    inference(avatar_split_clause,[],[f9707,f9704,f9709]) ).

fof(f9704,plain,
    ( spl0_1224
  <=> ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).

fof(f9707,plain,
    ( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1224 ),
    inference(forward_demodulation,[],[f9705,f3031]) ).

fof(f9705,plain,
    ( ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_1224 ),
    inference(avatar_component_clause,[],[f9704]) ).

fof(f9706,plain,
    spl0_1224,
    inference(avatar_split_clause,[],[f3020,f9704]) ).

fof(f3020,plain,
    ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
    inference(definition_unfolding,[],[f1388,f2544]) ).

fof(f1388,axiom,
    ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).

fof(f9702,plain,
    spl0_1223,
    inference(avatar_split_clause,[],[f3012,f9700]) ).

fof(f9700,plain,
    ( spl0_1223
  <=> ! [X86,X107,X87,X91] : c_Message_Omsg_OCrypt(X91,X107) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).

fof(f3012,plain,
    ! [X91,X86,X87,X107] : c_Message_Omsg_OCrypt(X91,X107) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
    inference(definition_unfolding,[],[f2823,f2812]) ).

fof(f2823,axiom,
    ! [X91,X86,X87,X107] : c_Message_OHPair(X86,X87) != c_Message_Omsg_OCrypt(X91,X107),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0) ).

fof(f9698,plain,
    ( spl0_1222
    | ~ spl0_69
    | ~ spl0_975 ),
    inference(avatar_split_clause,[],[f8624,f8352,f3774,f9696]) ).

fof(f9696,plain,
    ( spl0_1222
  <=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).

fof(f3774,plain,
    ( spl0_69
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f8352,plain,
    ( spl0_975
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X1)
        | c_times(X3,c_1,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).

fof(f8624,plain,
    ( ! [X0] : c_times(X0,c_1,tc_nat) = X0
    | ~ spl0_69
    | ~ spl0_975 ),
    inference(resolution,[],[f8353,f3776]) ).

fof(f3776,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_nat)
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f3774]) ).

fof(f8353,plain,
    ( ! [X3,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X1)
        | c_times(X3,c_1,X1) = X3 )
    | ~ spl0_975 ),
    inference(avatar_component_clause,[],[f8352]) ).

fof(f9694,plain,
    ( spl0_1221
    | ~ spl0_815
    | ~ spl0_1220 ),
    inference(avatar_split_clause,[],[f9690,f9687,f7623,f9692]) ).

fof(f9692,plain,
    ( spl0_1221
  <=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).

fof(f9687,plain,
    ( spl0_1220
  <=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).

fof(f9690,plain,
    ( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1)
    | ~ spl0_815
    | ~ spl0_1220 ),
    inference(forward_demodulation,[],[f9688,f7624]) ).

fof(f9688,plain,
    ( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1)
    | ~ spl0_1220 ),
    inference(avatar_component_clause,[],[f9687]) ).

fof(f9689,plain,
    spl0_1220,
    inference(avatar_split_clause,[],[f2980,f9687]) ).

fof(f2980,plain,
    ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1),
    inference(definition_unfolding,[],[f2709,f2716]) ).

fof(f2709,axiom,
    ! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).

fof(f9685,plain,
    spl0_1219,
    inference(avatar_split_clause,[],[f2920,f9683]) ).

fof(f9683,plain,
    ( spl0_1219
  <=> ! [X4,X27,X12,X111] :
        ( X12 = X111
        | c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).

fof(f2920,axiom,
    ! [X111,X27,X4,X12] :
      ( X12 = X111
      | c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_1) ).

fof(f9681,plain,
    spl0_1218,
    inference(avatar_split_clause,[],[f2919,f9679]) ).

fof(f9679,plain,
    ( spl0_1218
  <=> ! [X4,X111,X12,X27] :
        ( X4 = X27
        | c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).

fof(f2919,axiom,
    ! [X111,X27,X4,X12] :
      ( X4 = X27
      | c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_0) ).

fof(f9677,plain,
    spl0_1217,
    inference(avatar_split_clause,[],[f2898,f9675]) ).

fof(f9675,plain,
    ( spl0_1217
  <=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).

fof(f2898,axiom,
    ! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).

fof(f9673,plain,
    spl0_1216,
    inference(avatar_split_clause,[],[f2883,f9671]) ).

fof(f2883,axiom,
    ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).

fof(f9669,plain,
    spl0_1215,
    inference(avatar_split_clause,[],[f2865,f9667]) ).

fof(f2865,axiom,
    ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).

fof(f9665,plain,
    spl0_1214,
    inference(avatar_split_clause,[],[f2852,f9663]) ).

fof(f2852,axiom,
    ! [X88,X86] :
      ( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
      | c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).

fof(f9661,plain,
    spl0_1213,
    inference(avatar_split_clause,[],[f2800,f9659]) ).

fof(f9659,plain,
    ( spl0_1213
  <=> ! [X102,X86,X12] : c_Event_Oused(X102) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).

fof(f2800,axiom,
    ! [X86,X102,X12] : c_Event_Oused(X102) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Gets_0) ).

fof(f9657,plain,
    ( spl0_1212
    | ~ spl0_20
    | ~ spl0_975 ),
    inference(avatar_split_clause,[],[f8623,f8352,f3529,f9655]) ).

fof(f9655,plain,
    ( spl0_1212
  <=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).

fof(f3529,plain,
    ( spl0_20
  <=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f8623,plain,
    ( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
    | ~ spl0_20
    | ~ spl0_975 ),
    inference(resolution,[],[f8353,f3531]) ).

fof(f3531,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f3529]) ).

fof(f9653,plain,
    spl0_1211,
    inference(avatar_split_clause,[],[f2787,f9651]) ).

fof(f9651,plain,
    ( spl0_1211
  <=> ! [X96,X97,X94,X95] :
        ( X96 = X97
        | c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).

fof(f2787,axiom,
    ! [X96,X94,X97,X95] :
      ( X96 = X97
      | c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_1) ).

fof(f9649,plain,
    spl0_1210,
    inference(avatar_split_clause,[],[f2786,f9647]) ).

fof(f9647,plain,
    ( spl0_1210
  <=> ! [X95,X97,X94,X96] :
        ( X94 = X95
        | c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).

fof(f2786,axiom,
    ! [X96,X94,X97,X95] :
      ( X94 = X95
      | c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_ONotes(X94,X96) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_0) ).

fof(f9645,plain,
    spl0_1209,
    inference(avatar_split_clause,[],[f2785,f9643]) ).

fof(f9643,plain,
    ( spl0_1209
  <=> ! [X96,X97,X94,X95] :
        ( X96 = X97
        | c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).

fof(f2785,axiom,
    ! [X96,X94,X97,X95] :
      ( X96 = X97
      | c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_1) ).

fof(f9641,plain,
    spl0_1208,
    inference(avatar_split_clause,[],[f2784,f9639]) ).

fof(f9639,plain,
    ( spl0_1208
  <=> ! [X95,X97,X94,X96] :
        ( X94 = X95
        | c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).

fof(f2784,axiom,
    ! [X96,X94,X97,X95] :
      ( X94 = X95
      | c_Event_Oevent_OGets(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_0) ).

fof(f9637,plain,
    spl0_1207,
    inference(avatar_split_clause,[],[f2759,f9635]) ).

fof(f9635,plain,
    ( spl0_1207
  <=> ! [X89,X96,X97,X90] :
        ( X96 = X97
        | c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).

fof(f2759,axiom,
    ! [X90,X89,X96,X97] :
      ( X96 = X97
      | c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).

fof(f9633,plain,
    spl0_1206,
    inference(avatar_split_clause,[],[f2758,f9631]) ).

fof(f9631,plain,
    ( spl0_1206
  <=> ! [X96,X97,X90,X89] :
        ( X89 = X90
        | c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).

fof(f2758,axiom,
    ! [X90,X89,X96,X97] :
      ( X89 = X90
      | c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).

fof(f9629,plain,
    spl0_1205,
    inference(avatar_split_clause,[],[f2757,f9627]) ).

fof(f9627,plain,
    ( spl0_1205
  <=> ! [X100,X101,X98,X99] :
        ( X99 = X101
        | c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).

fof(f2757,axiom,
    ! [X101,X98,X99,X100] :
      ( X99 = X101
      | c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).

fof(f9625,plain,
    spl0_1204,
    inference(avatar_split_clause,[],[f2756,f9623]) ).

fof(f9623,plain,
    ( spl0_1204
  <=> ! [X101,X98,X100,X99] :
        ( X98 = X100
        | c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).

fof(f2756,axiom,
    ! [X101,X98,X99,X100] :
      ( X98 = X100
      | c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).

fof(f9621,plain,
    spl0_1203,
    inference(avatar_split_clause,[],[f2748,f9619]) ).

fof(f9619,plain,
    ( spl0_1203
  <=> ! [X87,X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).

fof(f2748,axiom,
    ! [X88,X86,X87] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).

fof(f9617,plain,
    spl0_1202,
    inference(avatar_split_clause,[],[f2671,f9615]) ).

fof(f9615,plain,
    ( spl0_1202
  <=> ! [X12,X1] :
        ( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
        | c_emptyset = c_Union(X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).

fof(f2671,axiom,
    ! [X1,X12] :
      ( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
      | c_emptyset = c_Union(X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).

fof(f9613,plain,
    ( spl0_1201
    | ~ spl0_69
    | ~ spl0_974 ),
    inference(avatar_split_clause,[],[f8622,f8348,f3774,f9611]) ).

fof(f9611,plain,
    ( spl0_1201
  <=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).

fof(f8348,plain,
    ( spl0_974
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Omonoid__mult(X1)
        | c_times(c_1,X3,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).

fof(f8622,plain,
    ( ! [X0] : c_times(c_1,X0,tc_nat) = X0
    | ~ spl0_69
    | ~ spl0_974 ),
    inference(resolution,[],[f8349,f3776]) ).

fof(f8349,plain,
    ( ! [X3,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X1)
        | c_times(c_1,X3,X1) = X3 )
    | ~ spl0_974 ),
    inference(avatar_component_clause,[],[f8348]) ).

fof(f9609,plain,
    spl0_1200,
    inference(avatar_split_clause,[],[f2654,f9607]) ).

fof(f9607,plain,
    ( spl0_1200
  <=> ! [X12,X1] :
        ( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
        | c_emptyset = c_Union(X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).

fof(f2654,axiom,
    ! [X1,X12] :
      ( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
      | c_emptyset = c_Union(X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).

fof(f9605,plain,
    spl0_1199,
    inference(avatar_split_clause,[],[f2618,f9603]) ).

fof(f9603,plain,
    ( spl0_1199
  <=> ! [X12,X1] :
        ( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
        | c_UNIV = c_Inter(X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f2618,axiom,
    ! [X1,X12] :
      ( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
      | c_UNIV = c_Inter(X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).

fof(f9601,plain,
    spl0_1198,
    inference(avatar_split_clause,[],[f2615,f9599]) ).

fof(f9599,plain,
    ( spl0_1198
  <=> ! [X12,X1] :
        ( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
        | c_UNIV = c_Inter(X12,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f2615,axiom,
    ! [X1,X12] :
      ( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
      | c_UNIV = c_Inter(X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).

fof(f9597,plain,
    spl0_1197,
    inference(avatar_split_clause,[],[f2388,f9595]) ).

fof(f2388,axiom,
    ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).

fof(f9593,plain,
    spl0_1196,
    inference(avatar_split_clause,[],[f2383,f9591]) ).

fof(f2383,axiom,
    ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).

fof(f9589,plain,
    spl0_1195,
    inference(avatar_split_clause,[],[f2366,f9587]) ).

fof(f2366,axiom,
    ! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).

fof(f9585,plain,
    spl0_1194,
    inference(avatar_split_clause,[],[f2364,f9583]) ).

fof(f2364,axiom,
    ! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).

fof(f9581,plain,
    spl0_1193,
    inference(avatar_split_clause,[],[f2342,f9579]) ).

fof(f9579,plain,
    ( spl0_1193
  <=> ! [X0,X21] :
        ( c_0 = X0
        | c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).

fof(f2342,axiom,
    ! [X21,X0] :
      ( c_0 = X0
      | c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).

fof(f9577,plain,
    spl0_1192,
    inference(avatar_split_clause,[],[f2341,f9575]) ).

fof(f9575,plain,
    ( spl0_1192
  <=> ! [X21] :
        ( c_0 = X21
        | ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).

fof(f2341,axiom,
    ! [X21] :
      ( c_0 = X21
      | ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).

fof(f9573,plain,
    spl0_1191,
    inference(avatar_split_clause,[],[f2294,f9571]) ).

fof(f9571,plain,
    ( spl0_1191
  <=> ! [X21,X0] :
        ( c_less(c_0,X21,tc_nat)
        | ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).

fof(f2294,axiom,
    ! [X21,X0] :
      ( c_less(c_0,X21,tc_nat)
      | ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).

fof(f9569,plain,
    ( spl0_1190
    | ~ spl0_20
    | ~ spl0_974 ),
    inference(avatar_split_clause,[],[f8621,f8348,f3529,f9567]) ).

fof(f9567,plain,
    ( spl0_1190
  <=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).

fof(f8621,plain,
    ( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
    | ~ spl0_20
    | ~ spl0_974 ),
    inference(resolution,[],[f8349,f3531]) ).

fof(f9565,plain,
    spl0_1189,
    inference(avatar_split_clause,[],[f2281,f9563]) ).

fof(f9563,plain,
    ( spl0_1189
  <=> ! [X0,X3] :
        ( c_less(c_0,X3,tc_nat)
        | ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).

fof(f2281,axiom,
    ! [X3,X0] :
      ( c_less(c_0,X3,tc_nat)
      | ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).

fof(f9561,plain,
    spl0_1188,
    inference(avatar_split_clause,[],[f2247,f9559]) ).

fof(f2247,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_0 = c_plus(X18,c_uminus(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).

fof(f9557,plain,
    spl0_1187,
    inference(avatar_split_clause,[],[f2219,f9555]) ).

fof(f9555,plain,
    ( spl0_1187
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = X18
        | c_0 != c_uminus(X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f2219,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_0 = X18
      | c_0 != c_uminus(X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).

fof(f9553,plain,
    spl0_1186,
    inference(avatar_split_clause,[],[f2213,f9551]) ).

fof(f9551,plain,
    ( spl0_1186
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).

fof(f2213,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).

fof(f9549,plain,
    spl0_1185,
    inference(avatar_split_clause,[],[f2211,f9547]) ).

fof(f9547,plain,
    ( spl0_1185
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).

fof(f2211,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).

fof(f9545,plain,
    spl0_1184,
    inference(avatar_split_clause,[],[f2197,f9543]) ).

fof(f2197,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_uminus(X18,X1) = c_minus(c_0,X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).

fof(f9541,plain,
    spl0_1183,
    inference(avatar_split_clause,[],[f2175,f9539]) ).

fof(f9539,plain,
    ( spl0_1183
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_0 = X18
        | c_0 != c_HOL_Oabs(X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).

fof(f2175,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_0 = X18
      | c_0 != c_HOL_Oabs(X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).

fof(f9537,plain,
    spl0_1182,
    inference(avatar_split_clause,[],[f2171,f9535]) ).

fof(f2171,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_0 = c_plus(c_uminus(X18,X1),X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).

fof(f9533,plain,
    spl0_1181,
    inference(avatar_split_clause,[],[f2039,f9531]) ).

fof(f2039,axiom,
    ! [X21,X15] :
      ( ~ c_lessequals(X15,X21,tc_nat)
      | c_0 = c_minus(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).

fof(f9529,plain,
    spl0_1180,
    inference(avatar_split_clause,[],[f2038,f9527]) ).

fof(f2038,axiom,
    ! [X21,X15] :
      ( c_lessequals(X15,X21,tc_nat)
      | c_0 != c_minus(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).

fof(f9525,plain,
    ( spl0_1179
    | ~ spl0_14
    | ~ spl0_973 ),
    inference(avatar_split_clause,[],[f8620,f8344,f3499,f9523]) ).

fof(f9523,plain,
    ( spl0_1179
  <=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).

fof(f8344,plain,
    ( spl0_973
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = c_minus(X18,X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f8620,plain,
    ( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
    | ~ spl0_14
    | ~ spl0_973 ),
    inference(resolution,[],[f8345,f3501]) ).

fof(f8345,plain,
    ( ! [X1,X18] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = c_minus(X18,X18,X1) )
    | ~ spl0_973 ),
    inference(avatar_component_clause,[],[f8344]) ).

fof(f9521,plain,
    spl0_1178,
    inference(avatar_split_clause,[],[f1833,f9519]) ).

fof(f1833,axiom,
    ! [X47] :
      ( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_2) ).

fof(f9517,plain,
    spl0_1177,
    inference(avatar_split_clause,[],[f1832,f9515]) ).

fof(f9515,plain,
    ( spl0_1177
  <=> ! [X47] :
        ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
        | c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).

fof(f1832,axiom,
    ! [X47] :
      ( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).

fof(f9513,plain,
    spl0_1176,
    inference(avatar_split_clause,[],[f1811,f9511]) ).

fof(f9511,plain,
    ( spl0_1176
  <=> ! [X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_0 = X15
        | c_0 != c_NatArith_Oof__nat(X15,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f1811,axiom,
    ! [X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_0 = X15
      | c_0 != c_NatArith_Oof__nat(X15,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).

fof(f9509,plain,
    spl0_1175,
    inference(avatar_split_clause,[],[f1759,f9507]) ).

fof(f9507,plain,
    ( spl0_1175
  <=> ! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).

fof(f1759,axiom,
    ! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).

fof(f9505,plain,
    spl0_1174,
    inference(avatar_split_clause,[],[f1730,f9503]) ).

fof(f9503,plain,
    ( spl0_1174
  <=> ! [X25,X1,X23] :
        ( X23 = X25
        | c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).

fof(f1730,axiom,
    ! [X1,X25,X23] :
      ( X23 = X25
      | c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).

fof(f9501,plain,
    spl0_1173,
    inference(avatar_split_clause,[],[f1603,f9499]) ).

fof(f9499,plain,
    ( spl0_1173
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f1603,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).

fof(f9497,plain,
    spl0_1172,
    inference(avatar_split_clause,[],[f1548,f9495]) ).

fof(f9495,plain,
    ( spl0_1172
  <=> ! [X50,X1] :
        ( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
        | c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).

fof(f1548,axiom,
    ! [X50,X1] :
      ( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
      | c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).

fof(f9493,plain,
    spl0_1171,
    inference(avatar_split_clause,[],[f1541,f9491]) ).

fof(f9491,plain,
    ( spl0_1171
  <=> ! [X54,X57,X55,X56] :
        ( X55 = X57
        | c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).

fof(f1541,axiom,
    ! [X56,X54,X57,X55] :
      ( X55 = X57
      | c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).

fof(f9489,plain,
    spl0_1170,
    inference(avatar_split_clause,[],[f1540,f9487]) ).

fof(f9487,plain,
    ( spl0_1170
  <=> ! [X55,X54,X56,X57] :
        ( X54 = X56
        | c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f1540,axiom,
    ! [X56,X54,X57,X55] :
      ( X54 = X56
      | c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).

fof(f9485,plain,
    spl0_1169,
    inference(avatar_split_clause,[],[f1509,f9483]) ).

fof(f9483,plain,
    ( spl0_1169
  <=> ! [X50,X1] :
        ( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
        | c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f1509,axiom,
    ! [X50,X1] :
      ( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
      | c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).

fof(f9481,plain,
    ( spl0_1168
    | ~ spl0_14
    | ~ spl0_972 ),
    inference(avatar_split_clause,[],[f8616,f8340,f3499,f9479]) ).

fof(f9479,plain,
    ( spl0_1168
  <=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f8340,plain,
    ( spl0_972
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_minus(X3,c_0,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).

fof(f8616,plain,
    ( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
    | ~ spl0_14
    | ~ spl0_972 ),
    inference(resolution,[],[f8341,f3501]) ).

fof(f8341,plain,
    ( ! [X3,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_minus(X3,c_0,X1) = X3 )
    | ~ spl0_972 ),
    inference(avatar_component_clause,[],[f8340]) ).

fof(f9477,plain,
    spl0_1167,
    inference(avatar_split_clause,[],[f1488,f9475]) ).

fof(f9475,plain,
    ( spl0_1167
  <=> ! [X48,X11] :
        ( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
        | c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f1488,axiom,
    ! [X48,X11] :
      ( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).

fof(f9473,plain,
    spl0_1166,
    inference(avatar_split_clause,[],[f1487,f9471]) ).

fof(f1487,axiom,
    ! [X48,X11] :
      ( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
      | ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).

fof(f9468,plain,
    spl0_1165,
    inference(avatar_split_clause,[],[f1467,f9466]) ).

fof(f1467,axiom,
    ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).

fof(f9464,plain,
    spl0_1164,
    inference(avatar_split_clause,[],[f1440,f9462]) ).

fof(f9462,plain,
    ( spl0_1164
  <=> ! [X48,X11] :
        ( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
        | c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f1440,axiom,
    ! [X48,X11] :
      ( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).

fof(f9460,plain,
    spl0_1163,
    inference(avatar_split_clause,[],[f1439,f9458]) ).

fof(f1439,axiom,
    ! [X48,X11] :
      ( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
      | ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).

fof(f9456,plain,
    spl0_1162,
    inference(avatar_split_clause,[],[f1430,f9454]) ).

fof(f9454,plain,
    ( spl0_1162
  <=> ! [X48,X11] :
        ( c_less(X11,X48,tc_IntDef_Oint)
        | ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f1430,axiom,
    ! [X48,X11] :
      ( c_less(X11,X48,tc_IntDef_Oint)
      | ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).

fof(f9452,plain,
    spl0_1161,
    inference(avatar_split_clause,[],[f1429,f9450]) ).

fof(f9450,plain,
    ( spl0_1161
  <=> ! [X48,X11] :
        ( c_less(c_0,X48,tc_IntDef_Oint)
        | ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f1429,axiom,
    ! [X48,X11] :
      ( c_less(c_0,X48,tc_IntDef_Oint)
      | ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).

fof(f9448,plain,
    spl0_1160,
    inference(avatar_split_clause,[],[f1428,f9446]) ).

fof(f9446,plain,
    ( spl0_1160
  <=> ! [X21,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f1428,axiom,
    ! [X21,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).

fof(f9444,plain,
    spl0_1159,
    inference(avatar_split_clause,[],[f1427,f9442]) ).

fof(f9442,plain,
    ( spl0_1159
  <=> ! [X21,X15] :
        ( c_less(X15,X21,tc_nat)
        | ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f1427,axiom,
    ! [X21,X15] :
      ( c_less(X15,X21,tc_nat)
      | ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).

fof(f9440,plain,
    spl0_1158,
    inference(avatar_split_clause,[],[f1426,f9438]) ).

fof(f9438,plain,
    ( spl0_1158
  <=> ! [X21,X15] :
        ( ~ c_lessequals(X15,X21,tc_nat)
        | c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f1426,axiom,
    ! [X21,X15] :
      ( ~ c_lessequals(X15,X21,tc_nat)
      | c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).

fof(f9436,plain,
    ( spl0_1157
    | ~ spl0_9
    | ~ spl0_971 ),
    inference(avatar_split_clause,[],[f8614,f8336,f3474,f9434]) ).

fof(f9434,plain,
    ( spl0_1157
  <=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f3474,plain,
    ( spl0_9
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f8336,plain,
    ( spl0_971
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
        | c_plus(c_0,X3,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).

fof(f8614,plain,
    ( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
    | ~ spl0_9
    | ~ spl0_971 ),
    inference(resolution,[],[f8337,f3476]) ).

fof(f3476,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f3474]) ).

fof(f8337,plain,
    ( ! [X3,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
        | c_plus(c_0,X3,X1) = X3 )
    | ~ spl0_971 ),
    inference(avatar_component_clause,[],[f8336]) ).

fof(f9432,plain,
    spl0_1156,
    inference(avatar_split_clause,[],[f1425,f9430]) ).

fof(f9430,plain,
    ( spl0_1156
  <=> ! [X21,X15] :
        ( c_lessequals(X15,X21,tc_nat)
        | ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f1425,axiom,
    ! [X21,X15] :
      ( c_lessequals(X15,X21,tc_nat)
      | ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).

fof(f9428,plain,
    spl0_1155,
    inference(avatar_split_clause,[],[f1407,f9426]) ).

fof(f1407,axiom,
    ! [X21,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).

fof(f9424,plain,
    spl0_1154,
    inference(avatar_split_clause,[],[f1404,f9422]) ).

fof(f9422,plain,
    ( spl0_1154
  <=> ! [X11,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = X11
        | c_0 != c_IntDef_Oof__int(X11,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f1404,axiom,
    ! [X11,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = X11
      | c_0 != c_IntDef_Oof__int(X11,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).

fof(f9420,plain,
    spl0_1153,
    inference(avatar_split_clause,[],[f1390,f9418]) ).

fof(f9418,plain,
    ( spl0_1153
  <=> ! [X21,X15] :
        ( c_0 = X15
        | c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).

fof(f1390,axiom,
    ! [X21,X15] :
      ( c_0 = X15
      | c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).

fof(f9416,plain,
    spl0_1152,
    inference(avatar_split_clause,[],[f1389,f9414]) ).

fof(f9414,plain,
    ( spl0_1152
  <=> ! [X21,X15] :
        ( c_0 = X21
        | c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).

fof(f1389,axiom,
    ! [X21,X15] :
      ( c_0 = X21
      | c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).

fof(f9412,plain,
    spl0_1151,
    inference(avatar_split_clause,[],[f1279,f9410]) ).

fof(f1279,axiom,
    ! [X1,X12] :
      ( c_0 = c_Finite__Set_Ocard(X12,X1)
      | c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).

fof(f9408,plain,
    spl0_1150,
    inference(avatar_split_clause,[],[f1275,f9406]) ).

fof(f1275,axiom,
    ! [X3,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).

fof(f9404,plain,
    spl0_1149,
    inference(avatar_split_clause,[],[f1265,f9402]) ).

fof(f1265,axiom,
    ! [X3,X1] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).

fof(f9400,plain,
    spl0_1148,
    inference(avatar_split_clause,[],[f1235,f9398]) ).

fof(f9398,plain,
    ( spl0_1148
  <=> ! [X21,X3] :
        ( ~ c_less(X3,X21,tc_nat)
        | c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f1235,axiom,
    ! [X21,X3] :
      ( ~ c_less(X3,X21,tc_nat)
      | c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).

fof(f9396,plain,
    spl0_1147,
    inference(avatar_split_clause,[],[f1224,f9394]) ).

fof(f9394,plain,
    ( spl0_1147
  <=> ! [X21] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_1 = c_div(X21,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f1224,axiom,
    ! [X21] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_1 = c_div(X21,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).

fof(f9391,plain,
    spl0_1146,
    inference(avatar_split_clause,[],[f1216,f9389]) ).

fof(f9389,plain,
    ( spl0_1146
  <=> ! [X21,X15] :
        ( ~ c_less(X15,X21,tc_nat)
        | c_0 = c_div(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f1216,axiom,
    ! [X21,X15] :
      ( ~ c_less(X15,X21,tc_nat)
      | c_0 = c_div(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).

fof(f9387,plain,
    spl0_1145,
    inference(avatar_split_clause,[],[f1199,f9385]) ).

fof(f9385,plain,
    ( spl0_1145
  <=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f1199,axiom,
    ! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom_0) ).

fof(f9383,plain,
    spl0_1144,
    inference(avatar_split_clause,[],[f1196,f9381]) ).

fof(f9381,plain,
    ( spl0_1144
  <=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f1196,axiom,
    ! [X2,X1,X9,X7,X16] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons_0) ).

fof(f9379,plain,
    spl0_1143,
    inference(avatar_split_clause,[],[f1194,f9377]) ).

fof(f9377,plain,
    ( spl0_1143
  <=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f1194,axiom,
    ! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons_0) ).

fof(f9375,plain,
    spl0_1142,
    inference(avatar_split_clause,[],[f1180,f9373]) ).

fof(f9373,plain,
    ( spl0_1142
  <=> ! [X2,X27,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f1180,axiom,
    ! [X2,X1,X27] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).

fof(f9371,plain,
    spl0_1141,
    inference(avatar_split_clause,[],[f1179,f9369]) ).

fof(f9369,plain,
    ( spl0_1141
  <=> ! [X2,X1,X18] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f1179,axiom,
    ! [X2,X18,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).

fof(f9367,plain,
    spl0_1140,
    inference(avatar_split_clause,[],[f1175,f9365]) ).

fof(f9365,plain,
    ( spl0_1140
  <=> ! [X18,X1,X42] :
        ( X18 = X42
        | c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f1175,axiom,
    ! [X18,X1,X42] :
      ( X18 = X42
      | c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).

fof(f9363,plain,
    spl0_1139,
    inference(avatar_split_clause,[],[f1170,f9361]) ).

fof(f9361,plain,
    ( spl0_1139
  <=> ! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f1170,axiom,
    ! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).

fof(f9359,plain,
    spl0_1138,
    inference(avatar_split_clause,[],[f1169,f9357]) ).

fof(f9357,plain,
    ( spl0_1138
  <=> ! [X0,X1] :
        ( c_Datatype_Ooption_ONone = X0
        | c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f1169,axiom,
    ! [X0,X1] :
      ( c_Datatype_Ooption_ONone = X0
      | c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).

fof(f9355,plain,
    spl0_1137,
    inference(avatar_split_clause,[],[f1168,f9353]) ).

fof(f9353,plain,
    ( spl0_1137
  <=> ! [X0,X1] :
        ( c_Datatype_Ooption_ONone = X0
        | c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f1168,axiom,
    ! [X0,X1] :
      ( c_Datatype_Ooption_ONone = X0
      | c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).

fof(f9351,plain,
    spl0_1136,
    inference(avatar_split_clause,[],[f105,f9349]) ).

fof(f9349,plain,
    ( spl0_1136
  <=> ! [X18,X27,X1] :
        ( X18 = X27
        | ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f105,axiom,
    ! [X18,X1,X27] :
      ( X18 = X27
      | ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

fof(f9347,plain,
    spl0_1135,
    inference(avatar_split_clause,[],[f103,f9345]) ).

fof(f9345,plain,
    ( spl0_1135
  <=> ! [X13,X12,X1] :
        ( ~ c_less(X12,X13,tc_set(X1))
        | c_lessequals(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f103,axiom,
    ! [X1,X12,X13] :
      ( ~ c_less(X12,X13,tc_set(X1))
      | c_lessequals(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).

fof(f9343,plain,
    spl0_1134,
    inference(avatar_split_clause,[],[f102,f9341]) ).

fof(f9341,plain,
    ( spl0_1134
  <=> ! [X13,X12,X1] :
        ( ~ c_lessequals(X13,X12,tc_set(X1))
        | ~ c_less(X12,X13,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f102,axiom,
    ! [X1,X12,X13] :
      ( ~ c_lessequals(X13,X12,tc_set(X1))
      | ~ c_less(X12,X13,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).

fof(f9308,plain,
    ( ~ spl0_1133
    | spl0_5
    | ~ spl0_1104 ),
    inference(avatar_split_clause,[],[f9300,f9004,f3454,f9305]) ).

fof(f9305,plain,
    ( spl0_1133
  <=> c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f9004,plain,
    ( spl0_1104
  <=> ! [X86,X88] :
        ( ~ c_in(X86,X88,tc_Message_Omsg)
        | c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f9300,plain,
    ( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
    | spl0_5
    | ~ spl0_1104 ),
    inference(resolution,[],[f9005,f3456]) ).

fof(f9005,plain,
    ( ! [X88,X86] :
        ( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
        | ~ c_in(X86,X88,tc_Message_Omsg) )
    | ~ spl0_1104 ),
    inference(avatar_component_clause,[],[f9004]) ).

fof(f9295,plain,
    ( spl0_1132
    | ~ spl0_817
    | ~ spl0_1089 ),
    inference(avatar_split_clause,[],[f9272,f8944,f7631,f9293]) ).

fof(f9293,plain,
    ( spl0_1132
  <=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f9272,plain,
    ( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
    | ~ spl0_817
    | ~ spl0_1089 ),
    inference(superposition,[],[f7632,f8945]) ).

fof(f9269,plain,
    ( spl0_1131
    | ~ spl0_915
    | ~ spl0_1071 ),
    inference(avatar_split_clause,[],[f9233,f8872,f8062,f9267]) ).

fof(f9267,plain,
    ( spl0_1131
  <=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f8062,plain,
    ( spl0_915
  <=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f9233,plain,
    ( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
    | ~ spl0_915
    | ~ spl0_1071 ),
    inference(resolution,[],[f8873,f8063]) ).

fof(f8063,plain,
    ( ! [X0] : c_lessequals(X0,X0,tc_nat)
    | ~ spl0_915 ),
    inference(avatar_component_clause,[],[f8062]) ).

fof(f9221,plain,
    ( spl0_1130
    | ~ spl0_817
    | ~ spl0_1061 ),
    inference(avatar_split_clause,[],[f9215,f8832,f7631,f9219]) ).

fof(f9219,plain,
    ( spl0_1130
  <=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f9215,plain,
    ( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
    | ~ spl0_817
    | ~ spl0_1061 ),
    inference(superposition,[],[f7632,f8833]) ).

fof(f9203,plain,
    ( spl0_1129
    | ~ spl0_9
    | ~ spl0_970 ),
    inference(avatar_split_clause,[],[f8612,f8332,f3474,f9201]) ).

fof(f8332,plain,
    ( spl0_970
  <=> ! [X1,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
        | c_plus(X3,c_0,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f8612,plain,
    ( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
    | ~ spl0_9
    | ~ spl0_970 ),
    inference(resolution,[],[f8333,f3476]) ).

fof(f8333,plain,
    ( ! [X3,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
        | c_plus(X3,c_0,X1) = X3 )
    | ~ spl0_970 ),
    inference(avatar_component_clause,[],[f8332]) ).

fof(f9175,plain,
    ( spl0_1128
    | ~ spl0_716
    | ~ spl0_911
    | ~ spl0_966 ),
    inference(avatar_split_clause,[],[f8601,f8316,f8021,f7200,f9172]) ).

fof(f9172,plain,
    ( spl0_1128
  <=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f8316,plain,
    ( spl0_966
  <=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f8601,plain,
    ( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
    | ~ spl0_716
    | ~ spl0_911
    | ~ spl0_966 ),
    inference(forward_demodulation,[],[f8599,f7202]) ).

fof(f8599,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_911
    | ~ spl0_966 ),
    inference(superposition,[],[f8317,f8023]) ).

fof(f8317,plain,
    ( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
    | ~ spl0_966 ),
    inference(avatar_component_clause,[],[f8316]) ).

fof(f9118,plain,
    ( spl0_1127
    | ~ spl0_87
    | ~ spl0_949 ),
    inference(avatar_split_clause,[],[f8572,f8248,f3864,f9116]) ).

fof(f9116,plain,
    ( spl0_1127
  <=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f3864,plain,
    ( spl0_87
  <=> class_LOrder_Omeet__semilorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f8248,plain,
    ( spl0_949
  <=> ! [X1,X3] :
        ( ~ class_LOrder_Omeet__semilorder(X1)
        | c_LOrder_Omeet(X3,X3,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).

fof(f8572,plain,
    ( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
    | ~ spl0_87
    | ~ spl0_949 ),
    inference(resolution,[],[f8249,f3866]) ).

fof(f3866,plain,
    ( class_LOrder_Omeet__semilorder(tc_nat)
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f3864]) ).

fof(f8249,plain,
    ( ! [X3,X1] :
        ( ~ class_LOrder_Omeet__semilorder(X1)
        | c_LOrder_Omeet(X3,X3,X1) = X3 )
    | ~ spl0_949 ),
    inference(avatar_component_clause,[],[f8248]) ).

fof(f9094,plain,
    spl0_1126,
    inference(avatar_split_clause,[],[f3331,f9092]) ).

fof(f9092,plain,
    ( spl0_1126
  <=> ! [X48] :
        ( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
        | c_less(c_1,X48,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f3331,plain,
    ! [X48] :
      ( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
      | c_less(c_1,X48,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3141,f2979]) ).

fof(f3141,plain,
    ! [X48] :
      ( c_less(c_1,X48,tc_IntDef_Oint)
      | ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
    inference(definition_unfolding,[],[f1346,f2544]) ).

fof(f1346,axiom,
    ! [X48] :
      ( c_less(c_1,X48,tc_IntDef_Oint)
      | ~ c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).

fof(f9090,plain,
    spl0_1125,
    inference(avatar_split_clause,[],[f3320,f9088]) ).

fof(f3320,plain,
    ! [X48] :
      ( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
      | ~ c_less(c_1,X48,tc_IntDef_Oint) ),
    inference(forward_demodulation,[],[f3125,f2979]) ).

fof(f3125,plain,
    ! [X48] :
      ( ~ c_less(c_1,X48,tc_IntDef_Oint)
      | c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
    inference(definition_unfolding,[],[f1347,f2544]) ).

fof(f1347,axiom,
    ! [X48] :
      ( ~ c_less(c_1,X48,tc_IntDef_Oint)
      | c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).

fof(f9086,plain,
    ( spl0_1124
    | ~ spl0_29
    | ~ spl0_949 ),
    inference(avatar_split_clause,[],[f8571,f8248,f3574,f9084]) ).

fof(f9084,plain,
    ( spl0_1124
  <=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f3574,plain,
    ( spl0_29
  <=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f8571,plain,
    ( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
    | ~ spl0_29
    | ~ spl0_949 ),
    inference(resolution,[],[f8249,f3576]) ).

fof(f3576,plain,
    ( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f3574]) ).

fof(f9082,plain,
    spl0_1123,
    inference(avatar_split_clause,[],[f3315,f9080]) ).

fof(f9080,plain,
    ( spl0_1123
  <=> ! [X21,X15] :
        ( c_1 != c_times(X15,X21,tc_nat)
        | c_1 = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f3315,plain,
    ! [X21,X15] :
      ( c_1 != c_times(X15,X21,tc_nat)
      | c_1 = X15 ),
    inference(forward_demodulation,[],[f3119,f2979]) ).

fof(f3119,plain,
    ! [X21,X15] :
      ( c_1 = X15
      | c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2092,f2544]) ).

fof(f2092,axiom,
    ! [X21,X15] :
      ( c_1 = X15
      | c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).

fof(f9078,plain,
    spl0_1122,
    inference(avatar_split_clause,[],[f3314,f9076]) ).

fof(f9076,plain,
    ( spl0_1122
  <=> ! [X21,X15] :
        ( c_1 != c_times(X15,X21,tc_nat)
        | c_1 = X21 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f3314,plain,
    ! [X21,X15] :
      ( c_1 != c_times(X15,X21,tc_nat)
      | c_1 = X21 ),
    inference(forward_demodulation,[],[f3118,f2979]) ).

fof(f3118,plain,
    ! [X21,X15] :
      ( c_1 = X21
      | c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f2093,f2544]) ).

fof(f2093,axiom,
    ! [X21,X15] :
      ( c_1 = X21
      | c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).

fof(f9074,plain,
    spl0_1121,
    inference(avatar_split_clause,[],[f3026,f9072]) ).

fof(f9072,plain,
    ( spl0_1121
  <=> ! [X13,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(X13,c_List_Olist_ONil),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f3026,plain,
    ! [X27,X12,X13] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(X13,c_List_Olist_ONil),tc_Message_Omsg),
    inference(definition_unfolding,[],[f2918,f2795]) ).

fof(f2918,axiom,
    ! [X27,X12,X13] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_OinitState(X13),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).

fof(f9070,plain,
    spl0_1120,
    inference(avatar_split_clause,[],[f3025,f9068]) ).

fof(f3025,plain,
    ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin),
    inference(definition_unfolding,[],[f2132,f2113]) ).

fof(f2132,axiom,
    ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).

fof(f9066,plain,
    spl0_1119,
    inference(avatar_split_clause,[],[f3010,f9064]) ).

fof(f9064,plain,
    ( spl0_1119
  <=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f3010,plain,
    ! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3,
    inference(definition_unfolding,[],[f2603,f2373]) ).

fof(f2603,axiom,
    ! [X3,X1] : c_inter(X3,X3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).

fof(f9062,plain,
    spl0_1118,
    inference(avatar_split_clause,[],[f3009,f9060]) ).

fof(f9060,plain,
    ( spl0_1118
  <=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f3009,plain,
    ! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3,
    inference(definition_unfolding,[],[f2601,f2373]) ).

fof(f2601,axiom,
    ! [X3,X1] : c_inter(c_UNIV,X3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).

fof(f9058,plain,
    spl0_1117,
    inference(avatar_split_clause,[],[f3008,f9056]) ).

fof(f9056,plain,
    ( spl0_1117
  <=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f3008,plain,
    ! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3,
    inference(definition_unfolding,[],[f2602,f2373]) ).

fof(f2602,axiom,
    ! [X3,X1] : c_inter(X3,c_UNIV,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).

fof(f9054,plain,
    spl0_1116,
    inference(avatar_split_clause,[],[f3002,f9052]) ).

fof(f9052,plain,
    ( spl0_1116
  <=> ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f3002,plain,
    ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),
    inference(definition_unfolding,[],[f1160,f2544]) ).

fof(f1160,axiom,
    ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).

fof(f9050,plain,
    spl0_1115,
    inference(avatar_split_clause,[],[f2994,f9048]) ).

fof(f9048,plain,
    ( spl0_1115
  <=> ! [X86,X109,X87] : c_Message_Omsg_OHash(X109) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f2994,plain,
    ! [X109,X86,X87] : c_Message_Omsg_OHash(X109) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
    inference(definition_unfolding,[],[f2824,f2812]) ).

fof(f2824,axiom,
    ! [X109,X86,X87] : c_Message_OHPair(X86,X87) != c_Message_Omsg_OHash(X109),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).

fof(f9046,plain,
    spl0_1114,
    inference(avatar_split_clause,[],[f2992,f9044]) ).

fof(f9044,plain,
    ( spl0_1114
  <=> ! [X86,X91,X87] : c_Message_Omsg_OKey(X91) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f2992,plain,
    ! [X91,X86,X87] : c_Message_Omsg_OKey(X91) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
    inference(definition_unfolding,[],[f2825,f2812]) ).

fof(f2825,axiom,
    ! [X91,X86,X87] : c_Message_Omsg_OKey(X91) != c_Message_OHPair(X86,X87),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).

fof(f9042,plain,
    ( spl0_1113
    | ~ spl0_94
    | ~ spl0_948 ),
    inference(avatar_split_clause,[],[f8570,f8244,f3899,f9040]) ).

fof(f9040,plain,
    ( spl0_1113
  <=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f3899,plain,
    ( spl0_94
  <=> class_LOrder_Ojoin__semilorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f8244,plain,
    ( spl0_948
  <=> ! [X1,X3] :
        ( ~ class_LOrder_Ojoin__semilorder(X1)
        | c_LOrder_Ojoin(X3,X3,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f8570,plain,
    ( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
    | ~ spl0_94
    | ~ spl0_948 ),
    inference(resolution,[],[f8245,f3901]) ).

fof(f3901,plain,
    ( class_LOrder_Ojoin__semilorder(tc_nat)
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f3899]) ).

fof(f8245,plain,
    ( ! [X3,X1] :
        ( ~ class_LOrder_Ojoin__semilorder(X1)
        | c_LOrder_Ojoin(X3,X3,X1) = X3 )
    | ~ spl0_948 ),
    inference(avatar_component_clause,[],[f8244]) ).

fof(f9038,plain,
    spl0_1112,
    inference(avatar_split_clause,[],[f2990,f9036]) ).

fof(f9036,plain,
    ( spl0_1112
  <=> ! [X86,X12,X87] : c_Message_Omsg_OAgent(X12) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f2990,plain,
    ! [X86,X87,X12] : c_Message_Omsg_OAgent(X12) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
    inference(definition_unfolding,[],[f2813,f2812]) ).

fof(f2813,axiom,
    ! [X86,X87,X12] : c_Message_Omsg_OAgent(X12) != c_Message_OHPair(X86,X87),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1_0) ).

fof(f9034,plain,
    spl0_1111,
    inference(avatar_split_clause,[],[f2988,f9032]) ).

fof(f9032,plain,
    ( spl0_1111
  <=> ! [X86,X87,X7] : c_Message_Omsg_ONonce(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f2988,plain,
    ! [X86,X7,X87] : c_Message_Omsg_ONonce(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
    inference(definition_unfolding,[],[f2826,f2812]) ).

fof(f2826,axiom,
    ! [X86,X7,X87] : c_Message_Omsg_ONonce(X7) != c_Message_OHPair(X86,X87),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).

fof(f9030,plain,
    spl0_1110,
    inference(avatar_split_clause,[],[f2986,f9028]) ).

fof(f9028,plain,
    ( spl0_1110
  <=> ! [X86,X87,X7] : c_Message_Omsg_ONumber(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f2986,plain,
    ! [X86,X7,X87] : c_Message_Omsg_ONumber(X7) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87),
    inference(definition_unfolding,[],[f2815,f2812]) ).

fof(f2815,axiom,
    ! [X86,X7,X87] : c_Message_Omsg_ONumber(X7) != c_Message_OHPair(X86,X87),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3_0) ).

fof(f9026,plain,
    spl0_1109,
    inference(avatar_split_clause,[],[f2932,f9024]) ).

fof(f9024,plain,
    ( spl0_1109
  <=> ! [X91] :
        ( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
        | c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f2932,axiom,
    ! [X91] :
      ( ~ c_in(X91,c_Message_OsymKeys,tc_nat)
      | c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_1) ).

fof(f9022,plain,
    spl0_1108,
    inference(avatar_split_clause,[],[f2931,f9020]) ).

fof(f9020,plain,
    ( spl0_1108
  <=> ! [X91] :
        ( c_in(X91,c_Message_OsymKeys,tc_nat)
        | ~ c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f2931,axiom,
    ! [X91] :
      ( c_in(X91,c_Message_OsymKeys,tc_nat)
      | ~ c_in(c_Message_OinvKey(X91),c_Message_OsymKeys,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_0) ).

fof(f9018,plain,
    spl0_1107,
    inference(avatar_split_clause,[],[f2930,f9016]) ).

fof(f9016,plain,
    ( spl0_1107
  <=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f2930,axiom,
    ! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).

fof(f9014,plain,
    spl0_1106,
    inference(avatar_split_clause,[],[f2916,f9012]) ).

fof(f9012,plain,
    ( spl0_1106
  <=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oused(X102),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f2916,axiom,
    ! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(X27,X12))),c_Event_Oused(X102),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).

fof(f9010,plain,
    spl0_1105,
    inference(avatar_split_clause,[],[f2886,f9008]) ).

fof(f9008,plain,
    ( spl0_1105
  <=> ! [X86,X88] :
        ( ~ c_in(X86,X88,tc_Message_Omsg)
        | c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f2886,axiom,
    ! [X88,X86] :
      ( ~ c_in(X86,X88,tc_Message_Omsg)
      | c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).

fof(f9006,plain,
    spl0_1104,
    inference(avatar_split_clause,[],[f2847,f9004]) ).

fof(f2847,axiom,
    ! [X88,X86] :
      ( ~ c_in(X86,X88,tc_Message_Omsg)
      | c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).

fof(f9002,plain,
    spl0_1103,
    inference(avatar_split_clause,[],[f2767,f9000]) ).

fof(f2767,axiom,
    ! [X88,X86] :
      ( ~ c_in(X86,X88,tc_Message_Omsg)
      | c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

fof(f8998,plain,
    ( spl0_1102
    | ~ spl0_30
    | ~ spl0_948 ),
    inference(avatar_split_clause,[],[f8569,f8244,f3579,f8996]) ).

fof(f8996,plain,
    ( spl0_1102
  <=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f3579,plain,
    ( spl0_30
  <=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f8569,plain,
    ( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
    | ~ spl0_30
    | ~ spl0_948 ),
    inference(resolution,[],[f8245,f3581]) ).

fof(f3581,plain,
    ( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f3579]) ).

fof(f8994,plain,
    spl0_1101,
    inference(avatar_split_clause,[],[f2750,f8992]) ).

fof(f8992,plain,
    ( spl0_1101
  <=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f2750,axiom,
    ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).

fof(f8990,plain,
    spl0_1100,
    inference(avatar_split_clause,[],[f2749,f8988]) ).

fof(f8988,plain,
    ( spl0_1100
  <=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f2749,axiom,
    ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).

fof(f8986,plain,
    spl0_1099,
    inference(avatar_split_clause,[],[f2747,f8984]) ).

fof(f8984,plain,
    ( spl0_1099
  <=> ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f2747,axiom,
    ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).

fof(f8982,plain,
    spl0_1098,
    inference(avatar_split_clause,[],[f2746,f8980]) ).

fof(f8980,plain,
    ( spl0_1098
  <=> ! [X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f2746,axiom,
    ! [X88,X86] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).

fof(f8978,plain,
    spl0_1097,
    inference(avatar_split_clause,[],[f2744,f8976]) ).

fof(f8976,plain,
    ( spl0_1097
  <=> ! [X12,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f2744,axiom,
    ! [X88,X12] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).

fof(f8974,plain,
    spl0_1096,
    inference(avatar_split_clause,[],[f2718,f8972]) ).

fof(f8972,plain,
    ( spl0_1096
  <=> ! [X5,X1] :
        ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f2718,axiom,
    ! [X1,X5] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).

fof(f8970,plain,
    spl0_1095,
    inference(avatar_split_clause,[],[f2717,f8968]) ).

fof(f8968,plain,
    ( spl0_1095
  <=> ! [X5,X1] :
        ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
        | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f2717,axiom,
    ! [X1,X5] :
      ( c_Wellfounded__Recursion_Oacyclic(X5,X1)
      | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).

fof(f8966,plain,
    spl0_1094,
    inference(avatar_split_clause,[],[f2702,f8964]) ).

fof(f8964,plain,
    ( spl0_1094
  <=> ! [X2,X27,X1,X18] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f2702,axiom,
    ! [X2,X18,X1,X27] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr_0) ).

fof(f8962,plain,
    spl0_1093,
    inference(avatar_split_clause,[],[f2667,f8960]) ).

fof(f8960,plain,
    ( spl0_1093
  <=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f2667,axiom,
    ! [X3,X1] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).

fof(f8958,plain,
    spl0_1092,
    inference(avatar_split_clause,[],[f2659,f8956]) ).

fof(f2659,axiom,
    ! [X1,X12] :
      ( c_emptyset = X12
      | c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).

fof(f8954,plain,
    spl0_1091,
    inference(avatar_split_clause,[],[f2636,f8952]) ).

fof(f8952,plain,
    ( spl0_1091
  <=> ! [X13,X12,X1] :
        ( c_emptyset = X13
        | c_emptyset != c_union(X12,X13,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f2636,axiom,
    ! [X1,X12,X13] :
      ( c_emptyset = X13
      | c_emptyset != c_union(X12,X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).

fof(f8950,plain,
    spl0_1090,
    inference(avatar_split_clause,[],[f2635,f8948]) ).

fof(f2635,axiom,
    ! [X1,X12,X13] :
      ( c_emptyset = X12
      | c_emptyset != c_union(X12,X13,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).

fof(f8946,plain,
    spl0_1089,
    inference(avatar_split_clause,[],[f2626,f8944]) ).

fof(f2626,axiom,
    ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).

fof(f8942,plain,
    spl0_1088,
    inference(avatar_split_clause,[],[f2390,f8940]) ).

fof(f8940,plain,
    ( spl0_1088
  <=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f2390,axiom,
    ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).

fof(f8938,plain,
    spl0_1087,
    inference(avatar_split_clause,[],[f2389,f8936]) ).

fof(f8936,plain,
    ( spl0_1087
  <=> ! [X1,X3] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f2389,axiom,
    ! [X3,X1] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).

fof(f8934,plain,
    spl0_1086,
    inference(avatar_split_clause,[],[f2382,f8932]) ).

fof(f8932,plain,
    ( spl0_1086
  <=> ! [X2,X1,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f2382,axiom,
    ! [X2,X3,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).

fof(f8930,plain,
    spl0_1085,
    inference(avatar_split_clause,[],[f2298,f8928]) ).

fof(f8928,plain,
    ( spl0_1085
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
        | c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f2298,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).

fof(f8926,plain,
    spl0_1084,
    inference(avatar_split_clause,[],[f2297,f8924]) ).

fof(f8924,plain,
    ( spl0_1084
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f2297,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).

fof(f8922,plain,
    spl0_1083,
    inference(avatar_split_clause,[],[f2293,f8920]) ).

fof(f8920,plain,
    ( spl0_1083
  <=> ! [X0,X21] :
        ( c_Parity_Oeven(X0,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f2293,axiom,
    ! [X21,X0] :
      ( c_Parity_Oeven(X0,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).

fof(f8918,plain,
    spl0_1082,
    inference(avatar_split_clause,[],[f2285,f8916]) ).

fof(f8916,plain,
    ( spl0_1082
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X3,tc_nat)
        | c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f2285,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X3,tc_nat)
      | c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).

fof(f8914,plain,
    ( ~ spl0_79
    | spl0_1081
    | ~ spl0_683
    | ~ spl0_944 ),
    inference(avatar_split_clause,[],[f8568,f8227,f7050,f8912,f3824]) ).

fof(f3824,plain,
    ( spl0_79
  <=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f7050,plain,
    ( spl0_683
  <=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f8227,plain,
    ( spl0_944
  <=> ! [X21,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f8568,plain,
    ( ! [X0] :
        ( c_in(X0,c_IntDef_ONats,tc_nat)
        | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
    | ~ spl0_683
    | ~ spl0_944 ),
    inference(superposition,[],[f8228,f7051]) ).

fof(f7051,plain,
    ( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
    | ~ spl0_683 ),
    inference(avatar_component_clause,[],[f7050]) ).

fof(f8228,plain,
    ( ! [X21,X1] :
        ( c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1)
        | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) )
    | ~ spl0_944 ),
    inference(avatar_component_clause,[],[f8227]) ).

fof(f8910,plain,
    spl0_1080,
    inference(avatar_split_clause,[],[f2284,f8908]) ).

fof(f8908,plain,
    ( spl0_1080
  <=> ! [X0,X3] :
        ( ~ c_Parity_Oeven(X0,tc_nat)
        | c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f2284,axiom,
    ! [X3,X0] :
      ( ~ c_Parity_Oeven(X0,tc_nat)
      | c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).

fof(f8906,plain,
    spl0_1079,
    inference(avatar_split_clause,[],[f2280,f8904]) ).

fof(f2280,axiom,
    ! [X3,X0] :
      ( c_Parity_Oeven(X0,tc_nat)
      | ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).

fof(f8902,plain,
    spl0_1078,
    inference(avatar_split_clause,[],[f2216,f8900]) ).

fof(f2216,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_uminus(c_uminus(X3,X1),X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).

fof(f8898,plain,
    spl0_1077,
    inference(avatar_split_clause,[],[f2154,f8896]) ).

fof(f8894,plain,
    spl0_1076,
    inference(avatar_split_clause,[],[f2150,f8892]) ).

fof(f8892,plain,
    ( spl0_1076
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f2150,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).

fof(f8890,plain,
    spl0_1075,
    inference(avatar_split_clause,[],[f2136,f8888]) ).

fof(f8888,plain,
    ( spl0_1075
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f2136,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).

fof(f8886,plain,
    spl0_1074,
    inference(avatar_split_clause,[],[f2118,f8884]) ).

fof(f2118,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).

fof(f8882,plain,
    spl0_1073,
    inference(avatar_split_clause,[],[f2032,f8880]) ).

fof(f8880,plain,
    ( spl0_1073
  <=> ! [X21,X15] :
        ( c_0 = X21
        | c_0 != c_plus(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f2032,axiom,
    ! [X21,X15] :
      ( c_0 = X21
      | c_0 != c_plus(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).

fof(f8878,plain,
    spl0_1072,
    inference(avatar_split_clause,[],[f2031,f8876]) ).

fof(f8876,plain,
    ( spl0_1072
  <=> ! [X21,X15] :
        ( c_0 = X15
        | c_0 != c_plus(X15,X21,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f2031,axiom,
    ! [X21,X15] :
      ( c_0 = X15
      | c_0 != c_plus(X15,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).

fof(f8874,plain,
    spl0_1071,
    inference(avatar_split_clause,[],[f1786,f8872]) ).

fof(f1786,axiom,
    ! [X59,X43] :
      ( ~ c_lessequals(X59,X43,tc_nat)
      | c_List_Olist_ONil = c_List_Oupt(X43,X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).

fof(f8870,plain,
    ( spl0_1070
    | ~ spl0_842
    | ~ spl0_860 ),
    inference(avatar_split_clause,[],[f8069,f7816,f7744,f8868]) ).

fof(f8868,plain,
    ( spl0_1070
  <=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f7744,plain,
    ( spl0_842
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f7816,plain,
    ( spl0_860
  <=> ! [X15] :
        ( c_0 = X15
        | ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f8069,plain,
    ( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
    | ~ spl0_842
    | ~ spl0_860 ),
    inference(resolution,[],[f7817,f7745]) ).

fof(f7745,plain,
    ( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_842 ),
    inference(avatar_component_clause,[],[f7744]) ).

fof(f7817,plain,
    ( ! [X15] :
        ( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
        | c_0 = X15 )
    | ~ spl0_860 ),
    inference(avatar_component_clause,[],[f7816]) ).

fof(f8866,plain,
    spl0_1069,
    inference(avatar_split_clause,[],[f1758,f8864]) ).

fof(f8864,plain,
    ( spl0_1069
  <=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f1758,axiom,
    ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).

fof(f8862,plain,
    spl0_1068,
    inference(avatar_split_clause,[],[f1757,f8860]) ).

fof(f8860,plain,
    ( spl0_1068
  <=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f1757,axiom,
    ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).

fof(f8858,plain,
    spl0_1067,
    inference(avatar_split_clause,[],[f1754,f8856]) ).

fof(f8856,plain,
    ( spl0_1067
  <=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f1754,axiom,
    ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).

fof(f8854,plain,
    spl0_1066,
    inference(avatar_split_clause,[],[f1746,f8852]) ).

fof(f8852,plain,
    ( spl0_1066
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X25
        | c_append(X23,X25,X1) != X23 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f1746,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X25
      | c_append(X23,X25,X1) != X23 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_0) ).

fof(f8850,plain,
    spl0_1065,
    inference(avatar_split_clause,[],[f1744,f8848]) ).

fof(f8848,plain,
    ( spl0_1065
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_append(X23,X25,X1) != X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f1744,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X23
      | c_append(X23,X25,X1) != X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).

fof(f8846,plain,
    spl0_1064,
    inference(avatar_split_clause,[],[f1740,f8844]) ).

fof(f8844,plain,
    ( spl0_1064
  <=> ! [X21,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f1740,axiom,
    ! [X21,X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).

fof(f8842,plain,
    spl0_1063,
    inference(avatar_split_clause,[],[f1720,f8840]) ).

fof(f8840,plain,
    ( spl0_1063
  <=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f1720,axiom,
    ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).

fof(f8838,plain,
    spl0_1062,
    inference(avatar_split_clause,[],[f1692,f8836]) ).

fof(f8836,plain,
    ( spl0_1062
  <=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f1692,axiom,
    ! [X3,X1,X23] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).

fof(f8834,plain,
    spl0_1061,
    inference(avatar_split_clause,[],[f1639,f8832]) ).

fof(f8830,plain,
    spl0_1060,
    inference(avatar_split_clause,[],[f1607,f8828]) ).

fof(f1607,axiom,
    ! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).

fof(f8826,plain,
    ( spl0_1059
    | ~ spl0_841
    | ~ spl0_860 ),
    inference(avatar_split_clause,[],[f8068,f7816,f7740,f8824]) ).

fof(f8824,plain,
    ( spl0_1059
  <=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f7740,plain,
    ( spl0_841
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f8068,plain,
    ( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
    | ~ spl0_841
    | ~ spl0_860 ),
    inference(resolution,[],[f7817,f7741]) ).

fof(f7741,plain,
    ( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ spl0_841 ),
    inference(avatar_component_clause,[],[f7740]) ).

fof(f8822,plain,
    spl0_1058,
    inference(avatar_split_clause,[],[f1597,f8820]) ).

fof(f8820,plain,
    ( spl0_1058
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f1597,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).

fof(f8818,plain,
    spl0_1057,
    inference(avatar_split_clause,[],[f1565,f8816]) ).

fof(f8816,plain,
    ( spl0_1057
  <=> ! [X1,X23,X58] :
        ( ~ c_List_Odistinct(X23,X1)
        | c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f1565,axiom,
    ! [X58,X1,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).

fof(f8814,plain,
    spl0_1056,
    inference(avatar_split_clause,[],[f1564,f8812]) ).

fof(f8812,plain,
    ( spl0_1056
  <=> ! [X21,X1,X23] :
        ( ~ c_List_Odistinct(X23,X1)
        | c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f1564,axiom,
    ! [X21,X1,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).

fof(f8810,plain,
    spl0_1055,
    inference(avatar_split_clause,[],[f1563,f8808]) ).

fof(f8808,plain,
    ( spl0_1055
  <=> ! [X21,X1,X23] :
        ( c_List_Odistinct(X23,X1)
        | ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f1563,axiom,
    ! [X21,X1,X23] :
      ( c_List_Odistinct(X23,X1)
      | ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).

fof(f8806,plain,
    spl0_1054,
    inference(avatar_split_clause,[],[f1560,f8804]) ).

fof(f8804,plain,
    ( spl0_1054
  <=> ! [X0,X1,X23] :
        ( ~ c_List_Odistinct(X23,X1)
        | c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f1560,axiom,
    ! [X0,X1,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).

fof(f8802,plain,
    spl0_1053,
    inference(avatar_split_clause,[],[f1559,f8800]) ).

fof(f8800,plain,
    ( spl0_1053
  <=> ! [X1,X23,X43] :
        ( ~ c_List_Odistinct(X23,X1)
        | c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f1559,axiom,
    ! [X1,X23,X43] :
      ( ~ c_List_Odistinct(X23,X1)
      | c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).

fof(f8798,plain,
    spl0_1052,
    inference(avatar_split_clause,[],[f1556,f8796]) ).

fof(f8796,plain,
    ( spl0_1052
  <=> ! [X25,X1,X23] :
        ( c_List_Odistinct(X25,X1)
        | ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f1556,axiom,
    ! [X1,X25,X23] :
      ( c_List_Odistinct(X25,X1)
      | ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).

fof(f8794,plain,
    spl0_1051,
    inference(avatar_split_clause,[],[f1555,f8792]) ).

fof(f8792,plain,
    ( spl0_1051
  <=> ! [X25,X1,X23] :
        ( c_List_Odistinct(X23,X1)
        | ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f1555,axiom,
    ! [X1,X25,X23] :
      ( c_List_Odistinct(X23,X1)
      | ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).

fof(f8790,plain,
    spl0_1050,
    inference(avatar_split_clause,[],[f1553,f8788]) ).

fof(f8788,plain,
    ( spl0_1050
  <=> ! [X41,X0,X23] :
        ( c_List_Odistinct(X23,X41)
        | ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f1553,axiom,
    ! [X41,X0,X23] :
      ( c_List_Odistinct(X23,X41)
      | ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).

fof(f8786,plain,
    spl0_1049,
    inference(avatar_split_clause,[],[f1528,f8784]) ).

fof(f8784,plain,
    ( spl0_1049
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X25
        | c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f1528,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X25
      | c_List_Olist_ONil != c_append(X23,X25,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).

fof(f8782,plain,
    ( spl0_1048
    | ~ spl0_646
    | ~ spl0_857 ),
    inference(avatar_split_clause,[],[f8057,f7804,f6122,f8779]) ).

fof(f8779,plain,
    ( spl0_1048
  <=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f7804,plain,
    ( spl0_857
  <=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f8057,plain,
    ( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
    | ~ spl0_646
    | ~ spl0_857 ),
    inference(superposition,[],[f7805,f6124]) ).

fof(f7805,plain,
    ( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
    | ~ spl0_857 ),
    inference(avatar_component_clause,[],[f7804]) ).

fof(f8777,plain,
    spl0_1047,
    inference(avatar_split_clause,[],[f1510,f8775]) ).

fof(f8775,plain,
    ( spl0_1047
  <=> ! [X25,X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f1510,axiom,
    ! [X1,X25,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Olist_ONil != c_append(X23,X25,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).

fof(f8773,plain,
    spl0_1046,
    inference(avatar_split_clause,[],[f1497,f8771]) ).

fof(f8771,plain,
    ( spl0_1046
  <=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f1497,axiom,
    ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).

fof(f8769,plain,
    spl0_1045,
    inference(avatar_split_clause,[],[f1496,f8767]) ).

fof(f8767,plain,
    ( spl0_1045
  <=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f1496,axiom,
    ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).

fof(f8765,plain,
    spl0_1044,
    inference(avatar_split_clause,[],[f1483,f8763]) ).

fof(f1483,axiom,
    ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).

fof(f8761,plain,
    spl0_1043,
    inference(avatar_split_clause,[],[f1471,f8759]) ).

fof(f8759,plain,
    ( spl0_1043
  <=> ! [X18] :
        ( c_0 = X18
        | c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f1471,axiom,
    ! [X18] :
      ( c_0 = X18
      | c_1 = c_div(X18,X18,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).

fof(f8757,plain,
    spl0_1042,
    inference(avatar_split_clause,[],[f1441,f8755]) ).

fof(f1441,axiom,
    ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).

fof(f8753,plain,
    spl0_1041,
    inference(avatar_split_clause,[],[f1423,f8751]) ).

fof(f8751,plain,
    ( spl0_1041
  <=> ! [X48] :
        ( ~ c_less(c_0,X48,tc_IntDef_Oint)
        | c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f1423,axiom,
    ! [X48] :
      ( ~ c_less(c_0,X48,tc_IntDef_Oint)
      | c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).

fof(f8749,plain,
    spl0_1040,
    inference(avatar_split_clause,[],[f1422,f8747]) ).

fof(f1422,axiom,
    ! [X48] :
      ( c_less(c_0,X48,tc_IntDef_Oint)
      | ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).

fof(f8745,plain,
    spl0_1039,
    inference(avatar_split_clause,[],[f1421,f8743]) ).

fof(f8743,plain,
    ( spl0_1039
  <=> ! [X21] :
        ( ~ c_less(c_0,X21,tc_nat)
        | c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f1421,axiom,
    ! [X21] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).

fof(f8741,plain,
    spl0_1038,
    inference(avatar_split_clause,[],[f1420,f8739]) ).

fof(f8739,plain,
    ( spl0_1038
  <=> ! [X21] :
        ( c_less(c_0,X21,tc_nat)
        | ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f1420,axiom,
    ! [X21] :
      ( c_less(c_0,X21,tc_nat)
      | ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).

fof(f8737,plain,
    spl0_1037,
    inference(avatar_split_clause,[],[f1380,f8735]) ).

fof(f8735,plain,
    ( spl0_1037
  <=> ! [X48] :
        ( c_lessequals(c_0,X48,tc_IntDef_Oint)
        | c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f1380,axiom,
    ! [X48] :
      ( c_lessequals(c_0,X48,tc_IntDef_Oint)
      | c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).

fof(f8733,plain,
    spl0_1036,
    inference(avatar_split_clause,[],[f1379,f8731]) ).

fof(f8731,plain,
    ( spl0_1036
  <=> ! [X48] :
        ( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
        | c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f1379,axiom,
    ! [X48] :
      ( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
      | c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).

fof(f8729,plain,
    spl0_1035,
    inference(avatar_split_clause,[],[f1349,f8727]) ).

fof(f1349,axiom,
    ! [X48] :
      ( c_0 = X48
      | ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).

fof(f8725,plain,
    spl0_1034,
    inference(avatar_split_clause,[],[f1246,f8723]) ).

fof(f8723,plain,
    ( spl0_1034
  <=> ! [X5,X12,X1] :
        ( c_emptyset = X12
        | c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f1246,axiom,
    ! [X1,X5,X12] :
      ( c_emptyset = X12
      | c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).

fof(f8721,plain,
    spl0_1033,
    inference(avatar_split_clause,[],[f1242,f8719]) ).

fof(f8719,plain,
    ( spl0_1033
  <=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

fof(f1242,axiom,
    ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).

fof(f8717,plain,
    spl0_1032,
    inference(avatar_split_clause,[],[f1240,f8715]) ).

fof(f8715,plain,
    ( spl0_1032
  <=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f1240,axiom,
    ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).

fof(f8713,plain,
    spl0_1031,
    inference(avatar_split_clause,[],[f1238,f8711]) ).

fof(f8711,plain,
    ( spl0_1031
  <=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f1238,axiom,
    ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).

fof(f8709,plain,
    spl0_1030,
    inference(avatar_split_clause,[],[f1193,f8707]) ).

fof(f8707,plain,
    ( spl0_1030
  <=> ! [X2,X16,X1,X18] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f1193,axiom,
    ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb_0) ).

fof(f8705,plain,
    spl0_1029,
    inference(avatar_split_clause,[],[f1190,f8703]) ).

fof(f8703,plain,
    ( spl0_1029
  <=> ! [X2,X1,X7,X9] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f1190,axiom,
    ! [X2,X1,X9,X7] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).

fof(f8701,plain,
    spl0_1028,
    inference(avatar_split_clause,[],[f63,f8699]) ).

fof(f8699,plain,
    ( spl0_1028
  <=> ! [X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
        | c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f63,axiom,
    ! [X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).

fof(f8697,plain,
    ( ~ spl0_57
    | spl0_1027
    | ~ spl0_875
    | ~ spl0_988 ),
    inference(avatar_split_clause,[],[f8618,f8404,f7876,f8694,f3714]) ).

fof(f8694,plain,
    ( spl0_1027
  <=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f7876,plain,
    ( spl0_875
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f8404,plain,
    ( spl0_988
  <=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f8618,plain,
    ( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
    | ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
    | ~ spl0_875
    | ~ spl0_988 ),
    inference(superposition,[],[f7877,f8406]) ).

fof(f8406,plain,
    ( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
    | ~ spl0_988 ),
    inference(avatar_component_clause,[],[f8404]) ).

fof(f7877,plain,
    ( ! [X1] :
        ( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
        | ~ class_Numeral_Onumber__ring(X1) )
    | ~ spl0_875 ),
    inference(avatar_component_clause,[],[f7876]) ).

fof(f8692,plain,
    spl0_1026,
    inference(avatar_split_clause,[],[f62,f8690]) ).

fof(f8690,plain,
    ( spl0_1026
  <=> ! [X5,X1] :
        ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
        | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f62,axiom,
    ! [X1,X5] :
      ( ~ c_Wellfounded__Recursion_Owf(X5,X1)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

fof(f8688,plain,
    spl0_1025,
    inference(avatar_split_clause,[],[f35,f8686]) ).

fof(f35,axiom,
    ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).

fof(f8684,plain,
    spl0_1024,
    inference(avatar_split_clause,[],[f34,f8682]) ).

fof(f34,axiom,
    ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).

fof(f8672,plain,
    ( ~ spl0_1023
    | ~ spl0_817
    | ~ spl0_997 ),
    inference(avatar_split_clause,[],[f8655,f8441,f7631,f8669]) ).

fof(f8669,plain,
    ( spl0_1023
  <=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f8655,plain,
    ( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
    | ~ spl0_817
    | ~ spl0_997 ),
    inference(superposition,[],[f7632,f8443]) ).

fof(f8547,plain,
    spl0_1022,
    inference(avatar_split_clause,[],[f3303,f8545]) ).

fof(f3303,plain,
    ! [X1] :
      ( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
      | ~ class_Numeral_Onumber__ring(X1) ),
    inference(forward_demodulation,[],[f2170,f2156]) ).

fof(f2170,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).

fof(f8543,plain,
    spl0_1021,
    inference(avatar_split_clause,[],[f3249,f8541]) ).

fof(f8541,plain,
    ( spl0_1021
  <=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f3249,plain,
    ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)),
    inference(forward_demodulation,[],[f3030,f2979]) ).

fof(f3030,plain,
    ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X15,tc_nat,tc_nat)),
    inference(definition_unfolding,[],[f1300,f2544]) ).

fof(f1300,axiom,
    ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X15,tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).

fof(f8538,plain,
    spl0_1020,
    inference(avatar_split_clause,[],[f3248,f8536]) ).

fof(f3248,plain,
    ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)),
    inference(forward_demodulation,[],[f3029,f2979]) ).

fof(f3029,plain,
    ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
    inference(definition_unfolding,[],[f1299,f2544]) ).

fof(f1299,axiom,
    ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Suc(c_0),tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).

fof(f8534,plain,
    spl0_1019,
    inference(avatar_split_clause,[],[f3014,f8532]) ).

fof(f3014,plain,
    ! [X7,X13] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_Oknows(X13,c_List_Olist_ONil)),tc_Message_Omsg),
    inference(definition_unfolding,[],[f2894,f2795]) ).

fof(f2894,axiom,
    ! [X7,X13] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oparts(c_Event_OinitState(X13)),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState_0) ).

fof(f8530,plain,
    spl0_1018,
    inference(avatar_split_clause,[],[f2985,f8528]) ).

fof(f8528,plain,
    ( spl0_1018
  <=> ! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).

fof(f2985,plain,
    ! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f65,f2544]) ).

fof(f65,axiom,
    ! [X21] : c_less(X21,c_Suc(X21),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

fof(f8526,plain,
    spl0_1017,
    inference(avatar_split_clause,[],[f2984,f8524]) ).

fof(f8524,plain,
    ( spl0_1017
  <=> ! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).

fof(f2984,plain,
    ! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f67,f2544]) ).

fof(f67,axiom,
    ! [X21] : c_less(c_0,c_Suc(X21),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).

fof(f8522,plain,
    spl0_1016,
    inference(avatar_split_clause,[],[f2927,f8520]) ).

fof(f8520,plain,
    ( spl0_1016
  <=> ! [X0,X3] :
        ( X0 = X3
        | c_Public_OshrK(X0) != c_Public_OshrK(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f2927,axiom,
    ! [X3,X0] :
      ( X0 = X3
      | c_Public_OshrK(X0) != c_Public_OshrK(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__injective_0) ).

fof(f8518,plain,
    spl0_1015,
    inference(avatar_split_clause,[],[f2925,f8516]) ).

fof(f8516,plain,
    ( spl0_1015
  <=> ! [X102,X12] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(X12,X102),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f2925,axiom,
    ! [X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oknows(X12,X102),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).

fof(f8514,plain,
    spl0_1014,
    inference(avatar_split_clause,[],[f2921,f8512]) ).

fof(f8512,plain,
    ( spl0_1014
  <=> ! [X102,X27,X12] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oused(X102),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f2921,axiom,
    ! [X27,X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(X27,X12)),c_Event_Oused(X102),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).

fof(f8510,plain,
    spl0_1013,
    inference(avatar_split_clause,[],[f2915,f8508]) ).

fof(f8508,plain,
    ( spl0_1013
  <=> ! [X4,X27,X12,X111] : c_Message_OinvKey(c_Public_OpublicKey(X27,X12)) != c_Public_OpublicKey(X4,X111) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f2915,axiom,
    ! [X111,X27,X4,X12] : c_Message_OinvKey(c_Public_OpublicKey(X27,X12)) != c_Public_OpublicKey(X4,X111),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).

fof(f8506,plain,
    spl0_1012,
    inference(avatar_split_clause,[],[f2899,f8504]) ).

fof(f8504,plain,
    ( spl0_1012
  <=> ! [X3] :
        ( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
        | c_Message_OinvKey(X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f2899,axiom,
    ! [X3] :
      ( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
      | c_Message_OinvKey(X3) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).

fof(f8502,plain,
    spl0_1011,
    inference(avatar_split_clause,[],[f2788,f8500]) ).

fof(f8500,plain,
    ( spl0_1011
  <=> ! [X103,X96,X104] : c_0 = c_Nat_Osize(c_Event_Oevent_OSays(X103,X104,X96),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).

fof(f2788,axiom,
    ! [X96,X104,X103] : c_0 = c_Nat_Osize(c_Event_Oevent_OSays(X103,X104,X96),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__1_0) ).

fof(f8498,plain,
    ( spl0_1010
    | ~ spl0_45
    | ~ spl0_885 ),
    inference(avatar_split_clause,[],[f8103,f7916,f3654,f8495]) ).

fof(f8495,plain,
    ( spl0_1010
  <=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).

fof(f7916,plain,
    ( spl0_885
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f8103,plain,
    ( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
    | ~ spl0_45
    | ~ spl0_885 ),
    inference(resolution,[],[f7917,f3656]) ).

fof(f3656,plain,
    ( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f3654]) ).

fof(f7917,plain,
    ( ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = c_OrderedGroup_Opprt(c_0,X1) )
    | ~ spl0_885 ),
    inference(avatar_component_clause,[],[f7916]) ).

fof(f8493,plain,
    spl0_1009,
    inference(avatar_split_clause,[],[f2777,f8491]) ).

fof(f8491,plain,
    ( spl0_1009
  <=> ! [X95,X97,X104,X103,X96] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_ONotes(X95,X97) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f2777,axiom,
    ! [X96,X97,X104,X95,X103] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_ONotes(X95,X97),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3_0) ).

fof(f8489,plain,
    spl0_1008,
    inference(avatar_split_clause,[],[f2775,f8487]) ).

fof(f8487,plain,
    ( spl0_1008
  <=> ! [X95,X97,X104,X103,X96] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OGets(X95,X97) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).

fof(f2775,axiom,
    ! [X96,X97,X104,X95,X103] : c_Event_Oevent_OSays(X103,X104,X96) != c_Event_Oevent_OGets(X95,X97),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1_0) ).

fof(f8485,plain,
    spl0_1007,
    inference(avatar_split_clause,[],[f2755,f8483]) ).

fof(f8483,plain,
    ( spl0_1007
  <=> ! [X96,X97] :
        ( X96 = X97
        | c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f2755,axiom,
    ! [X96,X97] :
      ( X96 = X97
      | c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).

fof(f8481,plain,
    spl0_1006,
    inference(avatar_split_clause,[],[f2754,f8479]) ).

fof(f8479,plain,
    ( spl0_1006
  <=> ! [X89,X90] :
        ( X89 = X90
        | c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f2754,axiom,
    ! [X90,X89] :
      ( X89 = X90
      | c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).

fof(f8477,plain,
    spl0_1005,
    inference(avatar_split_clause,[],[f2753,f8475]) ).

fof(f8475,plain,
    ( spl0_1005
  <=> ! [X89,X90] :
        ( X89 = X90
        | c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).

fof(f2753,axiom,
    ! [X90,X89] :
      ( X89 = X90
      | c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).

fof(f8473,plain,
    spl0_1004,
    inference(avatar_split_clause,[],[f2752,f8471]) ).

fof(f8471,plain,
    ( spl0_1004
  <=> ! [X89,X90] :
        ( X89 = X90
        | c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).

fof(f2752,axiom,
    ! [X90,X89] :
      ( X89 = X90
      | c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).

fof(f8469,plain,
    spl0_1003,
    inference(avatar_split_clause,[],[f2751,f8467]) ).

fof(f8467,plain,
    ( spl0_1003
  <=> ! [X94,X95] :
        ( X94 = X95
        | c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f2751,axiom,
    ! [X94,X95] :
      ( X94 = X95
      | c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).

fof(f8465,plain,
    spl0_1002,
    inference(avatar_split_clause,[],[f2741,f8463]) ).

fof(f2741,axiom,
    ! [X91,X92] :
      ( X91 = X92
      | c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).

fof(f8461,plain,
    spl0_1001,
    inference(avatar_split_clause,[],[f2736,f8459]) ).

fof(f8459,plain,
    ( spl0_1001
  <=> ! [X89,X90] :
        ( X89 = X90
        | c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f2736,axiom,
    ! [X90,X89] :
      ( X89 = X90
      | c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).

fof(f8457,plain,
    spl0_1000,
    inference(avatar_split_clause,[],[f2699,f8455]) ).

fof(f8455,plain,
    ( spl0_1000
  <=> ! [X12,X1] :
        ( c_emptyset = X12
        | ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f2699,axiom,
    ! [X1,X12] :
      ( c_emptyset = X12
      | ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).

fof(f8453,plain,
    ( spl0_999
    | ~ spl0_45
    | ~ spl0_884 ),
    inference(avatar_split_clause,[],[f8102,f7912,f3654,f8450]) ).

fof(f8450,plain,
    ( spl0_999
  <=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f7912,plain,
    ( spl0_884
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f8102,plain,
    ( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
    | ~ spl0_45
    | ~ spl0_884 ),
    inference(resolution,[],[f7913,f3656]) ).

fof(f7913,plain,
    ( ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_0 = c_OrderedGroup_Onprt(c_0,X1) )
    | ~ spl0_884 ),
    inference(avatar_component_clause,[],[f7912]) ).

fof(f8448,plain,
    spl0_998,
    inference(avatar_split_clause,[],[f2660,f8446]) ).

fof(f2660,axiom,
    ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).

fof(f8444,plain,
    spl0_997,
    inference(avatar_split_clause,[],[f2534,f8441]) ).

fof(f2534,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(f8439,plain,
    spl0_996,
    inference(avatar_split_clause,[],[f2492,f8437]) ).

fof(f8437,plain,
    ( spl0_996
  <=> ! [X18,X1] :
        ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
        | c_0 = c_times(X18,c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f2492,axiom,
    ! [X1,X18] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
      | c_0 = c_times(X18,c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).

fof(f8435,plain,
    spl0_995,
    inference(avatar_split_clause,[],[f2491,f8433]) ).

fof(f8433,plain,
    ( spl0_995
  <=> ! [X18,X1] :
        ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
        | c_0 = c_times(c_0,X18,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).

fof(f2491,axiom,
    ! [X1,X18] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
      | c_0 = c_times(c_0,X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).

fof(f8431,plain,
    spl0_994,
    inference(avatar_split_clause,[],[f2474,f8429]) ).

fof(f8429,plain,
    ( spl0_994
  <=> ! [X4,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_times(c_1,X4,X1) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f2474,axiom,
    ! [X1,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_times(c_1,X4,X1) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).

fof(f8427,plain,
    spl0_993,
    inference(avatar_split_clause,[],[f2473,f8425]) ).

fof(f8425,plain,
    ( spl0_993
  <=> ! [X27,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = c_times(X27,c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f2473,axiom,
    ! [X1,X27] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = c_times(X27,c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).

fof(f8423,plain,
    spl0_992,
    inference(avatar_split_clause,[],[f2470,f8421]) ).

fof(f8421,plain,
    ( spl0_992
  <=> ! [X4,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_times(X4,c_1,X1) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f2470,axiom,
    ! [X1,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_times(X4,c_1,X1) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).

fof(f8419,plain,
    spl0_991,
    inference(avatar_split_clause,[],[f2469,f8417]) ).

fof(f8417,plain,
    ( spl0_991
  <=> ! [X27,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = c_times(c_0,X27,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).

fof(f2469,axiom,
    ! [X1,X27] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = c_times(c_0,X27,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).

fof(f8415,plain,
    spl0_990,
    inference(avatar_split_clause,[],[f2379,f8413]) ).

fof(f8413,plain,
    ( spl0_990
  <=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f2379,axiom,
    ! [X3,X1] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).

fof(f8411,plain,
    spl0_989,
    inference(avatar_split_clause,[],[f2377,f8409]) ).

fof(f8409,plain,
    ( spl0_989
  <=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f2377,axiom,
    ! [X2,X3,X1] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).

fof(f8407,plain,
    ( spl0_988
    | ~ spl0_57
    | ~ spl0_881 ),
    inference(avatar_split_clause,[],[f8099,f7900,f3714,f8404]) ).

fof(f7900,plain,
    ( spl0_881
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).

fof(f8099,plain,
    ( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
    | ~ spl0_57
    | ~ spl0_881 ),
    inference(resolution,[],[f7901,f3716]) ).

fof(f7901,plain,
    ( ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
    | ~ spl0_881 ),
    inference(avatar_component_clause,[],[f7900]) ).

fof(f8402,plain,
    spl0_987,
    inference(avatar_split_clause,[],[f2371,f8400]) ).

fof(f8400,plain,
    ( spl0_987
  <=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).

fof(f2371,axiom,
    ! [X2,X3,X1] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).

fof(f8398,plain,
    spl0_986,
    inference(avatar_split_clause,[],[f2369,f8396]) ).

fof(f8396,plain,
    ( spl0_986
  <=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f2369,axiom,
    ! [X3,X1] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).

fof(f8394,plain,
    spl0_985,
    inference(avatar_split_clause,[],[f2357,f8392]) ).

fof(f8392,plain,
    ( spl0_985
  <=> ! [X18,X1] :
        ( ~ class_Power_Orecpower(X1)
        | c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f2357,axiom,
    ! [X1,X18] :
      ( ~ class_Power_Orecpower(X1)
      | c_1 = c_Nat_Opower(X18,c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).

fof(f8390,plain,
    spl0_984,
    inference(avatar_split_clause,[],[f2354,f8388]) ).

fof(f2354,axiom,
    ! [X3,X1] :
      ( ~ class_Power_Orecpower(X1)
      | c_Nat_Opower(X3,c_1,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).

fof(f8386,plain,
    spl0_983,
    inference(avatar_split_clause,[],[f2353,f8384]) ).

fof(f2353,axiom,
    ! [X21,X1] :
      ( ~ class_Power_Orecpower(X1)
      | c_1 = c_Nat_Opower(c_1,X21,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).

fof(f8382,plain,
    spl0_982,
    inference(avatar_split_clause,[],[f2292,f8380]) ).

fof(f8380,plain,
    ( spl0_982
  <=> ! [X0] :
        ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
        | c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).

fof(f2292,axiom,
    ! [X0] :
      ( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
      | c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).

fof(f8378,plain,
    spl0_981,
    inference(avatar_split_clause,[],[f2291,f8376]) ).

fof(f8376,plain,
    ( spl0_981
  <=> ! [X0] :
        ( c_Parity_Oeven(X0,tc_IntDef_Oint)
        | ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).

fof(f2291,axiom,
    ! [X0] :
      ( c_Parity_Oeven(X0,tc_IntDef_Oint)
      | ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).

fof(f8374,plain,
    spl0_980,
    inference(avatar_split_clause,[],[f2267,f8372]) ).

fof(f2267,axiom,
    ! [X2,X3] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_Orderings_Omax(X3,X3,X2) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).

fof(f8370,plain,
    spl0_979,
    inference(avatar_split_clause,[],[f2262,f8368]) ).

fof(f2262,axiom,
    ! [X2,X3] :
      ( ~ class_Orderings_Olinorder(X2)
      | c_Orderings_Omin(X3,X3,X2) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).

fof(f8366,plain,
    spl0_978,
    inference(avatar_split_clause,[],[f2251,f8364]) ).

fof(f8364,plain,
    ( spl0_978
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f2251,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).

fof(f8362,plain,
    spl0_977,
    inference(avatar_split_clause,[],[f2250,f8360]) ).

fof(f8360,plain,
    ( spl0_977
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X1)
        | c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f2250,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).

fof(f8358,plain,
    spl0_976,
    inference(avatar_split_clause,[],[f2241,f8356]) ).

fof(f2241,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).

fof(f8354,plain,
    spl0_975,
    inference(avatar_split_clause,[],[f2218,f8352]) ).

fof(f2218,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X1)
      | c_times(X3,c_1,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).

fof(f8350,plain,
    spl0_974,
    inference(avatar_split_clause,[],[f2217,f8348]) ).

fof(f2217,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X1)
      | c_times(c_1,X3,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).

fof(f8346,plain,
    spl0_973,
    inference(avatar_split_clause,[],[f2205,f8344]) ).

fof(f2205,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_0 = c_minus(X18,X18,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).

fof(f8342,plain,
    spl0_972,
    inference(avatar_split_clause,[],[f2198,f8340]) ).

fof(f2198,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_minus(X3,c_0,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).

fof(f8338,plain,
    spl0_971,
    inference(avatar_split_clause,[],[f2196,f8336]) ).

fof(f2196,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
      | c_plus(c_0,X3,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).

fof(f8334,plain,
    spl0_970,
    inference(avatar_split_clause,[],[f2185,f8332]) ).

fof(f2185,axiom,
    ! [X3,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
      | c_plus(X3,c_0,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).

fof(f8330,plain,
    spl0_969,
    inference(avatar_split_clause,[],[f2182,f8328]) ).

fof(f8328,plain,
    ( spl0_969
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).

fof(f2182,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).

fof(f8326,plain,
    spl0_968,
    inference(avatar_split_clause,[],[f2180,f8324]) ).

fof(f8324,plain,
    ( spl0_968
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).

fof(f2180,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).

fof(f8322,plain,
    spl0_967,
    inference(avatar_split_clause,[],[f2177,f8320]) ).

fof(f8320,plain,
    ( spl0_967
  <=> ! [X18,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).

fof(f2177,axiom,
    ! [X1,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

fof(f8318,plain,
    spl0_966,
    inference(avatar_split_clause,[],[f2153,f8316]) ).

fof(f2153,axiom,
    ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).

fof(f8314,plain,
    spl0_965,
    inference(avatar_split_clause,[],[f1865,f8312]) ).

fof(f8312,plain,
    ( spl0_965
  <=> ! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f1865,axiom,
    ! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).

fof(f8310,plain,
    spl0_964,
    inference(avatar_split_clause,[],[f1818,f8308]) ).

fof(f8308,plain,
    ( spl0_964
  <=> ! [X1,X15] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).

fof(f1818,axiom,
    ! [X1,X15] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).

fof(f8306,plain,
    spl0_963,
    inference(avatar_split_clause,[],[f1815,f8304]) ).

fof(f8304,plain,
    ( spl0_963
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f1815,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).

fof(f8302,plain,
    spl0_962,
    inference(avatar_split_clause,[],[f1805,f8300]) ).

fof(f8300,plain,
    ( spl0_962
  <=> ! [X21,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).

fof(f1805,axiom,
    ! [X21,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).

fof(f8298,plain,
    spl0_961,
    inference(avatar_split_clause,[],[f1779,f8296]) ).

fof(f8296,plain,
    ( spl0_961
  <=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f1779,axiom,
    ! [X3,X41,X0] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).

fof(f8294,plain,
    spl0_960,
    inference(avatar_split_clause,[],[f1750,f8292]) ).

fof(f8292,plain,
    ( spl0_960
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_emptyset != c_List_Oset(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).

fof(f1750,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_emptyset != c_List_Oset(X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).

fof(f8290,plain,
    spl0_959,
    inference(avatar_split_clause,[],[f1735,f8288]) ).

fof(f8288,plain,
    ( spl0_959
  <=> ! [X1,X23] :
        ( c_List_Olist_ONil = X23
        | c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).

fof(f1735,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Olist_ONil != c_List_Orotate1(X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).

fof(f8286,plain,
    spl0_958,
    inference(avatar_split_clause,[],[f1715,f8284]) ).

fof(f8284,plain,
    ( spl0_958
  <=> ! [X0,X1] :
        ( c_List_Olist_ONil = X0
        | c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).

fof(f1715,axiom,
    ! [X0,X1] :
      ( c_List_Olist_ONil = X0
      | c_List_Olist_ONil != c_List_Oremdups(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).

fof(f8282,plain,
    spl0_957,
    inference(avatar_split_clause,[],[f1588,f8280]) ).

fof(f8280,plain,
    ( spl0_957
  <=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).

fof(f1588,axiom,
    ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).

fof(f8278,plain,
    spl0_956,
    inference(avatar_split_clause,[],[f1579,f8276]) ).

fof(f8276,plain,
    ( spl0_956
  <=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f1579,axiom,
    ! [X3,X1,X23] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).

fof(f8274,plain,
    spl0_955,
    inference(avatar_split_clause,[],[f1562,f8272]) ).

fof(f8272,plain,
    ( spl0_955
  <=> ! [X1,X23] :
        ( ~ c_List_Odistinct(X23,X1)
        | c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f1562,axiom,
    ! [X1,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).

fof(f8270,plain,
    spl0_954,
    inference(avatar_split_clause,[],[f1561,f8268]) ).

fof(f8268,plain,
    ( spl0_954
  <=> ! [X1,X23] :
        ( c_List_Odistinct(X23,X1)
        | ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).

fof(f1561,axiom,
    ! [X1,X23] :
      ( c_List_Odistinct(X23,X1)
      | ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).

fof(f8266,plain,
    spl0_953,
    inference(avatar_split_clause,[],[f1550,f8264]) ).

fof(f8264,plain,
    ( spl0_953
  <=> ! [X1,X23] :
        ( ~ c_List_Odistinct(X23,X1)
        | c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f1550,axiom,
    ! [X1,X23] :
      ( ~ c_List_Odistinct(X23,X1)
      | c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).

fof(f8262,plain,
    spl0_952,
    inference(avatar_split_clause,[],[f1549,f8260]) ).

fof(f8260,plain,
    ( spl0_952
  <=> ! [X1,X23] :
        ( c_List_Odistinct(X23,X1)
        | ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f1549,axiom,
    ! [X1,X23] :
      ( c_List_Odistinct(X23,X1)
      | ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).

fof(f8258,plain,
    spl0_951,
    inference(avatar_split_clause,[],[f1537,f8256]) ).

fof(f8256,plain,
    ( spl0_951
  <=> ! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f1537,axiom,
    ! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).

fof(f8254,plain,
    spl0_950,
    inference(avatar_split_clause,[],[f1513,f8252]) ).

fof(f1513,axiom,
    ! [X1,X23] :
      ( c_List_Olist_ONil = X23
      | c_List_Olist_ONil != c_List_Orev(X23,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).

fof(f8250,plain,
    spl0_949,
    inference(avatar_split_clause,[],[f1499,f8248]) ).

fof(f1499,axiom,
    ! [X3,X1] :
      ( ~ class_LOrder_Omeet__semilorder(X1)
      | c_LOrder_Omeet(X3,X3,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).

fof(f8246,plain,
    spl0_948,
    inference(avatar_split_clause,[],[f1498,f8244]) ).

fof(f1498,axiom,
    ! [X3,X1] :
      ( ~ class_LOrder_Ojoin__semilorder(X1)
      | c_LOrder_Ojoin(X3,X3,X1) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).

fof(f8242,plain,
    ( ~ spl0_946
    | spl0_947
    | ~ spl0_715
    | ~ spl0_875 ),
    inference(avatar_split_clause,[],[f8093,f7876,f7195,f8239,f8235]) ).

fof(f8235,plain,
    ( spl0_946
  <=> class_Numeral_Onumber__ring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f8239,plain,
    ( spl0_947
  <=> c_IntDef_Oiszero(c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f8093,plain,
    ( c_IntDef_Oiszero(c_0,tc_nat)
    | ~ class_Numeral_Onumber__ring(tc_nat)
    | ~ spl0_715
    | ~ spl0_875 ),
    inference(superposition,[],[f7877,f7197]) ).

fof(f8233,plain,
    spl0_945,
    inference(avatar_split_clause,[],[f1490,f8231]) ).

fof(f1490,axiom,
    ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).

fof(f8229,plain,
    spl0_944,
    inference(avatar_split_clause,[],[f1419,f8227]) ).

fof(f1419,axiom,
    ! [X21,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).

fof(f8225,plain,
    spl0_943,
    inference(avatar_split_clause,[],[f1392,f8223]) ).

fof(f1392,axiom,
    ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).

fof(f8221,plain,
    spl0_942,
    inference(avatar_split_clause,[],[f1385,f8219]) ).

fof(f1385,axiom,
    ! [X48] :
      ( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
      | c_0 = c_IntDef_Onat(X48) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).

fof(f8217,plain,
    spl0_941,
    inference(avatar_split_clause,[],[f1376,f8215]) ).

fof(f8215,plain,
    ( spl0_941
  <=> ! [X21] :
        ( c_0 = X21
        | ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f1376,axiom,
    ! [X21] :
      ( c_0 = X21
      | ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).

fof(f8213,plain,
    spl0_940,
    inference(avatar_split_clause,[],[f1375,f8211]) ).

fof(f1375,axiom,
    ! [X21,X15] :
      ( X15 = X21
      | c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).

fof(f8209,plain,
    spl0_939,
    inference(avatar_split_clause,[],[f1308,f8207]) ).

fof(f8207,plain,
    ( spl0_939
  <=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f1308,axiom,
    ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).

fof(f8205,plain,
    spl0_938,
    inference(avatar_split_clause,[],[f1298,f8203]) ).

fof(f8203,plain,
    ( spl0_938
  <=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f1298,axiom,
    ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).

fof(f8201,plain,
    spl0_937,
    inference(avatar_split_clause,[],[f1297,f8199]) ).

fof(f8199,plain,
    ( spl0_937
  <=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f1297,axiom,
    ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).

fof(f8197,plain,
    spl0_936,
    inference(avatar_split_clause,[],[f1177,f8195]) ).

fof(f8195,plain,
    ( spl0_936
  <=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f1177,axiom,
    ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).

fof(f8193,plain,
    ( spl0_935
    | ~ spl0_26
    | ~ spl0_868 ),
    inference(avatar_split_clause,[],[f8073,f7848,f3559,f8190]) ).

fof(f8190,plain,
    ( spl0_935
  <=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f3559,plain,
    ( spl0_26
  <=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f7848,plain,
    ( spl0_868
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | c_1 = c_NatArith_Oof__nat(c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f8073,plain,
    ( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
    | ~ spl0_26
    | ~ spl0_868 ),
    inference(resolution,[],[f7849,f3561]) ).

fof(f3561,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f3559]) ).

fof(f7849,plain,
    ( ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | c_1 = c_NatArith_Oof__nat(c_1,X1) )
    | ~ spl0_868 ),
    inference(avatar_component_clause,[],[f7848]) ).

fof(f8188,plain,
    spl0_934,
    inference(avatar_split_clause,[],[f1171,f8186]) ).

fof(f8186,plain,
    ( spl0_934
  <=> ! [X1,X40] :
        ( c_Datatype_Ooption_ONone = X40
        | c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f1171,axiom,
    ! [X40,X1] :
      ( c_Datatype_Ooption_ONone = X40
      | c_emptyset != c_Datatype_Oo2s(X40,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).

fof(f8183,plain,
    spl0_933,
    inference(avatar_split_clause,[],[f1167,f8181]) ).

fof(f8181,plain,
    ( spl0_933
  <=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f1167,axiom,
    ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).

fof(f8179,plain,
    spl0_932,
    inference(avatar_split_clause,[],[f252,f8177]) ).

fof(f8177,plain,
    ( spl0_932
  <=> ! [X38,X37] :
        ( ~ class_Finite__Set_Ofinite(X38)
        | ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_sum(X38,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f252,axiom,
    ! [X38,X37] :
      ( ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_sum(X38,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).

fof(f8175,plain,
    spl0_931,
    inference(avatar_split_clause,[],[f246,f8173]) ).

fof(f8173,plain,
    ( spl0_931
  <=> ! [X38,X37] :
        ( ~ class_Finite__Set_Ofinite(X38)
        | ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_prod(X38,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f246,axiom,
    ! [X38,X37] :
      ( ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_prod(X38,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).

fof(f8171,plain,
    spl0_930,
    inference(avatar_split_clause,[],[f196,f8169]) ).

fof(f8169,plain,
    ( spl0_930
  <=> ! [X38,X37] :
        ( ~ class_Finite__Set_Ofinite(X38)
        | ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_fun(X38,X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f196,axiom,
    ! [X38,X37] :
      ( ~ class_Finite__Set_Ofinite(X38)
      | ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_fun(X38,X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).

fof(f8167,plain,
    spl0_929,
    inference(avatar_split_clause,[],[f94,f8165]) ).

fof(f8165,plain,
    ( spl0_929
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f94,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

fof(f8163,plain,
    spl0_928,
    inference(avatar_split_clause,[],[f93,f8161]) ).

fof(f8161,plain,
    ( spl0_928
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f93,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

fof(f8159,plain,
    spl0_927,
    inference(avatar_split_clause,[],[f92,f8157]) ).

fof(f8157,plain,
    ( spl0_927
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f92,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

fof(f8155,plain,
    spl0_926,
    inference(avatar_split_clause,[],[f91,f8153]) ).

fof(f8153,plain,
    ( spl0_926
  <=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f91,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

fof(f8151,plain,
    spl0_925,
    inference(avatar_split_clause,[],[f89,f8149]) ).

fof(f8149,plain,
    ( spl0_925
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f89,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

fof(f8147,plain,
    ( spl0_924
    | ~ spl0_53
    | ~ spl0_867 ),
    inference(avatar_split_clause,[],[f8071,f7844,f3694,f8144]) ).

fof(f8144,plain,
    ( spl0_924
  <=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f3694,plain,
    ( spl0_53
  <=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f7844,plain,
    ( spl0_867
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f8071,plain,
    ( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
    | ~ spl0_53
    | ~ spl0_867 ),
    inference(resolution,[],[f7845,f3696]) ).

fof(f3696,plain,
    ( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f3694]) ).

fof(f7845,plain,
    ( ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_0 = c_NatArith_Oof__nat(c_0,X1) )
    | ~ spl0_867 ),
    inference(avatar_component_clause,[],[f7844]) ).

fof(f8142,plain,
    spl0_923,
    inference(avatar_split_clause,[],[f88,f8140]) ).

fof(f88,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

fof(f8138,plain,
    spl0_922,
    inference(avatar_split_clause,[],[f87,f8136]) ).

fof(f8136,plain,
    ( spl0_922
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f87,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

fof(f8134,plain,
    spl0_921,
    inference(avatar_split_clause,[],[f86,f8132]) ).

fof(f8132,plain,
    ( spl0_921
  <=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f86,axiom,
    ! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

fof(f8130,plain,
    spl0_920,
    inference(avatar_split_clause,[],[f37,f8128]) ).

fof(f37,axiom,
    ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).

fof(f8121,plain,
    ( spl0_919
    | ~ spl0_27
    | ~ spl0_859 ),
    inference(avatar_split_clause,[],[f8065,f7812,f3564,f8118]) ).

fof(f8118,plain,
    ( spl0_919
  <=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f7812,plain,
    ( spl0_859
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_1 = c_IntDef_Oof__int(c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f8065,plain,
    ( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
    | ~ spl0_27
    | ~ spl0_859 ),
    inference(resolution,[],[f7813,f3566]) ).

fof(f7813,plain,
    ( ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_1 = c_IntDef_Oof__int(c_1,X1) )
    | ~ spl0_859 ),
    inference(avatar_component_clause,[],[f7812]) ).

fof(f8116,plain,
    ( spl0_918
    | ~ spl0_55
    | ~ spl0_858 ),
    inference(avatar_split_clause,[],[f8060,f7808,f3704,f8113]) ).

fof(f8113,plain,
    ( spl0_918
  <=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f7808,plain,
    ( spl0_858
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f8060,plain,
    ( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
    | ~ spl0_55
    | ~ spl0_858 ),
    inference(resolution,[],[f7809,f3706]) ).

fof(f7809,plain,
    ( ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_0 = c_IntDef_Oof__int(c_0,X1) )
    | ~ spl0_858 ),
    inference(avatar_component_clause,[],[f7808]) ).

fof(f8109,plain,
    ( spl0_917
    | ~ spl0_647
    | ~ spl0_855 ),
    inference(avatar_split_clause,[],[f8054,f7796,f6127,f8106]) ).

fof(f8054,plain,
    ( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_855 ),
    inference(superposition,[],[f7797,f6129]) ).

fof(f8098,plain,
    ( spl0_916
    | ~ spl0_646
    | ~ spl0_855 ),
    inference(avatar_split_clause,[],[f8053,f7796,f6122,f8095]) ).

fof(f8095,plain,
    ( spl0_916
  <=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f8053,plain,
    ( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_855 ),
    inference(superposition,[],[f7797,f6124]) ).

fof(f8064,plain,
    ( spl0_915
    | ~ spl0_838
    | ~ spl0_849 ),
    inference(avatar_split_clause,[],[f8047,f7772,f7718,f8062]) ).

fof(f7718,plain,
    ( spl0_838
  <=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f8047,plain,
    ( ! [X0] : c_lessequals(X0,X0,tc_nat)
    | ~ spl0_838
    | ~ spl0_849 ),
    inference(superposition,[],[f7773,f7719]) ).

fof(f7719,plain,
    ( ! [X3] : c_div(X3,c_1,tc_nat) = X3
    | ~ spl0_838 ),
    inference(avatar_component_clause,[],[f7718]) ).

fof(f8036,plain,
    spl0_914,
    inference(avatar_split_clause,[],[f3328,f8034]) ).

fof(f8034,plain,
    ( spl0_914
  <=> ! [X15] :
        ( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
        | c_1 = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f3328,plain,
    ! [X15] :
      ( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
      | c_1 = X15 ),
    inference(forward_demodulation,[],[f3327,f2979]) ).

fof(f3327,plain,
    ! [X15] :
      ( c_1 = X15
      | ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f3138,f2979]) ).

fof(f3138,plain,
    ! [X15] :
      ( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X15
      | ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f1227,f2544,f2544]) ).

fof(f1227,axiom,
    ! [X15] :
      ( c_Suc(c_0) = X15
      | ~ c_Divides_Oop_Advd(X15,c_Suc(c_0),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).

fof(f8032,plain,
    spl0_913,
    inference(avatar_split_clause,[],[f3236,f8030]) ).

fof(f8030,plain,
    ( spl0_913
  <=> ! [X13,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f3236,plain,
    ! [X1,X13] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1),
    inference(forward_demodulation,[],[f3001,f2386]) ).

fof(f2386,axiom,
    ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).

fof(f3001,plain,
    ! [X1,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X1),X13,X1,X1),
    inference(definition_unfolding,[],[f2604,f2373]) ).

fof(f2604,axiom,
    ! [X1,X13] : c_emptyset = c_inter(c_emptyset,X13,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).

fof(f8028,plain,
    spl0_912,
    inference(avatar_split_clause,[],[f3005,f8026]) ).

fof(f8024,plain,
    spl0_911,
    inference(avatar_split_clause,[],[f3003,f8021]) ).

fof(f3003,plain,
    c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
    inference(definition_unfolding,[],[f2133,f2113]) ).

fof(f2133,axiom,
    c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).

fof(f8019,plain,
    spl0_910,
    inference(avatar_split_clause,[],[f2999,f8017]) ).

fof(f8017,plain,
    ( spl0_910
  <=> ! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(X32,c_List_Olist_ONil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f2999,plain,
    ! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(X32,c_List_Olist_ONil))),
    inference(definition_unfolding,[],[f2909,f2795]) ).

fof(f2909,axiom,
    ! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(X32))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OkeysFor__parts__initState_0) ).

fof(f8015,plain,
    spl0_909,
    inference(avatar_split_clause,[],[f2979,f8012]) ).

fof(f8012,plain,
    ( spl0_909
  <=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f8010,plain,
    spl0_908,
    inference(avatar_split_clause,[],[f2975,f8008]) ).

fof(f8008,plain,
    ( spl0_908
  <=> ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f2975,plain,
    ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2023,f2544]) ).

fof(f2023,axiom,
    ! [X15] : c_0 != c_Suc(X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).

fof(f8006,plain,
    spl0_907,
    inference(avatar_split_clause,[],[f2928,f8004]) ).

fof(f8004,plain,
    ( spl0_907
  <=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Message_OinvKey(c_Public_OpublicKey(X27,X32)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).

fof(f2928,axiom,
    ! [X27,X12,X32] : c_Public_OshrK(X12) != c_Message_OinvKey(c_Public_OpublicKey(X27,X32)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__priK_0) ).

fof(f8002,plain,
    spl0_906,
    inference(avatar_split_clause,[],[f2926,f8000]) ).

fof(f8000,plain,
    ( spl0_906
  <=> ! [X102,X12] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oused(X102),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).

fof(f2926,axiom,
    ! [X12,X102] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(X12)),c_Event_Oused(X102),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).

fof(f7998,plain,
    spl0_905,
    inference(avatar_split_clause,[],[f2910,f7996]) ).

fof(f7996,plain,
    ( spl0_905
  <=> ! [X27,X12] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X27,X12)),c_Message_OsymKeys,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).

fof(f2910,axiom,
    ! [X27,X12] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X27,X12)),c_Message_OsymKeys,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK_0) ).

fof(f7994,plain,
    spl0_904,
    inference(avatar_split_clause,[],[f2906,f7992]) ).

fof(f7992,plain,
    ( spl0_904
  <=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__rec(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).

fof(f2906,axiom,
    ! [X3,X1,X45] : c_Public_Okeymode_Okeymode__rec(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Orecs__2_0) ).

fof(f7990,plain,
    spl0_903,
    inference(avatar_split_clause,[],[f2905,f7988]) ).

fof(f7988,plain,
    ( spl0_903
  <=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__rec(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f2905,axiom,
    ! [X3,X1,X44] : c_Public_Okeymode_Okeymode__rec(X3,X44,c_Public_Okeymode_OSignature,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Orecs__1_0) ).

fof(f7986,plain,
    spl0_902,
    inference(avatar_split_clause,[],[f2902,f7984]) ).

fof(f7984,plain,
    ( spl0_902
  <=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__case(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).

fof(f2902,axiom,
    ! [X3,X1,X45] : c_Public_Okeymode_Okeymode__case(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Ocases__2_0) ).

fof(f7982,plain,
    spl0_901,
    inference(avatar_split_clause,[],[f2901,f7980]) ).

fof(f7980,plain,
    ( spl0_901
  <=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__case(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).

fof(f2901,axiom,
    ! [X3,X1,X44] : c_Public_Okeymode_Okeymode__case(X3,X44,c_Public_Okeymode_OSignature,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Ocases__1_0) ).

fof(f7978,plain,
    spl0_900,
    inference(avatar_split_clause,[],[f2891,f7976]) ).

fof(f7976,plain,
    ( spl0_900
  <=> ! [X86,X91] : ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f2891,axiom,
    ! [X91,X86] : ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OCrypt__notin__used__empty_0) ).

fof(f7974,plain,
    spl0_899,
    inference(avatar_split_clause,[],[f2790,f7972]) ).

fof(f7972,plain,
    ( spl0_899
  <=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_ONotes(X94,X96),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f2790,axiom,
    ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_ONotes(X94,X96),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__3_0) ).

fof(f7970,plain,
    spl0_898,
    inference(avatar_split_clause,[],[f2789,f7968]) ).

fof(f7968,plain,
    ( spl0_898
  <=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_OGets(X94,X96),tc_Event_Oevent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f2789,axiom,
    ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_OGets(X94,X96),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__2_0) ).

fof(f7966,plain,
    spl0_897,
    inference(avatar_split_clause,[],[f2779,f7964]) ).

fof(f7964,plain,
    ( spl0_897
  <=> ! [X96,X97,X94,X95] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f2779,axiom,
    ! [X96,X94,X97,X95] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X94,X96),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5_0) ).

fof(f7962,plain,
    spl0_896,
    inference(avatar_split_clause,[],[f2705,f7960]) ).

fof(f7960,plain,
    ( spl0_896
  <=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).

fof(f2705,axiom,
    ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).

fof(f7958,plain,
    spl0_895,
    inference(avatar_split_clause,[],[f2684,f7956]) ).

fof(f2684,axiom,
    ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

fof(f7954,plain,
    spl0_894,
    inference(avatar_split_clause,[],[f2668,f7952]) ).

fof(f7952,plain,
    ( spl0_894
  <=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).

fof(f2668,axiom,
    ! [X1,X12] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).

fof(f7950,plain,
    spl0_893,
    inference(avatar_split_clause,[],[f2648,f7948]) ).

fof(f7948,plain,
    ( spl0_893
  <=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f2648,axiom,
    ! [X3,X1] : c_Union(c_Pow(X3,X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).

fof(f7946,plain,
    spl0_892,
    inference(avatar_split_clause,[],[f2590,f7944]) ).

fof(f2590,axiom,
    ! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).

fof(f7942,plain,
    spl0_891,
    inference(avatar_split_clause,[],[f2588,f7940]) ).

fof(f7940,plain,
    ( spl0_891
  <=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).

fof(f2588,axiom,
    ! [X1,X12] : c_emptyset = c_minus(X12,X12,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).

fof(f7938,plain,
    spl0_890,
    inference(avatar_split_clause,[],[f2587,f7936]) ).

fof(f7936,plain,
    ( spl0_890
  <=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).

fof(f2587,axiom,
    ! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).

fof(f7934,plain,
    spl0_889,
    inference(avatar_split_clause,[],[f2549,f7932]) ).

fof(f7932,plain,
    ( spl0_889
  <=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).

fof(f2549,axiom,
    ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).

fof(f7930,plain,
    spl0_888,
    inference(avatar_split_clause,[],[f2394,f7928]) ).

fof(f7928,plain,
    ( spl0_888
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | c_1 = c_HOL_Oabs(c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).

fof(f2394,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_1 = c_HOL_Oabs(c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).

fof(f7926,plain,
    spl0_887,
    inference(avatar_split_clause,[],[f2374,f7924]) ).

fof(f7924,plain,
    ( spl0_887
  <=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).

fof(f2374,axiom,
    ! [X2,X1,X85] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).

fof(f7922,plain,
    spl0_886,
    inference(avatar_split_clause,[],[f2372,f7920]) ).

fof(f7920,plain,
    ( spl0_886
  <=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).

fof(f2372,axiom,
    ! [X3,X1] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).

fof(f7918,plain,
    spl0_885,
    inference(avatar_split_clause,[],[f2243,f7916]) ).

fof(f2243,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_0 = c_OrderedGroup_Opprt(c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).

fof(f7914,plain,
    spl0_884,
    inference(avatar_split_clause,[],[f2238,f7912]) ).

fof(f2238,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X1)
      | c_0 = c_OrderedGroup_Onprt(c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).

fof(f7910,plain,
    spl0_883,
    inference(avatar_split_clause,[],[f2220,f7908]) ).

fof(f7908,plain,
    ( spl0_883
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X1)
        | c_0 = c_uminus(c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).

fof(f2220,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_0 = c_uminus(c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).

fof(f7906,plain,
    spl0_882,
    inference(avatar_split_clause,[],[f2173,f7904]) ).

fof(f7904,plain,
    ( spl0_882
  <=> ! [X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
        | c_0 = c_HOL_Oabs(c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).

fof(f2173,axiom,
    ! [X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_0 = c_HOL_Oabs(c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).

fof(f7902,plain,
    spl0_881,
    inference(avatar_split_clause,[],[f2169,f7900]) ).

fof(f2169,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).

fof(f7898,plain,
    spl0_880,
    inference(avatar_split_clause,[],[f2162,f7896]) ).

fof(f7896,plain,
    ( spl0_880
  <=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).

fof(f2162,axiom,
    ! [X3,X1,X45] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).

fof(f7894,plain,
    spl0_879,
    inference(avatar_split_clause,[],[f2161,f7892]) ).

fof(f7892,plain,
    ( spl0_879
  <=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f2161,axiom,
    ! [X3,X1,X44] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).

fof(f7890,plain,
    spl0_878,
    inference(avatar_split_clause,[],[f2158,f7888]) ).

fof(f7888,plain,
    ( spl0_878
  <=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f2158,axiom,
    ! [X3,X1,X45] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).

fof(f7886,plain,
    spl0_877,
    inference(avatar_split_clause,[],[f2157,f7884]) ).

fof(f7884,plain,
    ( spl0_877
  <=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f2157,axiom,
    ! [X3,X1,X44] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).

fof(f7882,plain,
    spl0_876,
    inference(avatar_split_clause,[],[f2144,f7880]) ).

fof(f7880,plain,
    ( spl0_876
  <=> ! [X1] :
        ( ~ class_Numeral_Onumber__ring(X1)
        | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f2144,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).

fof(f7878,plain,
    spl0_875,
    inference(avatar_split_clause,[],[f2143,f7876]) ).

fof(f2143,axiom,
    ! [X1] :
      ( ~ class_Numeral_Onumber__ring(X1)
      | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).

fof(f7874,plain,
    spl0_874,
    inference(avatar_split_clause,[],[f2089,f7872]) ).

fof(f2089,axiom,
    ! [X21] :
      ( c_0 = X21
      | c_less(c_0,X21,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).

fof(f7870,plain,
    spl0_873,
    inference(avatar_split_clause,[],[f2088,f7868]) ).

fof(f2088,axiom,
    ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).

fof(f7866,plain,
    spl0_872,
    inference(avatar_split_clause,[],[f2087,f7864]) ).

fof(f7864,plain,
    ( spl0_872
  <=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f2087,axiom,
    ! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).

fof(f7862,plain,
    spl0_871,
    inference(avatar_split_clause,[],[f2048,f7860]) ).

fof(f7860,plain,
    ( spl0_871
  <=> ! [X21] :
        ( c_0 = X21
        | ~ c_less(X21,c_1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).

fof(f2048,axiom,
    ! [X21] :
      ( c_0 = X21
      | ~ c_less(X21,c_1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).

fof(f7858,plain,
    spl0_870,
    inference(avatar_split_clause,[],[f2042,f7856]) ).

fof(f2042,axiom,
    ! [X43] :
      ( c_0 = X43
      | ~ c_lessequals(X43,c_0,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).

fof(f7854,plain,
    spl0_869,
    inference(avatar_split_clause,[],[f2040,f7852]) ).

fof(f2040,axiom,
    ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).

fof(f7850,plain,
    spl0_868,
    inference(avatar_split_clause,[],[f1808,f7848]) ).

fof(f1808,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | c_1 = c_NatArith_Oof__nat(c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).

fof(f7846,plain,
    spl0_867,
    inference(avatar_split_clause,[],[f1804,f7844]) ).

fof(f1804,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_0 = c_NatArith_Oof__nat(c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).

fof(f7842,plain,
    spl0_866,
    inference(avatar_split_clause,[],[f1790,f7840]) ).

fof(f7840,plain,
    ( spl0_866
  <=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f1790,axiom,
    ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).

fof(f7838,plain,
    spl0_865,
    inference(avatar_split_clause,[],[f1788,f7836]) ).

fof(f7836,plain,
    ( spl0_865
  <=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f1788,axiom,
    ! [X82,X41,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).

fof(f7834,plain,
    spl0_864,
    inference(avatar_split_clause,[],[f1732,f7832]) ).

fof(f1732,axiom,
    ! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).

fof(f7830,plain,
    spl0_863,
    inference(avatar_split_clause,[],[f1711,f7828]) ).

fof(f7828,plain,
    ( spl0_863
  <=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f1711,axiom,
    ! [X0,X1,X25] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).

fof(f7826,plain,
    spl0_862,
    inference(avatar_split_clause,[],[f1631,f7824]) ).

fof(f7824,plain,
    ( spl0_862
  <=> ! [X41,X43,X47] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f1631,axiom,
    ! [X41,X47,X43] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).

fof(f7822,plain,
    spl0_861,
    inference(avatar_split_clause,[],[f1542,f7820]) ).

fof(f7820,plain,
    ( spl0_861
  <=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f1542,axiom,
    ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).

fof(f7818,plain,
    spl0_860,
    inference(avatar_split_clause,[],[f1478,f7816]) ).

fof(f1478,axiom,
    ! [X15] :
      ( c_0 = X15
      | ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).

fof(f7814,plain,
    spl0_859,
    inference(avatar_split_clause,[],[f1401,f7812]) ).

fof(f1401,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_1 = c_IntDef_Oof__int(c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).

fof(f7810,plain,
    spl0_858,
    inference(avatar_split_clause,[],[f1396,f7808]) ).

fof(f1396,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | c_0 = c_IntDef_Oof__int(c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).

fof(f7806,plain,
    spl0_857,
    inference(avatar_split_clause,[],[f1387,f7804]) ).

fof(f1387,axiom,
    ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).

fof(f7802,plain,
    spl0_856,
    inference(avatar_split_clause,[],[f1373,f7800]) ).

fof(f7800,plain,
    ( spl0_856
  <=> ! [X21] :
        ( c_0 = X21
        | c_0 != c_IntDef_Oint(X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f1373,axiom,
    ! [X21] :
      ( c_0 = X21
      | c_0 != c_IntDef_Oint(X21) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).

fof(f7798,plain,
    spl0_855,
    inference(avatar_split_clause,[],[f1367,f7796]) ).

fof(f1367,axiom,
    ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).

fof(f7794,plain,
    spl0_854,
    inference(avatar_split_clause,[],[f1253,f7792]) ).

fof(f7792,plain,
    ( spl0_854
  <=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f1253,axiom,
    ! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).

fof(f7790,plain,
    spl0_853,
    inference(avatar_split_clause,[],[f1252,f7788]) ).

fof(f7788,plain,
    ( spl0_853
  <=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f1252,axiom,
    ! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).

fof(f7786,plain,
    spl0_852,
    inference(avatar_split_clause,[],[f1249,f7784]) ).

fof(f7784,plain,
    ( spl0_852
  <=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f1249,axiom,
    ! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).

fof(f7782,plain,
    spl0_851,
    inference(avatar_split_clause,[],[f1248,f7780]) ).

fof(f7780,plain,
    ( spl0_851
  <=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f1248,axiom,
    ! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).

fof(f7778,plain,
    spl0_850,
    inference(avatar_split_clause,[],[f1225,f7776]) ).

fof(f7776,plain,
    ( spl0_850
  <=> ! [X15] :
        ( c_0 = X15
        | ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f1225,axiom,
    ! [X15] :
      ( c_0 = X15
      | ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).

fof(f7774,plain,
    spl0_849,
    inference(avatar_split_clause,[],[f1215,f7772]) ).

fof(f1215,axiom,
    ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).

fof(f7770,plain,
    spl0_848,
    inference(avatar_split_clause,[],[f1202,f7768]) ).

fof(f7768,plain,
    ( spl0_848
  <=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f1202,axiom,
    ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).

fof(f7766,plain,
    spl0_847,
    inference(avatar_split_clause,[],[f1181,f7764]) ).

fof(f7764,plain,
    ( spl0_847
  <=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).

fof(f1181,axiom,
    ! [X3,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).

fof(f7762,plain,
    spl0_846,
    inference(avatar_split_clause,[],[f95,f7760]) ).

fof(f7760,plain,
    ( spl0_846
  <=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f95,axiom,
    ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).

fof(f7758,plain,
    spl0_845,
    inference(avatar_split_clause,[],[f90,f7756]) ).

fof(f7756,plain,
    ( spl0_845
  <=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f90,axiom,
    ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).

fof(f7754,plain,
    spl0_844,
    inference(avatar_split_clause,[],[f61,f7752]) ).

fof(f7752,plain,
    ( spl0_844
  <=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f61,axiom,
    ! [X1,X12] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

fof(f7750,plain,
    spl0_843,
    inference(avatar_split_clause,[],[f45,f7748]) ).

fof(f7748,plain,
    ( spl0_843
  <=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f45,axiom,
    ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).

fof(f7746,plain,
    spl0_842,
    inference(avatar_split_clause,[],[f42,f7744]) ).

fof(f42,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).

fof(f7742,plain,
    spl0_841,
    inference(avatar_split_clause,[],[f41,f7740]) ).

fof(f41,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).

fof(f7738,plain,
    spl0_840,
    inference(avatar_split_clause,[],[f26,f7736]) ).

fof(f7736,plain,
    ( spl0_840
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f26,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).

fof(f7734,plain,
    spl0_839,
    inference(avatar_split_clause,[],[f25,f7732]) ).

fof(f7732,plain,
    ( spl0_839
  <=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f25,axiom,
    ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).

fof(f7720,plain,
    spl0_838,
    inference(avatar_split_clause,[],[f3246,f7718]) ).

fof(f3246,plain,
    ! [X3] : c_div(X3,c_1,tc_nat) = X3,
    inference(forward_demodulation,[],[f3019,f2979]) ).

fof(f3019,plain,
    ! [X3] : c_div(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X3,
    inference(definition_unfolding,[],[f1214,f2544]) ).

fof(f1214,axiom,
    ! [X3] : c_div(X3,c_Suc(c_0),tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).

fof(f7716,plain,
    spl0_837,
    inference(avatar_split_clause,[],[f3244,f7713]) ).

fof(f7713,plain,
    ( spl0_837
  <=> c_1 = c_times(c_1,c_1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f3244,plain,
    c_1 = c_times(c_1,c_1,tc_nat),
    inference(forward_demodulation,[],[f3016,f2979]) ).

fof(f3016,plain,
    c_times(c_1,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
    inference(definition_unfolding,[],[f2064,f2544]) ).

fof(f2064,axiom,
    c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).

fof(f7711,plain,
    spl0_836,
    inference(avatar_split_clause,[],[f3242,f7709]) ).

fof(f3242,plain,
    ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat),
    inference(forward_demodulation,[],[f3015,f2979]) ).

fof(f3015,plain,
    ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1231,f2544]) ).

fof(f1231,axiom,
    ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Suc(c_0),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).

fof(f7707,plain,
    spl0_835,
    inference(avatar_split_clause,[],[f3241,f7704]) ).

fof(f3241,plain,
    c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
    inference(forward_demodulation,[],[f1867,f2156]) ).

fof(f1867,axiom,
    c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).

fof(f7702,plain,
    spl0_834,
    inference(avatar_split_clause,[],[f3239,f7700]) ).

fof(f7700,plain,
    ( spl0_834
  <=> ! [X41,X3] : c_append(c_List_Olist_ONil,X3,X41) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f3239,plain,
    ! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3,
    inference(forward_demodulation,[],[f3007,f1514]) ).

fof(f1514,axiom,
    ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).

fof(f3007,plain,
    ! [X41,X3] : c_append(c_List_Orev(c_List_Olist_ONil,X41),X3,X41) = X3,
    inference(definition_unfolding,[],[f1586,f1585]) ).

fof(f1586,axiom,
    ! [X3,X41] : c_List_Oitrev(c_List_Olist_ONil,X3,X41) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).

fof(f7698,plain,
    spl0_833,
    inference(avatar_split_clause,[],[f3237,f7695]) ).

fof(f7695,plain,
    ( spl0_833
  <=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f3237,plain,
    c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
    inference(forward_demodulation,[],[f3004,f2156]) ).

fof(f3004,plain,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
    inference(definition_unfolding,[],[f2125,f2129]) ).

fof(f2125,axiom,
    c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).

fof(f7693,plain,
    spl0_832,
    inference(avatar_split_clause,[],[f2929,f7691]) ).

fof(f7691,plain,
    ( spl0_832
  <=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Public_OpublicKey(X27,X32) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f2929,axiom,
    ! [X27,X12,X32] : c_Public_OshrK(X12) != c_Public_OpublicKey(X27,X32),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__pubK_0) ).

fof(f7689,plain,
    spl0_831,
    inference(avatar_split_clause,[],[f2911,f7687]) ).

fof(f7687,plain,
    ( spl0_831
  <=> ! [X27,X12] : ~ c_in(c_Public_OpublicKey(X27,X12),c_Message_OsymKeys,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f2911,axiom,
    ! [X27,X12] : ~ c_in(c_Public_OpublicKey(X27,X12),c_Message_OsymKeys,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK_0) ).

fof(f7685,plain,
    spl0_830,
    inference(avatar_split_clause,[],[f2900,f7683]) ).

fof(f2900,axiom,
    ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__shrK_0) ).

fof(f7681,plain,
    spl0_829,
    inference(avatar_split_clause,[],[f2895,f7679]) ).

fof(f7679,plain,
    ( spl0_829
  <=> ! [X7] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f2895,axiom,
    ! [X7] : ~ c_in(c_Message_Omsg_ONonce(X7),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__used__empty_0) ).

fof(f7677,plain,
    spl0_828,
    inference(avatar_split_clause,[],[f2871,f7675]) ).

fof(f7675,plain,
    ( spl0_828
  <=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f2871,axiom,
    ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).

fof(f7673,plain,
    spl0_827,
    inference(avatar_split_clause,[],[f2869,f7671]) ).

fof(f7671,plain,
    ( spl0_827
  <=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f2869,axiom,
    ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).

fof(f7669,plain,
    spl0_826,
    inference(avatar_split_clause,[],[f2862,f7667]) ).

fof(f7667,plain,
    ( spl0_826
  <=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f2862,axiom,
    ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).

fof(f7665,plain,
    spl0_825,
    inference(avatar_split_clause,[],[f2854,f7663]) ).

fof(f7663,plain,
    ( spl0_825
  <=> ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f2854,axiom,
    ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).

fof(f7661,plain,
    spl0_824,
    inference(avatar_split_clause,[],[f2845,f7659]) ).

fof(f7659,plain,
    ( spl0_824
  <=> ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f2845,axiom,
    ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).

fof(f7657,plain,
    spl0_823,
    inference(avatar_split_clause,[],[f2803,f7655]) ).

fof(f7655,plain,
    ( spl0_823
  <=> ! [X12,X88] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f2803,axiom,
    ! [X88,X12] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).

fof(f7653,plain,
    spl0_822,
    inference(avatar_split_clause,[],[f2763,f7651]) ).

fof(f2763,axiom,
    ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).

fof(f7649,plain,
    spl0_821,
    inference(avatar_split_clause,[],[f2762,f7647]) ).

fof(f2762,axiom,
    ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).

fof(f7645,plain,
    spl0_820,
    inference(avatar_split_clause,[],[f2761,f7643]) ).

fof(f2761,axiom,
    ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).

fof(f7641,plain,
    spl0_819,
    inference(avatar_split_clause,[],[f2760,f7639]) ).

fof(f2760,axiom,
    ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).

fof(f7637,plain,
    spl0_818,
    inference(avatar_split_clause,[],[f2738,f7635]) ).

fof(f7635,plain,
    ( spl0_818
  <=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f2738,axiom,
    ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).

fof(f7633,plain,
    spl0_817,
    inference(avatar_split_clause,[],[f2687,f7631]) ).

fof(f2687,axiom,
    ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).

fof(f7629,plain,
    spl0_816,
    inference(avatar_split_clause,[],[f2639,f7627]) ).

fof(f7627,plain,
    ( spl0_816
  <=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f2639,axiom,
    ! [X3,X1] : c_union(X3,c_emptyset,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).

fof(f7625,plain,
    spl0_815,
    inference(avatar_split_clause,[],[f2638,f7623]) ).

fof(f2638,axiom,
    ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).

fof(f7621,plain,
    spl0_814,
    inference(avatar_split_clause,[],[f2634,f7619]) ).

fof(f2634,axiom,
    ! [X3,X1] : c_union(X3,X3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).

fof(f7617,plain,
    spl0_813,
    inference(avatar_split_clause,[],[f2633,f7615]) ).

fof(f7615,plain,
    ( spl0_813
  <=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f2633,axiom,
    ! [X1,X12] : c_UNIV = c_union(X12,c_UNIV,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).

fof(f7613,plain,
    spl0_812,
    inference(avatar_split_clause,[],[f2632,f7611]) ).

fof(f2632,axiom,
    ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).

fof(f7609,plain,
    spl0_811,
    inference(avatar_split_clause,[],[f2580,f7607]) ).

fof(f2580,axiom,
    ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).

fof(f7605,plain,
    spl0_810,
    inference(avatar_split_clause,[],[f2576,f7603]) ).

fof(f7603,plain,
    ( spl0_810
  <=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f2576,axiom,
    ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).

fof(f7601,plain,
    spl0_809,
    inference(avatar_split_clause,[],[f2511,f7599]) ).

fof(f7599,plain,
    ( spl0_809
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_lessequals(c_0,c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f2511,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_lessequals(c_0,c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).

fof(f7597,plain,
    spl0_808,
    inference(avatar_split_clause,[],[f2499,f7595]) ).

fof(f7595,plain,
    ( spl0_808
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_less(c_0,c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f2499,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | c_less(c_0,c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).

fof(f7593,plain,
    spl0_807,
    inference(avatar_split_clause,[],[f2494,f7591]) ).

fof(f7591,plain,
    ( spl0_807
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_less(c_1,c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f2494,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_less(c_1,c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).

fof(f7589,plain,
    spl0_806,
    inference(avatar_split_clause,[],[f2493,f7587]) ).

fof(f7587,plain,
    ( spl0_806
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X1)
        | ~ c_lessequals(c_1,c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f2493,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X1)
      | ~ c_lessequals(c_1,c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).

fof(f7585,plain,
    spl0_805,
    inference(avatar_split_clause,[],[f2381,f7583]) ).

fof(f7583,plain,
    ( spl0_805
  <=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f2381,axiom,
    ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).

fof(f7581,plain,
    spl0_804,
    inference(avatar_split_clause,[],[f2380,f7579]) ).

fof(f7579,plain,
    ( spl0_804
  <=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f2380,axiom,
    ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).

fof(f7577,plain,
    spl0_803,
    inference(avatar_split_clause,[],[f2378,f7575]) ).

fof(f7575,plain,
    ( spl0_803
  <=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f2378,axiom,
    ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).

fof(f7573,plain,
    spl0_802,
    inference(avatar_split_clause,[],[f2370,f7571]) ).

fof(f7571,plain,
    ( spl0_802
  <=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f2370,axiom,
    ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).

fof(f7569,plain,
    spl0_801,
    inference(avatar_split_clause,[],[f2368,f7567]) ).

fof(f7567,plain,
    ( spl0_801
  <=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f2368,axiom,
    ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).

fof(f7565,plain,
    spl0_800,
    inference(avatar_split_clause,[],[f2344,f7563]) ).

fof(f2344,axiom,
    ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).

fof(f7561,plain,
    spl0_799,
    inference(avatar_split_clause,[],[f2269,f7559]) ).

fof(f2269,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | ~ c_less(X0,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).

fof(f7557,plain,
    spl0_798,
    inference(avatar_split_clause,[],[f2156,f7554]) ).

fof(f7552,plain,
    spl0_797,
    inference(avatar_split_clause,[],[f2102,f7550]) ).

fof(f2102,axiom,
    ! [X3] : c_minus(X3,c_0,tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).

fof(f7548,plain,
    spl0_796,
    inference(avatar_split_clause,[],[f2100,f7546]) ).

fof(f2100,axiom,
    ! [X3] : c_plus(c_0,X3,tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).

fof(f7544,plain,
    spl0_795,
    inference(avatar_split_clause,[],[f2098,f7542]) ).

fof(f7542,plain,
    ( spl0_795
  <=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).

fof(f2098,axiom,
    ! [X21] : c_0 = c_times(c_0,X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).

fof(f7540,plain,
    spl0_794,
    inference(avatar_split_clause,[],[f2056,f7538]) ).

fof(f2056,axiom,
    ! [X15] : c_0 = c_times(X15,c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).

fof(f7536,plain,
    spl0_793,
    inference(avatar_split_clause,[],[f2054,f7534]) ).

fof(f7534,plain,
    ( spl0_793
  <=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f2054,axiom,
    ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).

fof(f7532,plain,
    spl0_792,
    inference(avatar_split_clause,[],[f2053,f7530]) ).

fof(f7530,plain,
    ( spl0_792
  <=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f2053,axiom,
    ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).

fof(f7528,plain,
    spl0_791,
    inference(avatar_split_clause,[],[f2051,f7526]) ).

fof(f7526,plain,
    ( spl0_791
  <=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f2051,axiom,
    ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).

fof(f7524,plain,
    spl0_790,
    inference(avatar_split_clause,[],[f2050,f7522]) ).

fof(f7522,plain,
    ( spl0_790
  <=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f2050,axiom,
    ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).

fof(f7520,plain,
    spl0_789,
    inference(avatar_split_clause,[],[f2041,f7518]) ).

fof(f2041,axiom,
    ! [X15] : c_0 = c_minus(X15,X15,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).

fof(f7516,plain,
    spl0_788,
    inference(avatar_split_clause,[],[f2034,f7514]) ).

fof(f2034,axiom,
    ! [X21] : c_0 = c_minus(c_0,X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).

fof(f7512,plain,
    spl0_787,
    inference(avatar_split_clause,[],[f2026,f7510]) ).

fof(f2026,axiom,
    ! [X3] : c_plus(X3,c_0,tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

fof(f7508,plain,
    spl0_786,
    inference(avatar_split_clause,[],[f1787,f7506]) ).

fof(f1787,axiom,
    ! [X0,X1,X81] : c_List_Olist_OCons(X0,X81,X1) != X81,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).

fof(f7504,plain,
    spl0_785,
    inference(avatar_split_clause,[],[f1763,f7502]) ).

fof(f7502,plain,
    ( spl0_785
  <=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f1763,axiom,
    ! [X1,X12] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).

fof(f7500,plain,
    spl0_784,
    inference(avatar_split_clause,[],[f1762,f7498]) ).

fof(f7498,plain,
    ( spl0_784
  <=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f1762,axiom,
    ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).

fof(f7496,plain,
    spl0_783,
    inference(avatar_split_clause,[],[f1741,f7494]) ).

fof(f7494,plain,
    ( spl0_783
  <=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f1741,axiom,
    ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).

fof(f7492,plain,
    spl0_782,
    inference(avatar_split_clause,[],[f1722,f7490]) ).

fof(f1722,axiom,
    ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).

fof(f7488,plain,
    spl0_781,
    inference(avatar_split_clause,[],[f1719,f7486]) ).

fof(f7486,plain,
    ( spl0_781
  <=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f1719,axiom,
    ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).

fof(f7484,plain,
    spl0_780,
    inference(avatar_split_clause,[],[f1707,f7482]) ).

fof(f1707,axiom,
    ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).

fof(f7480,plain,
    spl0_779,
    inference(avatar_split_clause,[],[f1628,f7478]) ).

fof(f7478,plain,
    ( spl0_779
  <=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).

fof(f1628,axiom,
    ! [X65,X41] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).

fof(f7476,plain,
    spl0_778,
    inference(avatar_split_clause,[],[f1623,f7474]) ).

fof(f7474,plain,
    ( spl0_778
  <=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f1623,axiom,
    ! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).

fof(f7472,plain,
    spl0_777,
    inference(avatar_split_clause,[],[f1615,f7470]) ).

fof(f7470,plain,
    ( spl0_777
  <=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f1615,axiom,
    ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).

fof(f7468,plain,
    spl0_776,
    inference(avatar_split_clause,[],[f1598,f7466]) ).

fof(f7466,plain,
    ( spl0_776
  <=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f1598,axiom,
    ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).

fof(f7464,plain,
    spl0_775,
    inference(avatar_split_clause,[],[f1569,f7462]) ).

fof(f7462,plain,
    ( spl0_775
  <=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f1569,axiom,
    ! [X3,X1] : c_List_Odrop(c_0,X3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).

fof(f7460,plain,
    spl0_774,
    inference(avatar_split_clause,[],[f1568,f7458]) ).

fof(f7458,plain,
    ( spl0_774
  <=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f1568,axiom,
    ! [X21,X41] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).

fof(f7456,plain,
    spl0_773,
    inference(avatar_split_clause,[],[f1534,f7454]) ).

fof(f7454,plain,
    ( spl0_773
  <=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f1534,axiom,
    ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).

fof(f7452,plain,
    spl0_772,
    inference(avatar_split_clause,[],[f1494,f7450]) ).

fof(f1494,axiom,
    ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).

fof(f7448,plain,
    spl0_771,
    inference(avatar_split_clause,[],[f1491,f7446]) ).

fof(f1491,axiom,
    ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).

fof(f7444,plain,
    spl0_770,
    inference(avatar_split_clause,[],[f1489,f7442]) ).

fof(f1489,axiom,
    ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).

fof(f7440,plain,
    spl0_769,
    inference(avatar_split_clause,[],[f1474,f7438]) ).

fof(f7438,plain,
    ( spl0_769
  <=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f1474,axiom,
    ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).

fof(f7436,plain,
    spl0_768,
    inference(avatar_split_clause,[],[f1466,f7434]) ).

fof(f7434,plain,
    ( spl0_768
  <=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f1466,axiom,
    ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).

fof(f7432,plain,
    spl0_767,
    inference(avatar_split_clause,[],[f1464,f7430]) ).

fof(f7430,plain,
    ( spl0_767
  <=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f1464,axiom,
    ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).

fof(f7428,plain,
    spl0_766,
    inference(avatar_split_clause,[],[f1432,f7426]) ).

fof(f1432,axiom,
    ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).

fof(f7424,plain,
    spl0_765,
    inference(avatar_split_clause,[],[f1364,f7422]) ).

fof(f7422,plain,
    ( spl0_765
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | c_in(c_1,c_IntDef_ONats,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f1364,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | c_in(c_1,c_IntDef_ONats,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).

fof(f7420,plain,
    spl0_764,
    inference(avatar_split_clause,[],[f1363,f7418]) ).

fof(f7418,plain,
    ( spl0_764
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | c_in(c_0,c_IntDef_ONats,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).

fof(f1363,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | c_in(c_0,c_IntDef_ONats,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).

fof(f7416,plain,
    spl0_763,
    inference(avatar_split_clause,[],[f1358,f7414]) ).

fof(f7414,plain,
    ( spl0_763
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_in(c_1,c_IntDef_OInts,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f1358,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_in(c_1,c_IntDef_OInts,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).

fof(f7412,plain,
    spl0_762,
    inference(avatar_split_clause,[],[f1357,f7410]) ).

fof(f7410,plain,
    ( spl0_762
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_in(c_0,c_IntDef_OInts,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f1357,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
      | c_in(c_0,c_IntDef_OInts,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).

fof(f7408,plain,
    spl0_761,
    inference(avatar_split_clause,[],[f1350,f7405]) ).

fof(f7405,plain,
    ( spl0_761
  <=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f1350,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(f7403,plain,
    spl0_760,
    inference(avatar_split_clause,[],[f1245,f7401]) ).

fof(f7401,plain,
    ( spl0_760
  <=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f1245,axiom,
    ! [X1,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).

fof(f7399,plain,
    spl0_759,
    inference(avatar_split_clause,[],[f1241,f7397]) ).

fof(f1241,axiom,
    ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).

fof(f7395,plain,
    spl0_758,
    inference(avatar_split_clause,[],[f1230,f7393]) ).

fof(f1230,axiom,
    ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).

fof(f7391,plain,
    spl0_757,
    inference(avatar_split_clause,[],[f1213,f7389]) ).

fof(f7389,plain,
    ( spl0_757
  <=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f1213,axiom,
    ! [X15] : c_0 = c_div(c_0,X15,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).

fof(f7387,plain,
    spl0_756,
    inference(avatar_split_clause,[],[f1212,f7385]) ).

fof(f7385,plain,
    ( spl0_756
  <=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f1212,axiom,
    ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).

fof(f7383,plain,
    spl0_755,
    inference(avatar_split_clause,[],[f1211,f7381]) ).

fof(f7381,plain,
    ( spl0_755
  <=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f1211,axiom,
    ! [X18] : c_0 = c_div(X18,c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).

fof(f7379,plain,
    spl0_754,
    inference(avatar_split_clause,[],[f1183,f7377]) ).

fof(f7377,plain,
    ( spl0_754
  <=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f1183,axiom,
    ! [X3,X1] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).

fof(f7375,plain,
    spl0_753,
    inference(avatar_split_clause,[],[f1182,f7373]) ).

fof(f7373,plain,
    ( spl0_753
  <=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f1182,axiom,
    ! [X3,X1] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).

fof(f7371,plain,
    spl0_752,
    inference(avatar_split_clause,[],[f1176,f7369]) ).

fof(f7369,plain,
    ( spl0_752
  <=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f1176,axiom,
    ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).

fof(f7367,plain,
    spl0_751,
    inference(avatar_split_clause,[],[f68,f7365]) ).

fof(f68,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X1)
      | c_lessequals(X0,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

fof(f7363,plain,
    spl0_750,
    inference(avatar_split_clause,[],[f2970,f7360]) ).

fof(f2970,axiom,
    c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f7358,plain,
    spl0_749,
    inference(avatar_split_clause,[],[f2972,f7355]) ).

fof(f2972,axiom,
    c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f7353,plain,
    ( spl0_748
    | ~ spl0_646
    | ~ spl0_688 ),
    inference(avatar_split_clause,[],[f7340,f7071,f6122,f7350]) ).

fof(f7350,plain,
    ( spl0_748
  <=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f7340,plain,
    ( c_lessequals(c_0,c_1,tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_688 ),
    inference(superposition,[],[f7072,f6124]) ).

fof(f7346,plain,
    ( ~ spl0_747
    | ~ spl0_647
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f7332,f7063,f6127,f7343]) ).

fof(f7343,plain,
    ( spl0_747
  <=> c_less(c_0,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f7063,plain,
    ( spl0_686
  <=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f7332,plain,
    ( ~ c_less(c_0,c_0,tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_686 ),
    inference(superposition,[],[f7064,f6129]) ).

fof(f7064,plain,
    ( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
    | ~ spl0_686 ),
    inference(avatar_component_clause,[],[f7063]) ).

fof(f7337,plain,
    ( ~ spl0_746
    | ~ spl0_646
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f7331,f7063,f6122,f7334]) ).

fof(f7334,plain,
    ( spl0_746
  <=> c_less(c_1,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f7331,plain,
    ( ~ c_less(c_1,c_0,tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_686 ),
    inference(superposition,[],[f7064,f6124]) ).

fof(f7330,plain,
    spl0_745,
    inference(avatar_split_clause,[],[f3243,f7327]) ).

fof(f7327,plain,
    ( spl0_745
  <=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f3243,plain,
    c_0 = c_uminus(c_0,tc_IntDef_Oint),
    inference(forward_demodulation,[],[f1391,f1374]) ).

fof(f1374,axiom,
    c_0 = c_IntDef_Oint(c_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).

fof(f1391,axiom,
    c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).

fof(f7325,plain,
    spl0_744,
    inference(avatar_split_clause,[],[f3238,f7323]) ).

fof(f7323,plain,
    ( spl0_744
  <=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f3238,plain,
    ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3,
    inference(forward_demodulation,[],[f3006,f2979]) ).

fof(f3006,plain,
    ! [X3] : c_Binomial_Obinomial(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X3,
    inference(definition_unfolding,[],[f1161,f2544]) ).

fof(f1161,axiom,
    ! [X3] : c_Binomial_Obinomial(X3,c_Suc(c_0)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).

fof(f7321,plain,
    spl0_743,
    inference(avatar_split_clause,[],[f2978,f7318]) ).

fof(f7316,plain,
    spl0_742,
    inference(avatar_split_clause,[],[f2923,f7314]) ).

fof(f2923,axiom,
    ! [X86] : c_in(c_Public_OshrK(X86),c_Message_OsymKeys,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).

fof(f7312,plain,
    spl0_741,
    inference(avatar_split_clause,[],[f2908,f7309]) ).

fof(f7309,plain,
    ( spl0_741
  <=> c_0 = c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f2908,axiom,
    c_0 = c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Osize__2_0) ).

fof(f7307,plain,
    spl0_740,
    inference(avatar_split_clause,[],[f2907,f7304]) ).

fof(f7304,plain,
    ( spl0_740
  <=> c_0 = c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f2907,axiom,
    c_0 = c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Osize__1_0) ).

fof(f7302,plain,
    spl0_739,
    inference(avatar_split_clause,[],[f2740,f7300]) ).

fof(f2740,axiom,
    ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).

fof(f7298,plain,
    spl0_738,
    inference(avatar_split_clause,[],[f2739,f7295]) ).

fof(f7295,plain,
    ( spl0_738
  <=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f2739,axiom,
    c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).

fof(f7293,plain,
    spl0_737,
    inference(avatar_split_clause,[],[f2737,f7290]) ).

fof(f7290,plain,
    ( spl0_737
  <=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f2737,axiom,
    c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).

fof(f7288,plain,
    spl0_736,
    inference(avatar_split_clause,[],[f2714,f7286]) ).

fof(f7286,plain,
    ( spl0_736
  <=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f2714,axiom,
    ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).

fof(f7284,plain,
    spl0_735,
    inference(avatar_split_clause,[],[f2698,f7282]) ).

fof(f2698,axiom,
    ! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).

fof(f7280,plain,
    spl0_734,
    inference(avatar_split_clause,[],[f2691,f7278]) ).

fof(f7278,plain,
    ( spl0_734
  <=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f2691,axiom,
    ! [X1,X12] : ~ c_less(X12,c_emptyset,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).

fof(f7276,plain,
    spl0_733,
    inference(avatar_split_clause,[],[f2651,f7274]) ).

fof(f7274,plain,
    ( spl0_733
  <=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f2651,axiom,
    ! [X1] : c_emptyset = c_Union(c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).

fof(f7272,plain,
    spl0_732,
    inference(avatar_split_clause,[],[f2649,f7270]) ).

fof(f7270,plain,
    ( spl0_732
  <=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f2649,axiom,
    ! [X1] : c_UNIV = c_Union(c_UNIV,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).

fof(f7268,plain,
    spl0_731,
    inference(avatar_split_clause,[],[f2625,f7266]) ).

fof(f7266,plain,
    ( spl0_731
  <=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f2625,axiom,
    ! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).

fof(f7264,plain,
    spl0_730,
    inference(avatar_split_clause,[],[f2619,f7262]) ).

fof(f7262,plain,
    ( spl0_730
  <=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f2619,axiom,
    ! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).

fof(f7260,plain,
    spl0_729,
    inference(avatar_split_clause,[],[f2612,f7258]) ).

fof(f7258,plain,
    ( spl0_729
  <=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f2612,axiom,
    ! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).

fof(f7256,plain,
    spl0_728,
    inference(avatar_split_clause,[],[f2567,f7253]) ).

fof(f7253,plain,
    ( spl0_728
  <=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f2567,axiom,
    c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).

fof(f7251,plain,
    spl0_727,
    inference(avatar_split_clause,[],[f2528,f7248]) ).

fof(f7248,plain,
    ( spl0_727
  <=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f2528,axiom,
    c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).

fof(f7246,plain,
    spl0_726,
    inference(avatar_split_clause,[],[f2386,f7244]) ).

fof(f7242,plain,
    spl0_725,
    inference(avatar_split_clause,[],[f2164,f7239]) ).

fof(f7239,plain,
    ( spl0_725
  <=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f2164,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(f7237,plain,
    spl0_724,
    inference(avatar_split_clause,[],[f2163,f7234]) ).

fof(f7234,plain,
    ( spl0_724
  <=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f2163,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(f7232,plain,
    spl0_723,
    inference(avatar_split_clause,[],[f2152,f7230]) ).

fof(f7230,plain,
    ( spl0_723
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oneg(c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f2152,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).

fof(f7228,plain,
    spl0_722,
    inference(avatar_split_clause,[],[f2151,f7226]) ).

fof(f7226,plain,
    ( spl0_722
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X1)
        | ~ c_IntDef_Oneg(c_0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f2151,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X1)
      | ~ c_IntDef_Oneg(c_0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).

fof(f7224,plain,
    spl0_721,
    inference(avatar_split_clause,[],[f2135,f7222]) ).

fof(f7222,plain,
    ( spl0_721
  <=> ! [X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
        | ~ c_IntDef_Oiszero(c_1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f2135,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
      | ~ c_IntDef_Oiszero(c_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).

fof(f7220,plain,
    spl0_720,
    inference(avatar_split_clause,[],[f2130,f7218]) ).

fof(f2130,axiom,
    ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).

fof(f7216,plain,
    spl0_719,
    inference(avatar_split_clause,[],[f2115,f7214]) ).

fof(f7214,plain,
    ( spl0_719
  <=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f7212,plain,
    spl0_718,
    inference(avatar_split_clause,[],[f2114,f7210]) ).

fof(f7208,plain,
    spl0_717,
    inference(avatar_split_clause,[],[f2106,f7205]) ).

fof(f2106,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(f7203,plain,
    spl0_716,
    inference(avatar_split_clause,[],[f2105,f7200]) ).

fof(f2105,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(f7198,plain,
    spl0_715,
    inference(avatar_split_clause,[],[f1866,f7195]) ).

fof(f1866,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(f7193,plain,
    spl0_714,
    inference(avatar_split_clause,[],[f1785,f7191]) ).

fof(f7191,plain,
    ( spl0_714
  <=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f1785,axiom,
    ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).

fof(f7189,plain,
    spl0_713,
    inference(avatar_split_clause,[],[f1778,f7187]) ).

fof(f7187,plain,
    ( spl0_713
  <=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f1778,axiom,
    ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).

fof(f7185,plain,
    spl0_712,
    inference(avatar_split_clause,[],[f1753,f7183]) ).

fof(f7183,plain,
    ( spl0_712
  <=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f1753,axiom,
    ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).

fof(f7181,plain,
    spl0_711,
    inference(avatar_split_clause,[],[f1736,f7179]) ).

fof(f7179,plain,
    ( spl0_711
  <=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f1736,axiom,
    ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).

fof(f7177,plain,
    spl0_710,
    inference(avatar_split_clause,[],[f1718,f7175]) ).

fof(f7175,plain,
    ( spl0_710
  <=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f1718,axiom,
    ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).

fof(f7173,plain,
    spl0_709,
    inference(avatar_split_clause,[],[f1688,f7170]) ).

fof(f7170,plain,
    ( spl0_709
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f1688,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(f7168,plain,
    spl0_708,
    inference(avatar_split_clause,[],[f1687,f7165]) ).

fof(f7165,plain,
    ( spl0_708
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f1687,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(f7163,plain,
    spl0_707,
    inference(avatar_split_clause,[],[f1686,f7160]) ).

fof(f7160,plain,
    ( spl0_707
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f1686,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(f7158,plain,
    spl0_706,
    inference(avatar_split_clause,[],[f1685,f7155]) ).

fof(f7155,plain,
    ( spl0_706
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f1685,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(f7153,plain,
    spl0_705,
    inference(avatar_split_clause,[],[f1684,f7150]) ).

fof(f7150,plain,
    ( spl0_705
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f1684,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(f7148,plain,
    spl0_704,
    inference(avatar_split_clause,[],[f1683,f7145]) ).

fof(f7145,plain,
    ( spl0_704
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f1683,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(f7143,plain,
    spl0_703,
    inference(avatar_split_clause,[],[f1682,f7140]) ).

fof(f7140,plain,
    ( spl0_703
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f1682,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(f7138,plain,
    spl0_702,
    inference(avatar_split_clause,[],[f1681,f7135]) ).

fof(f7135,plain,
    ( spl0_702
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f1681,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(f7133,plain,
    spl0_701,
    inference(avatar_split_clause,[],[f1680,f7130]) ).

fof(f7130,plain,
    ( spl0_701
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f1680,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(f7128,plain,
    spl0_700,
    inference(avatar_split_clause,[],[f1679,f7125]) ).

fof(f7125,plain,
    ( spl0_700
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f1679,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(f7123,plain,
    spl0_699,
    inference(avatar_split_clause,[],[f1678,f7120]) ).

fof(f7120,plain,
    ( spl0_699
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f1678,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(f7118,plain,
    spl0_698,
    inference(avatar_split_clause,[],[f1677,f7115]) ).

fof(f7115,plain,
    ( spl0_698
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f1677,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(f7113,plain,
    spl0_697,
    inference(avatar_split_clause,[],[f1676,f7110]) ).

fof(f7110,plain,
    ( spl0_697
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f1676,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(f7108,plain,
    spl0_696,
    inference(avatar_split_clause,[],[f1675,f7105]) ).

fof(f7105,plain,
    ( spl0_696
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f1675,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(f7103,plain,
    spl0_695,
    inference(avatar_split_clause,[],[f1674,f7100]) ).

fof(f7100,plain,
    ( spl0_695
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f1674,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(f7098,plain,
    spl0_694,
    inference(avatar_split_clause,[],[f1673,f7095]) ).

fof(f7095,plain,
    ( spl0_694
  <=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f1673,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(f7093,plain,
    spl0_693,
    inference(avatar_split_clause,[],[f1638,f7091]) ).

fof(f7091,plain,
    ( spl0_693
  <=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f1638,axiom,
    ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).

fof(f7089,plain,
    spl0_692,
    inference(avatar_split_clause,[],[f1567,f7087]) ).

fof(f7087,plain,
    ( spl0_692
  <=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f1567,axiom,
    ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).

fof(f7085,plain,
    spl0_691,
    inference(avatar_split_clause,[],[f1543,f7083]) ).

fof(f7083,plain,
    ( spl0_691
  <=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f1543,axiom,
    ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).

fof(f7081,plain,
    spl0_690,
    inference(avatar_split_clause,[],[f1536,f7079]) ).

fof(f7079,plain,
    ( spl0_690
  <=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f1536,axiom,
    ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).

fof(f7077,plain,
    spl0_689,
    inference(avatar_split_clause,[],[f1514,f7075]) ).

fof(f7075,plain,
    ( spl0_689
  <=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f7073,plain,
    spl0_688,
    inference(avatar_split_clause,[],[f1424,f7071]) ).

fof(f1424,axiom,
    ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).

fof(f7069,plain,
    spl0_687,
    inference(avatar_split_clause,[],[f1384,f7067]) ).

fof(f1384,axiom,
    ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).

fof(f7065,plain,
    spl0_686,
    inference(avatar_split_clause,[],[f1378,f7063]) ).

fof(f1378,axiom,
    ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).

fof(f7061,plain,
    ~ spl0_685,
    inference(avatar_split_clause,[],[f1309,f7058]) ).

fof(f1309,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(f7056,plain,
    spl0_684,
    inference(avatar_split_clause,[],[f1296,f7054]) ).

fof(f7054,plain,
    ( spl0_684
  <=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f1296,axiom,
    ! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).

fof(f7052,plain,
    spl0_683,
    inference(avatar_split_clause,[],[f1295,f7050]) ).

fof(f1295,axiom,
    ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).

fof(f7048,plain,
    spl0_682,
    inference(avatar_split_clause,[],[f1278,f7046]) ).

fof(f7046,plain,
    ( spl0_682
  <=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f1278,axiom,
    ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).

fof(f7044,plain,
    spl0_681,
    inference(avatar_split_clause,[],[f1255,f7041]) ).

fof(f7041,plain,
    ( spl0_681
  <=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f1255,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(f7039,plain,
    spl0_680,
    inference(avatar_split_clause,[],[f1254,f7036]) ).

fof(f7036,plain,
    ( spl0_680
  <=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f1254,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(f7034,plain,
    spl0_679,
    inference(avatar_split_clause,[],[f1184,f7031]) ).

fof(f7031,plain,
    ( spl0_679
  <=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f1184,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(f7029,plain,
    spl0_678,
    inference(avatar_split_clause,[],[f1174,f7027]) ).

fof(f7027,plain,
    ( spl0_678
  <=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f1174,axiom,
    ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2_0) ).

fof(f7025,plain,
    spl0_677,
    inference(avatar_split_clause,[],[f1172,f7023]) ).

fof(f7023,plain,
    ( spl0_677
  <=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f1172,axiom,
    ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).

fof(f7021,plain,
    spl0_676,
    inference(avatar_split_clause,[],[f1165,f7019]) ).

fof(f7019,plain,
    ( spl0_676
  <=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f1165,axiom,
    ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).

fof(f7017,plain,
    spl0_675,
    inference(avatar_split_clause,[],[f1164,f7015]) ).

fof(f7015,plain,
    ( spl0_675
  <=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f1164,axiom,
    ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).

fof(f7013,plain,
    spl0_674,
    inference(avatar_split_clause,[],[f250,f7011]) ).

fof(f7011,plain,
    ( spl0_674
  <=> ! [X37] :
        ( ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_set(X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f250,axiom,
    ! [X37] :
      ( ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_set(X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).

fof(f7009,plain,
    spl0_673,
    inference(avatar_split_clause,[],[f128,f7007]) ).

fof(f7007,plain,
    ( spl0_673
  <=> ! [X37] :
        ( ~ class_Finite__Set_Ofinite(X37)
        | class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f128,axiom,
    ! [X37] :
      ( ~ class_Finite__Set_Ofinite(X37)
      | class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).

fof(f7005,plain,
    spl0_672,
    inference(avatar_split_clause,[],[f112,f7003]) ).

fof(f112,axiom,
    ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

fof(f7001,plain,
    spl0_671,
    inference(avatar_split_clause,[],[f101,f6999]) ).

fof(f101,axiom,
    ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

fof(f6997,plain,
    spl0_670,
    inference(avatar_split_clause,[],[f44,f6995]) ).

fof(f6995,plain,
    ( spl0_670
  <=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f44,axiom,
    ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).

fof(f6993,plain,
    spl0_669,
    inference(avatar_split_clause,[],[f28,f6991]) ).

fof(f6991,plain,
    ( spl0_669
  <=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f28,axiom,
    ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).

fof(f6989,plain,
    ( ~ spl0_668
    | ~ spl0_647
    | ~ spl0_649 ),
    inference(avatar_split_clause,[],[f6979,f6137,f6127,f6986]) ).

fof(f6986,plain,
    ( spl0_668
  <=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f6137,plain,
    ( spl0_649
  <=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f6979,plain,
    ( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
    | ~ spl0_647
    | ~ spl0_649 ),
    inference(superposition,[],[f6138,f6129]) ).

fof(f6138,plain,
    ( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
    | ~ spl0_649 ),
    inference(avatar_component_clause,[],[f6137]) ).

fof(f6984,plain,
    ( ~ spl0_667
    | ~ spl0_646
    | ~ spl0_649 ),
    inference(avatar_split_clause,[],[f6978,f6137,f6122,f6981]) ).

fof(f6981,plain,
    ( spl0_667
  <=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f6978,plain,
    ( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
    | ~ spl0_646
    | ~ spl0_649 ),
    inference(superposition,[],[f6138,f6124]) ).

fof(f6217,plain,
    spl0_666,
    inference(avatar_split_clause,[],[f3253,f6214]) ).

fof(f3253,plain,
    c_less(c_0,c_1,tc_IntDef_Oint),
    inference(forward_demodulation,[],[f1486,f1464]) ).

fof(f1486,axiom,
    ! [X0] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).

fof(f6212,plain,
    spl0_665,
    inference(avatar_split_clause,[],[f3234,f6209]) ).

fof(f6209,plain,
    ( spl0_665
  <=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f3234,plain,
    c_lessequals(c_0,c_0,tc_IntDef_Oint),
    inference(forward_demodulation,[],[f1377,f1374]) ).

fof(f1377,axiom,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).

fof(f6207,plain,
    spl0_664,
    inference(avatar_split_clause,[],[f3233,f6205]) ).

fof(f6205,plain,
    ( spl0_664
  <=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f3233,plain,
    ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat),
    inference(forward_demodulation,[],[f2983,f2979]) ).

fof(f2983,plain,
    ! [X16] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X16,tc_nat),
    inference(definition_unfolding,[],[f24,f2544]) ).

fof(f24,axiom,
    ! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).

fof(f6203,plain,
    spl0_663,
    inference(avatar_split_clause,[],[f3231,f6200]) ).

fof(f3231,plain,
    c_1 = c_IntDef_Onat(c_1),
    inference(forward_demodulation,[],[f2981,f2979]) ).

fof(f2981,plain,
    c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
    inference(definition_unfolding,[],[f1344,f2544]) ).

fof(f1344,axiom,
    c_Suc(c_0) = c_IntDef_Onat(c_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).

fof(f6198,plain,
    spl0_662,
    inference(avatar_split_clause,[],[f2853,f6195]) ).

fof(f2853,axiom,
    c_emptyset = c_Message_Oanalz(c_emptyset),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).

fof(f6193,plain,
    spl0_661,
    inference(avatar_split_clause,[],[f2773,f6190]) ).

fof(f6190,plain,
    ( spl0_661
  <=> c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f2773,axiom,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).

fof(f6188,plain,
    ~ spl0_660,
    inference(avatar_split_clause,[],[f2772,f6185]) ).

fof(f6185,plain,
    ( spl0_660
  <=> c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f2772,axiom,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).

fof(f6183,plain,
    spl0_659,
    inference(avatar_split_clause,[],[f2770,f6180]) ).

fof(f2770,axiom,
    c_emptyset = c_Message_Oparts(c_emptyset),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).

fof(f6178,plain,
    spl0_658,
    inference(avatar_split_clause,[],[f2743,f6175]) ).

fof(f6175,plain,
    ( spl0_658
  <=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f2743,axiom,
    c_emptyset = c_Message_OkeysFor(c_emptyset),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).

fof(f6173,plain,
    spl0_657,
    inference(avatar_split_clause,[],[f2734,f6171]) ).

fof(f6171,plain,
    ( spl0_657
  <=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f2734,axiom,
    ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5_0) ).

fof(f6169,plain,
    spl0_656,
    inference(avatar_split_clause,[],[f2731,f6167]) ).

fof(f6167,plain,
    ( spl0_656
  <=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f2731,axiom,
    ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2_0) ).

fof(f6165,plain,
    spl0_655,
    inference(avatar_split_clause,[],[f2672,f6163]) ).

fof(f2672,axiom,
    ! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

fof(f6161,plain,
    spl0_654,
    inference(avatar_split_clause,[],[f2155,f6158]) ).

fof(f6158,plain,
    ( spl0_654
  <=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f2155,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(f6156,plain,
    spl0_653,
    inference(avatar_split_clause,[],[f2091,f6154]) ).

fof(f6154,plain,
    ( spl0_653
  <=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f2091,axiom,
    ! [X21] : ~ c_less(X21,c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).

fof(f6152,plain,
    spl0_652,
    inference(avatar_split_clause,[],[f2049,f6149]) ).

fof(f2049,axiom,
    c_less(c_0,c_1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).

fof(f6147,plain,
    spl0_651,
    inference(avatar_split_clause,[],[f1709,f6145]) ).

fof(f6145,plain,
    ( spl0_651
  <=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f1709,axiom,
    ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).

fof(f6143,plain,
    spl0_650,
    inference(avatar_split_clause,[],[f1482,f6141]) ).

fof(f1482,axiom,
    ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).

fof(f6139,plain,
    spl0_649,
    inference(avatar_split_clause,[],[f1393,f6137]) ).

fof(f1393,axiom,
    ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).

fof(f6135,plain,
    spl0_648,
    inference(avatar_split_clause,[],[f1386,f6132]) ).

fof(f6132,plain,
    ( spl0_648
  <=> c_0 = c_IntDef_Onat(c_0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f1386,axiom,
    c_0 = c_IntDef_Onat(c_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).

fof(f6130,plain,
    spl0_647,
    inference(avatar_split_clause,[],[f1374,f6127]) ).

fof(f6125,plain,
    spl0_646,
    inference(avatar_split_clause,[],[f1371,f6122]) ).

fof(f1371,axiom,
    c_1 = c_IntDef_Oint(c_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).

fof(f6120,plain,
    spl0_645,
    inference(avatar_split_clause,[],[f1229,f6118]) ).

fof(f6118,plain,
    ( spl0_645
  <=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f1229,axiom,
    ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).

fof(f6116,plain,
    spl0_644,
    inference(avatar_split_clause,[],[f1159,f6114]) ).

fof(f6114,plain,
    ( spl0_644
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f1159,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).

fof(f6112,plain,
    spl0_643,
    inference(avatar_split_clause,[],[f1158,f6110]) ).

fof(f6110,plain,
    ( spl0_643
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f1158,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).

fof(f6108,plain,
    spl0_642,
    inference(avatar_split_clause,[],[f1157,f6106]) ).

fof(f6106,plain,
    ( spl0_642
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f1157,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).

fof(f6104,plain,
    spl0_641,
    inference(avatar_split_clause,[],[f1156,f6102]) ).

fof(f6102,plain,
    ( spl0_641
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f1156,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).

fof(f6100,plain,
    spl0_640,
    inference(avatar_split_clause,[],[f1155,f6098]) ).

fof(f6098,plain,
    ( spl0_640
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f1155,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).

fof(f6096,plain,
    spl0_639,
    inference(avatar_split_clause,[],[f1154,f6094]) ).

fof(f6094,plain,
    ( spl0_639
  <=> ! [X39] :
        ( ~ class_Wellfounded__Recursion_Owellorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f1154,axiom,
    ! [X39] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).

fof(f6092,plain,
    spl0_638,
    inference(avatar_split_clause,[],[f1153,f6090]) ).

fof(f6090,plain,
    ( spl0_638
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f1153,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

fof(f6088,plain,
    spl0_637,
    inference(avatar_split_clause,[],[f1148,f6086]) ).

fof(f6086,plain,
    ( spl0_637
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f1148,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

fof(f6084,plain,
    spl0_636,
    inference(avatar_split_clause,[],[f1147,f6082]) ).

fof(f6082,plain,
    ( spl0_636
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f1147,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

fof(f6080,plain,
    spl0_635,
    inference(avatar_split_clause,[],[f1146,f6078]) ).

fof(f6078,plain,
    ( spl0_635
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f1146,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

fof(f6076,plain,
    spl0_634,
    inference(avatar_split_clause,[],[f1145,f6074]) ).

fof(f6074,plain,
    ( spl0_634
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f1145,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

fof(f6072,plain,
    spl0_633,
    inference(avatar_split_clause,[],[f1144,f6070]) ).

fof(f6070,plain,
    ( spl0_633
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f1144,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

fof(f6068,plain,
    spl0_632,
    inference(avatar_split_clause,[],[f1143,f6066]) ).

fof(f6066,plain,
    ( spl0_632
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f1143,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

fof(f6064,plain,
    spl0_631,
    inference(avatar_split_clause,[],[f1140,f6062]) ).

fof(f6062,plain,
    ( spl0_631
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f1140,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

fof(f6060,plain,
    spl0_630,
    inference(avatar_split_clause,[],[f1139,f6058]) ).

fof(f6058,plain,
    ( spl0_630
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f1139,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

fof(f6056,plain,
    spl0_629,
    inference(avatar_split_clause,[],[f1138,f6054]) ).

fof(f6054,plain,
    ( spl0_629
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f1138,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).

fof(f6052,plain,
    spl0_628,
    inference(avatar_split_clause,[],[f1135,f6050]) ).

fof(f6050,plain,
    ( spl0_628
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f1135,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).

fof(f6048,plain,
    spl0_627,
    inference(avatar_split_clause,[],[f1132,f6046]) ).

fof(f6046,plain,
    ( spl0_627
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f1132,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).

fof(f6044,plain,
    spl0_626,
    inference(avatar_split_clause,[],[f1131,f6042]) ).

fof(f6042,plain,
    ( spl0_626
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f1131,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).

fof(f6040,plain,
    spl0_625,
    inference(avatar_split_clause,[],[f1130,f6038]) ).

fof(f6038,plain,
    ( spl0_625
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f1130,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).

fof(f6036,plain,
    spl0_624,
    inference(avatar_split_clause,[],[f1129,f6034]) ).

fof(f6034,plain,
    ( spl0_624
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f1129,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).

fof(f6032,plain,
    spl0_623,
    inference(avatar_split_clause,[],[f1126,f6030]) ).

fof(f6030,plain,
    ( spl0_623
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__1(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f1126,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__1(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).

fof(f6028,plain,
    spl0_622,
    inference(avatar_split_clause,[],[f1125,f6026]) ).

fof(f6026,plain,
    ( spl0_622
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f1125,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

fof(f6024,plain,
    spl0_621,
    inference(avatar_split_clause,[],[f1120,f6022]) ).

fof(f6022,plain,
    ( spl0_621
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f1120,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

fof(f6020,plain,
    spl0_620,
    inference(avatar_split_clause,[],[f1117,f6018]) ).

fof(f6018,plain,
    ( spl0_620
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f1117,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

fof(f6016,plain,
    spl0_619,
    inference(avatar_split_clause,[],[f1116,f6014]) ).

fof(f6014,plain,
    ( spl0_619
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f1116,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

fof(f6012,plain,
    spl0_618,
    inference(avatar_split_clause,[],[f1115,f6010]) ).

fof(f6010,plain,
    ( spl0_618
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f1115,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

fof(f6008,plain,
    spl0_617,
    inference(avatar_split_clause,[],[f1113,f6006]) ).

fof(f6006,plain,
    ( spl0_617
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__0(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f1113,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__0(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).

fof(f6004,plain,
    spl0_616,
    inference(avatar_split_clause,[],[f1107,f6002]) ).

fof(f6002,plain,
    ( spl0_616
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Osemiring__0(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f1107,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Osemiring__0(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).

fof(f6000,plain,
    spl0_615,
    inference(avatar_split_clause,[],[f1099,f5998]) ).

fof(f5998,plain,
    ( spl0_615
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f1099,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).

fof(f5996,plain,
    spl0_614,
    inference(avatar_split_clause,[],[f1098,f5994]) ).

fof(f5994,plain,
    ( spl0_614
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f1098,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).

fof(f5992,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f1097,f5990]) ).

fof(f5990,plain,
    ( spl0_613
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f1097,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).

fof(f5988,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f1096,f5986]) ).

fof(f5986,plain,
    ( spl0_612
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f1096,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).

fof(f5984,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f1095,f5982]) ).

fof(f5982,plain,
    ( spl0_611
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f1095,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).

fof(f5980,plain,
    spl0_610,
    inference(avatar_split_clause,[],[f1093,f5978]) ).

fof(f5978,plain,
    ( spl0_610
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f1093,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).

fof(f5976,plain,
    spl0_609,
    inference(avatar_split_clause,[],[f1092,f5974]) ).

fof(f5974,plain,
    ( spl0_609
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f1092,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).

fof(f5972,plain,
    spl0_608,
    inference(avatar_split_clause,[],[f1091,f5970]) ).

fof(f5970,plain,
    ( spl0_608
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f1091,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).

fof(f5968,plain,
    spl0_607,
    inference(avatar_split_clause,[],[f1090,f5966]) ).

fof(f5966,plain,
    ( spl0_607
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f1090,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).

fof(f5964,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f1089,f5962]) ).

fof(f5962,plain,
    ( spl0_606
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f1089,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).

fof(f5960,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f1084,f5958]) ).

fof(f5958,plain,
    ( spl0_605
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f1084,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).

fof(f5956,plain,
    spl0_604,
    inference(avatar_split_clause,[],[f1083,f5954]) ).

fof(f5954,plain,
    ( spl0_604
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f1083,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).

fof(f5952,plain,
    spl0_603,
    inference(avatar_split_clause,[],[f1082,f5950]) ).

fof(f5950,plain,
    ( spl0_603
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring__1(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f1082,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring__1(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).

fof(f5948,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f1080,f5946]) ).

fof(f5946,plain,
    ( spl0_602
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f1080,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).

fof(f5944,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f1078,f5942]) ).

fof(f5942,plain,
    ( spl0_601
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f1078,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).

fof(f5940,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f1073,f5938]) ).

fof(f5938,plain,
    ( spl0_600
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f1073,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).

fof(f5936,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f1072,f5934]) ).

fof(f5934,plain,
    ( spl0_599
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f1072,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).

fof(f5932,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f1071,f5930]) ).

fof(f5930,plain,
    ( spl0_598
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f1071,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).

fof(f5928,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f1070,f5926]) ).

fof(f5926,plain,
    ( spl0_597
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f1070,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).

fof(f5924,plain,
    spl0_596,
    inference(avatar_split_clause,[],[f1068,f5922]) ).

fof(f5922,plain,
    ( spl0_596
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f1068,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).

fof(f5920,plain,
    spl0_595,
    inference(avatar_split_clause,[],[f1067,f5918]) ).

fof(f5918,plain,
    ( spl0_595
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f1067,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).

fof(f5916,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f1062,f5914]) ).

fof(f5914,plain,
    ( spl0_594
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f1062,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).

fof(f5912,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f1059,f5910]) ).

fof(f5910,plain,
    ( spl0_593
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f1059,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).

fof(f5908,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f1058,f5906]) ).

fof(f5906,plain,
    ( spl0_592
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f1058,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).

fof(f5904,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f1057,f5902]) ).

fof(f5902,plain,
    ( spl0_591
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f1057,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).

fof(f5900,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f1056,f5898]) ).

fof(f5898,plain,
    ( spl0_590
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f1056,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).

fof(f5896,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f1053,f5894]) ).

fof(f5894,plain,
    ( spl0_589
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f1053,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).

fof(f5892,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f1052,f5890]) ).

fof(f5890,plain,
    ( spl0_588
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f1052,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).

fof(f5888,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f1051,f5886]) ).

fof(f5886,plain,
    ( spl0_587
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f1051,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).

fof(f5884,plain,
    spl0_586,
    inference(avatar_split_clause,[],[f1050,f5882]) ).

fof(f5882,plain,
    ( spl0_586
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f1050,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).

fof(f5880,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f1049,f5878]) ).

fof(f5878,plain,
    ( spl0_585
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f1049,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).

fof(f5876,plain,
    spl0_584,
    inference(avatar_split_clause,[],[f1048,f5874]) ).

fof(f5874,plain,
    ( spl0_584
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f1048,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).

fof(f5872,plain,
    spl0_583,
    inference(avatar_split_clause,[],[f1047,f5870]) ).

fof(f5870,plain,
    ( spl0_583
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f1047,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).

fof(f5868,plain,
    spl0_582,
    inference(avatar_split_clause,[],[f1046,f5866]) ).

fof(f5866,plain,
    ( spl0_582
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f1046,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).

fof(f5864,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f1044,f5862]) ).

fof(f5862,plain,
    ( spl0_581
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f1044,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).

fof(f5860,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f1043,f5858]) ).

fof(f5858,plain,
    ( spl0_580
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f1043,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).

fof(f5856,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f1042,f5854]) ).

fof(f5854,plain,
    ( spl0_579
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f1042,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).

fof(f5852,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f1041,f5850]) ).

fof(f5850,plain,
    ( spl0_578
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f1041,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).

fof(f5848,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f1040,f5846]) ).

fof(f5846,plain,
    ( spl0_577
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f1040,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).

fof(f5844,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f1035,f5842]) ).

fof(f5842,plain,
    ( spl0_576
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f1035,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).

fof(f5840,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f1034,f5838]) ).

fof(f5838,plain,
    ( spl0_575
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f1034,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).

fof(f5836,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f1033,f5834]) ).

fof(f5834,plain,
    ( spl0_574
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__ring(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f1033,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__ring(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).

fof(f5832,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f1030,f5830]) ).

fof(f5830,plain,
    ( spl0_573
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f1030,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).

fof(f5828,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f1027,f5826]) ).

fof(f5826,plain,
    ( spl0_572
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f1027,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

fof(f5824,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f1026,f5822]) ).

fof(f5822,plain,
    ( spl0_571
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f1026,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

fof(f5820,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f1024,f5818]) ).

fof(f5818,plain,
    ( spl0_570
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f1024,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

fof(f5816,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f1023,f5814]) ).

fof(f5814,plain,
    ( spl0_569
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f1023,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

fof(f5812,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f1022,f5810]) ).

fof(f5810,plain,
    ( spl0_568
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f1022,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

fof(f5808,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f1021,f5806]) ).

fof(f5806,plain,
    ( spl0_567
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f1021,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

fof(f5804,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f1018,f5802]) ).

fof(f5802,plain,
    ( spl0_566
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f1018,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

fof(f5800,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f1017,f5798]) ).

fof(f5798,plain,
    ( spl0_565
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f1017,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

fof(f5796,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f989,f5794]) ).

fof(f5794,plain,
    ( spl0_564
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f989,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

fof(f5792,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f987,f5790]) ).

fof(f5790,plain,
    ( spl0_563
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f987,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

fof(f5788,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f984,f5786]) ).

fof(f5786,plain,
    ( spl0_562
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f984,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

fof(f5784,plain,
    spl0_561,
    inference(avatar_split_clause,[],[f983,f5782]) ).

fof(f5782,plain,
    ( spl0_561
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f983,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

fof(f5780,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f982,f5778]) ).

fof(f5778,plain,
    ( spl0_560
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f982,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

fof(f5776,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f981,f5774]) ).

fof(f5774,plain,
    ( spl0_559
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f981,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

fof(f5772,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f980,f5770]) ).

fof(f5770,plain,
    ( spl0_558
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f980,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

fof(f5768,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f979,f5766]) ).

fof(f5766,plain,
    ( spl0_557
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f979,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

fof(f5764,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f977,f5762]) ).

fof(f5762,plain,
    ( spl0_556
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f977,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

fof(f5760,plain,
    spl0_555,
    inference(avatar_split_clause,[],[f976,f5758]) ).

fof(f5758,plain,
    ( spl0_555
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f976,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

fof(f5756,plain,
    spl0_554,
    inference(avatar_split_clause,[],[f974,f5754]) ).

fof(f5754,plain,
    ( spl0_554
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f974,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

fof(f5752,plain,
    spl0_553,
    inference(avatar_split_clause,[],[f971,f5750]) ).

fof(f5750,plain,
    ( spl0_553
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f971,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

fof(f5748,plain,
    spl0_552,
    inference(avatar_split_clause,[],[f970,f5746]) ).

fof(f5746,plain,
    ( spl0_552
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f970,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

fof(f5744,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f968,f5742]) ).

fof(f5742,plain,
    ( spl0_551
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f968,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

fof(f5740,plain,
    spl0_550,
    inference(avatar_split_clause,[],[f967,f5738]) ).

fof(f5738,plain,
    ( spl0_550
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f967,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

fof(f5736,plain,
    spl0_549,
    inference(avatar_split_clause,[],[f966,f5734]) ).

fof(f5734,plain,
    ( spl0_549
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f966,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

fof(f5732,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f965,f5730]) ).

fof(f5730,plain,
    ( spl0_548
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f965,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

fof(f5728,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f964,f5726]) ).

fof(f5726,plain,
    ( spl0_547
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f964,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

fof(f5724,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f963,f5722]) ).

fof(f5722,plain,
    ( spl0_546
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f963,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

fof(f5720,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f962,f5718]) ).

fof(f5718,plain,
    ( spl0_545
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f962,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

fof(f5716,plain,
    spl0_544,
    inference(avatar_split_clause,[],[f961,f5714]) ).

fof(f5714,plain,
    ( spl0_544
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f961,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

fof(f5712,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f957,f5710]) ).

fof(f5710,plain,
    ( spl0_543
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f957,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

fof(f5708,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f956,f5706]) ).

fof(f5706,plain,
    ( spl0_542
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f956,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

fof(f5704,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f955,f5702]) ).

fof(f5702,plain,
    ( spl0_541
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f955,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

fof(f5700,plain,
    spl0_540,
    inference(avatar_split_clause,[],[f954,f5698]) ).

fof(f5698,plain,
    ( spl0_540
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f954,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

fof(f5696,plain,
    spl0_539,
    inference(avatar_split_clause,[],[f949,f5694]) ).

fof(f5694,plain,
    ( spl0_539
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f949,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

fof(f5692,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f947,f5690]) ).

fof(f5690,plain,
    ( spl0_538
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f947,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

fof(f5688,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f946,f5686]) ).

fof(f5686,plain,
    ( spl0_537
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f946,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

fof(f5684,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f945,f5682]) ).

fof(f5682,plain,
    ( spl0_536
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f945,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

fof(f5680,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f944,f5678]) ).

fof(f5678,plain,
    ( spl0_535
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f944,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

fof(f5676,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f942,f5674]) ).

fof(f5674,plain,
    ( spl0_534
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f942,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

fof(f5672,plain,
    spl0_533,
    inference(avatar_split_clause,[],[f941,f5670]) ).

fof(f5670,plain,
    ( spl0_533
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f941,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

fof(f5668,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f940,f5666]) ).

fof(f5666,plain,
    ( spl0_532
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f940,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

fof(f5664,plain,
    spl0_531,
    inference(avatar_split_clause,[],[f939,f5662]) ).

fof(f5662,plain,
    ( spl0_531
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f939,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

fof(f5660,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f938,f5658]) ).

fof(f5658,plain,
    ( spl0_530
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f938,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

fof(f5656,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f937,f5654]) ).

fof(f5654,plain,
    ( spl0_529
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f937,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

fof(f5652,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f936,f5650]) ).

fof(f5650,plain,
    ( spl0_528
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f936,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

fof(f5648,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f935,f5646]) ).

fof(f5646,plain,
    ( spl0_527
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f935,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

fof(f5644,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f934,f5642]) ).

fof(f5642,plain,
    ( spl0_526
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f934,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

fof(f5640,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f933,f5638]) ).

fof(f5638,plain,
    ( spl0_525
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f933,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

fof(f5636,plain,
    spl0_524,
    inference(avatar_split_clause,[],[f932,f5634]) ).

fof(f5634,plain,
    ( spl0_524
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f932,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

fof(f5632,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f931,f5630]) ).

fof(f5630,plain,
    ( spl0_523
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f931,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

fof(f5628,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f930,f5626]) ).

fof(f5626,plain,
    ( spl0_522
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f930,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).

fof(f5624,plain,
    spl0_521,
    inference(avatar_split_clause,[],[f929,f5622]) ).

fof(f5622,plain,
    ( spl0_521
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f929,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).

fof(f5620,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f928,f5618]) ).

fof(f5618,plain,
    ( spl0_520
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f928,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).

fof(f5616,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f927,f5614]) ).

fof(f5614,plain,
    ( spl0_519
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f927,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).

fof(f5612,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f926,f5610]) ).

fof(f5610,plain,
    ( spl0_518
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f926,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).

fof(f5608,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f925,f5606]) ).

fof(f5606,plain,
    ( spl0_517
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f925,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).

fof(f5604,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f924,f5602]) ).

fof(f5602,plain,
    ( spl0_516
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f924,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).

fof(f5600,plain,
    spl0_515,
    inference(avatar_split_clause,[],[f923,f5598]) ).

fof(f5598,plain,
    ( spl0_515
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f923,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).

fof(f5596,plain,
    spl0_514,
    inference(avatar_split_clause,[],[f922,f5594]) ).

fof(f5594,plain,
    ( spl0_514
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f922,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).

fof(f5592,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f921,f5590]) ).

fof(f5590,plain,
    ( spl0_513
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f921,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).

fof(f5588,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f920,f5586]) ).

fof(f5586,plain,
    ( spl0_512
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f920,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).

fof(f5584,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f919,f5582]) ).

fof(f5582,plain,
    ( spl0_511
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f919,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).

fof(f5580,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f918,f5578]) ).

fof(f5578,plain,
    ( spl0_510
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f918,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).

fof(f5576,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f917,f5574]) ).

fof(f5574,plain,
    ( spl0_509
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f917,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).

fof(f5572,plain,
    spl0_508,
    inference(avatar_split_clause,[],[f916,f5570]) ).

fof(f5570,plain,
    ( spl0_508
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f916,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).

fof(f5568,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f915,f5566]) ).

fof(f5566,plain,
    ( spl0_507
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f915,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).

fof(f5564,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f914,f5562]) ).

fof(f5562,plain,
    ( spl0_506
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f914,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).

fof(f5560,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f913,f5558]) ).

fof(f5558,plain,
    ( spl0_505
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f913,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).

fof(f5556,plain,
    spl0_504,
    inference(avatar_split_clause,[],[f912,f5554]) ).

fof(f5554,plain,
    ( spl0_504
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f912,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).

fof(f5552,plain,
    spl0_503,
    inference(avatar_split_clause,[],[f911,f5550]) ).

fof(f5550,plain,
    ( spl0_503
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f911,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).

fof(f5548,plain,
    spl0_502,
    inference(avatar_split_clause,[],[f910,f5546]) ).

fof(f5546,plain,
    ( spl0_502
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f910,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).

fof(f5544,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f909,f5542]) ).

fof(f5542,plain,
    ( spl0_501
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f909,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).

fof(f5540,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f908,f5538]) ).

fof(f5538,plain,
    ( spl0_500
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f908,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).

fof(f5536,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f905,f5534]) ).

fof(f5534,plain,
    ( spl0_499
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f905,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).

fof(f5532,plain,
    spl0_498,
    inference(avatar_split_clause,[],[f903,f5530]) ).

fof(f5530,plain,
    ( spl0_498
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f903,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).

fof(f5528,plain,
    spl0_497,
    inference(avatar_split_clause,[],[f902,f5526]) ).

fof(f5526,plain,
    ( spl0_497
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f902,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).

fof(f5524,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f900,f5522]) ).

fof(f5522,plain,
    ( spl0_496
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f900,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).

fof(f5520,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f897,f5518]) ).

fof(f5518,plain,
    ( spl0_495
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f897,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).

fof(f5516,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f896,f5514]) ).

fof(f5514,plain,
    ( spl0_494
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f896,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).

fof(f5512,plain,
    spl0_493,
    inference(avatar_split_clause,[],[f895,f5510]) ).

fof(f5510,plain,
    ( spl0_493
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f895,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).

fof(f5508,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f893,f5506]) ).

fof(f5506,plain,
    ( spl0_492
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f893,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).

fof(f5504,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f892,f5502]) ).

fof(f5502,plain,
    ( spl0_491
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f892,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).

fof(f5500,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f891,f5498]) ).

fof(f5498,plain,
    ( spl0_490
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f891,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).

fof(f5496,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f888,f5494]) ).

fof(f5494,plain,
    ( spl0_489
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f888,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).

fof(f5492,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f887,f5490]) ).

fof(f5490,plain,
    ( spl0_488
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f887,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).

fof(f5488,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f886,f5486]) ).

fof(f5486,plain,
    ( spl0_487
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f886,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).

fof(f5484,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f885,f5482]) ).

fof(f5482,plain,
    ( spl0_486
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f885,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).

fof(f5480,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f883,f5478]) ).

fof(f5478,plain,
    ( spl0_485
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f883,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group__join(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

fof(f5476,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f882,f5474]) ).

fof(f5474,plain,
    ( spl0_484
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f882,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group__meet(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

fof(f5472,plain,
    spl0_483,
    inference(avatar_split_clause,[],[f881,f5470]) ).

fof(f5470,plain,
    ( spl0_483
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f881,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group__abs(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

fof(f5468,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f880,f5466]) ).

fof(f5466,plain,
    ( spl0_482
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Opordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f880,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Opordered__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

fof(f5464,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f879,f5462]) ).

fof(f5462,plain,
    ( spl0_481
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Olordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f879,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Olordered__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

fof(f5460,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f878,f5458]) ).

fof(f5458,plain,
    ( spl0_480
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f878,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

fof(f5456,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f877,f5454]) ).

fof(f5454,plain,
    ( spl0_479
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f877,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

fof(f5452,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f876,f5450]) ).

fof(f5450,plain,
    ( spl0_478
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f876,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

fof(f5448,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f875,f5446]) ).

fof(f5446,plain,
    ( spl0_477
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f875,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Oaxclass__abs__if(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

fof(f5444,plain,
    spl0_476,
    inference(avatar_split_clause,[],[f874,f5442]) ).

fof(f5442,plain,
    ( spl0_476
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f874,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

fof(f5440,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f873,f5438]) ).

fof(f5438,plain,
    ( spl0_475
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f873,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

fof(f5436,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f872,f5434]) ).

fof(f5434,plain,
    ( spl0_474
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f872,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

fof(f5432,plain,
    spl0_473,
    inference(avatar_split_clause,[],[f871,f5430]) ).

fof(f5430,plain,
    ( spl0_473
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f871,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

fof(f5428,plain,
    spl0_472,
    inference(avatar_split_clause,[],[f870,f5426]) ).

fof(f5426,plain,
    ( spl0_472
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f870,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

fof(f5424,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f869,f5422]) ).

fof(f5422,plain,
    ( spl0_471
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f869,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

fof(f5420,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f868,f5418]) ).

fof(f5418,plain,
    ( spl0_470
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f868,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

fof(f5416,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f867,f5414]) ).

fof(f5414,plain,
    ( spl0_469
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f867,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

fof(f5412,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f865,f5410]) ).

fof(f5410,plain,
    ( spl0_468
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f865,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

fof(f5408,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f864,f5406]) ).

fof(f5406,plain,
    ( spl0_467
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f864,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

fof(f5404,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f863,f5402]) ).

fof(f5402,plain,
    ( spl0_466
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f863,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

fof(f5400,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f862,f5398]) ).

fof(f5398,plain,
    ( spl0_465
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f862,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

fof(f5396,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f861,f5394]) ).

fof(f5394,plain,
    ( spl0_464
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f861,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

fof(f5392,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f856,f5390]) ).

fof(f5390,plain,
    ( spl0_463
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f856,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).

fof(f5388,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f855,f5386]) ).

fof(f5386,plain,
    ( spl0_462
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f855,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).

fof(f5384,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f854,f5382]) ).

fof(f5382,plain,
    ( spl0_461
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f854,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

fof(f5380,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f853,f5378]) ).

fof(f5378,plain,
    ( spl0_460
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f853,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).

fof(f5376,plain,
    spl0_459,
    inference(avatar_split_clause,[],[f852,f5374]) ).

fof(f5374,plain,
    ( spl0_459
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f852,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).

fof(f5372,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f851,f5370]) ).

fof(f5370,plain,
    ( spl0_458
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f851,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Ocomm__semiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).

fof(f5368,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f850,f5366]) ).

fof(f5366,plain,
    ( spl0_457
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f850,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).

fof(f5364,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f849,f5362]) ).

fof(f5362,plain,
    ( spl0_456
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oidom(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f849,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oidom(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).

fof(f5360,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f847,f5358]) ).

fof(f5358,plain,
    ( spl0_455
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__semidom(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f847,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__semidom(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).

fof(f5356,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f846,f5354]) ).

fof(f5354,plain,
    ( spl0_454
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f846,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

fof(f5352,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f845,f5350]) ).

fof(f5350,plain,
    ( spl0_453
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f845,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).

fof(f5348,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f844,f5346]) ).

fof(f5346,plain,
    ( spl0_452
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f844,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group__join(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).

fof(f5344,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f843,f5342]) ).

fof(f5342,plain,
    ( spl0_451
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f843,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group__meet(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).

fof(f5340,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f842,f5338]) ).

fof(f5338,plain,
    ( spl0_450
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f842,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Olordered__ab__group__abs(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

fof(f5336,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f840,f5334]) ).

fof(f5334,plain,
    ( spl0_449
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f840,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).

fof(f5332,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f839,f5330]) ).

fof(f5330,plain,
    ( spl0_448
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Olordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f839,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Olordered__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).

fof(f5328,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f838,f5326]) ).

fof(f5326,plain,
    ( spl0_447
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f838,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__ring__strict(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).

fof(f5324,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f837,f5322]) ).

fof(f5322,plain,
    ( spl0_446
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f837,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oaxclass__abs__if(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).

fof(f5320,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f836,f5318]) ).

fof(f5318,plain,
    ( spl0_445
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f836,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).

fof(f5316,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f835,f5314]) ).

fof(f5314,plain,
    ( spl0_444
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f835,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

fof(f5312,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f834,f5310]) ).

fof(f5310,plain,
    ( spl0_443
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f834,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).

fof(f5308,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f833,f5306]) ).

fof(f5306,plain,
    ( spl0_442
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f833,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

fof(f5304,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f832,f5302]) ).

fof(f5302,plain,
    ( spl0_441
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f832,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).

fof(f5300,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f831,f5298]) ).

fof(f5298,plain,
    ( spl0_440
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f831,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

fof(f5296,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f830,f5294]) ).

fof(f5294,plain,
    ( spl0_439
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f830,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

fof(f5292,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f829,f5290]) ).

fof(f5290,plain,
    ( spl0_438
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f829,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).

fof(f5288,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f828,f5286]) ).

fof(f5286,plain,
    ( spl0_437
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f828,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).

fof(f5284,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f827,f5282]) ).

fof(f5282,plain,
    ( spl0_436
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f827,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).

fof(f5280,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f826,f5278]) ).

fof(f5278,plain,
    ( spl0_435
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f826,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).

fof(f5276,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f825,f5274]) ).

fof(f5274,plain,
    ( spl0_434
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f825,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

fof(f5272,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f824,f5270]) ).

fof(f5270,plain,
    ( spl0_433
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f824,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).

fof(f5268,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f823,f5266]) ).

fof(f5266,plain,
    ( spl0_432
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f823,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

fof(f5264,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f822,f5262]) ).

fof(f5262,plain,
    ( spl0_431
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f822,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).

fof(f5260,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f821,f5258]) ).

fof(f5258,plain,
    ( spl0_430
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f821,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).

fof(f5256,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f820,f5254]) ).

fof(f5254,plain,
    ( spl0_429
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f820,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).

fof(f5252,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f819,f5250]) ).

fof(f5250,plain,
    ( spl0_428
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f819,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).

fof(f5248,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f816,f5246]) ).

fof(f5246,plain,
    ( spl0_427
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f816,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).

fof(f5244,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f814,f5242]) ).

fof(f5242,plain,
    ( spl0_426
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f814,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).

fof(f5240,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f812,f5238]) ).

fof(f5238,plain,
    ( spl0_425
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f812,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

fof(f5236,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f809,f5234]) ).

fof(f5234,plain,
    ( spl0_424
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f809,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).

fof(f5232,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f808,f5230]) ).

fof(f5230,plain,
    ( spl0_423
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f808,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).

fof(f5228,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f807,f5226]) ).

fof(f5226,plain,
    ( spl0_422
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f807,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).

fof(f5224,plain,
    spl0_421,
    inference(avatar_split_clause,[],[f806,f5222]) ).

fof(f5222,plain,
    ( spl0_421
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f806,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).

fof(f5220,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f804,f5218]) ).

fof(f5218,plain,
    ( spl0_420
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f804,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).

fof(f5216,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f803,f5214]) ).

fof(f5214,plain,
    ( spl0_419
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f803,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).

fof(f5212,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f802,f5210]) ).

fof(f5210,plain,
    ( spl0_418
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f802,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).

fof(f5208,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f801,f5206]) ).

fof(f5206,plain,
    ( spl0_417
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f801,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).

fof(f5204,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f800,f5202]) ).

fof(f5202,plain,
    ( spl0_416
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f800,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).

fof(f5200,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f799,f5198]) ).

fof(f5198,plain,
    ( spl0_415
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f799,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).

fof(f5196,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f798,f5194]) ).

fof(f5194,plain,
    ( spl0_414
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f798,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).

fof(f5192,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f797,f5190]) ).

fof(f5190,plain,
    ( spl0_413
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Ocomm__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f797,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Ocomm__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).

fof(f5188,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f796,f5186]) ).

fof(f5186,plain,
    ( spl0_412
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__idom(X39)
        | class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f796,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__idom(X39)
      | class_Ring__and__Field_Ocomm__ring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).

fof(f5184,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f732,f5182]) ).

fof(f5182,plain,
    ( spl0_411
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f732,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

fof(f5180,plain,
    spl0_410,
    inference(avatar_split_clause,[],[f729,f5178]) ).

fof(f5178,plain,
    ( spl0_410
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f729,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

fof(f5176,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f728,f5174]) ).

fof(f5174,plain,
    ( spl0_409
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f728,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

fof(f5172,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f727,f5170]) ).

fof(f5170,plain,
    ( spl0_408
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f727,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__comm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

fof(f5168,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f726,f5166]) ).

fof(f5166,plain,
    ( spl0_407
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f726,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

fof(f5164,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f725,f5162]) ).

fof(f5162,plain,
    ( spl0_406
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f725,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

fof(f5160,plain,
    spl0_405,
    inference(avatar_split_clause,[],[f724,f5158]) ).

fof(f5158,plain,
    ( spl0_405
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f724,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

fof(f5156,plain,
    spl0_404,
    inference(avatar_split_clause,[],[f723,f5154]) ).

fof(f5154,plain,
    ( spl0_404
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f723,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

fof(f5152,plain,
    spl0_403,
    inference(avatar_split_clause,[],[f722,f5150]) ).

fof(f5150,plain,
    ( spl0_403
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f722,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Oordered__semiring__strict(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

fof(f5148,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f721,f5146]) ).

fof(f5146,plain,
    ( spl0_402
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f721,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

fof(f5144,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f720,f5142]) ).

fof(f5142,plain,
    ( spl0_401
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f720,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

fof(f5140,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f719,f5138]) ).

fof(f5138,plain,
    ( spl0_400
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f719,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

fof(f5136,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f718,f5134]) ).

fof(f5134,plain,
    ( spl0_399
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f718,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

fof(f5132,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f716,f5130]) ).

fof(f5130,plain,
    ( spl0_398
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f716,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

fof(f5128,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f715,f5126]) ).

fof(f5126,plain,
    ( spl0_397
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f715,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

fof(f5124,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f714,f5122]) ).

fof(f5122,plain,
    ( spl0_396
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f714,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

fof(f5120,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f713,f5118]) ).

fof(f5118,plain,
    ( spl0_395
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f713,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

fof(f5116,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f712,f5114]) ).

fof(f5114,plain,
    ( spl0_394
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f712,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

fof(f5112,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f711,f5110]) ).

fof(f5110,plain,
    ( spl0_393
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f711,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

fof(f5108,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f710,f5106]) ).

fof(f5106,plain,
    ( spl0_392
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f710,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

fof(f5104,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f709,f5102]) ).

fof(f5102,plain,
    ( spl0_391
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f709,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

fof(f5100,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f706,f5098]) ).

fof(f5098,plain,
    ( spl0_390
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f706,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

fof(f5096,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f705,f5094]) ).

fof(f5094,plain,
    ( spl0_389
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f705,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

fof(f5092,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f704,f5090]) ).

fof(f5090,plain,
    ( spl0_388
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f704,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).

fof(f5088,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f703,f5086]) ).

fof(f5086,plain,
    ( spl0_387
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Opordered__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f703,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Opordered__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).

fof(f5084,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f702,f5082]) ).

fof(f5082,plain,
    ( spl0_386
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f702,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).

fof(f5080,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f701,f5078]) ).

fof(f5078,plain,
    ( spl0_385
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f701,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).

fof(f5076,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f700,f5074]) ).

fof(f5074,plain,
    ( spl0_384
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f700,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).

fof(f5072,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f698,f5070]) ).

fof(f5070,plain,
    ( spl0_383
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f698,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group__join(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).

fof(f5068,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f697,f5066]) ).

fof(f5066,plain,
    ( spl0_382
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f697,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).

fof(f5064,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f696,f5062]) ).

fof(f5062,plain,
    ( spl0_381
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f696,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group__meet(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).

fof(f5060,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f695,f5058]) ).

fof(f5058,plain,
    ( spl0_380
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f695,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).

fof(f5056,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f694,f5054]) ).

fof(f5054,plain,
    ( spl0_379
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f694,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).

fof(f5052,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f693,f5050]) ).

fof(f5050,plain,
    ( spl0_378
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f693,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).

fof(f5048,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f692,f5046]) ).

fof(f5046,plain,
    ( spl0_377
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f692,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).

fof(f5044,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f691,f5042]) ).

fof(f5042,plain,
    ( spl0_376
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f691,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Olordered__ab__group__abs(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).

fof(f5040,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f688,f5038]) ).

fof(f5038,plain,
    ( spl0_375
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f688,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).

fof(f5036,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f686,f5034]) ).

fof(f5034,plain,
    ( spl0_374
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f686,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).

fof(f5032,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f685,f5030]) ).

fof(f5030,plain,
    ( spl0_373
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f685,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).

fof(f5028,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f683,f5026]) ).

fof(f5026,plain,
    ( spl0_372
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f683,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).

fof(f5024,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f680,f5022]) ).

fof(f5022,plain,
    ( spl0_371
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f680,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).

fof(f5020,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f679,f5018]) ).

fof(f5018,plain,
    ( spl0_370
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f679,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).

fof(f5016,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f678,f5014]) ).

fof(f5014,plain,
    ( spl0_369
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f678,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).

fof(f5012,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f677,f5010]) ).

fof(f5010,plain,
    ( spl0_368
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f677,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).

fof(f5008,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f676,f5006]) ).

fof(f5006,plain,
    ( spl0_367
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f676,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).

fof(f5004,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f675,f5002]) ).

fof(f5002,plain,
    ( spl0_366
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f675,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).

fof(f5000,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f674,f4998]) ).

fof(f4998,plain,
    ( spl0_365
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Olordered__ring(X39)
        | class_Ring__and__Field_Opordered__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f674,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Olordered__ring(X39)
      | class_Ring__and__Field_Opordered__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).

fof(f4996,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f673,f4994]) ).

fof(f4994,plain,
    ( spl0_364
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f673,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).

fof(f4992,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f672,f4990]) ).

fof(f4990,plain,
    ( spl0_363
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f672,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).

fof(f4988,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f671,f4986]) ).

fof(f4986,plain,
    ( spl0_362
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f671,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).

fof(f4984,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f670,f4982]) ).

fof(f4982,plain,
    ( spl0_361
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f670,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).

fof(f4980,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f668,f4978]) ).

fof(f4978,plain,
    ( spl0_360
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f668,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).

fof(f4976,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f666,f4974]) ).

fof(f4974,plain,
    ( spl0_359
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f666,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).

fof(f4972,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f663,f4970]) ).

fof(f4970,plain,
    ( spl0_358
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f663,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).

fof(f4968,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f661,f4966]) ).

fof(f4966,plain,
    ( spl0_357
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f661,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).

fof(f4964,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f659,f4962]) ).

fof(f4962,plain,
    ( spl0_356
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f659,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).

fof(f4960,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f656,f4958]) ).

fof(f4958,plain,
    ( spl0_355
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f656,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).

fof(f4956,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f655,f4954]) ).

fof(f4954,plain,
    ( spl0_354
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Oring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f655,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Oring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).

fof(f4952,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f654,f4950]) ).

fof(f4950,plain,
    ( spl0_353
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f654,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).

fof(f4948,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f653,f4946]) ).

fof(f4946,plain,
    ( spl0_352
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f653,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).

fof(f4944,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f651,f4942]) ).

fof(f4942,plain,
    ( spl0_351
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f651,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).

fof(f4940,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f650,f4938]) ).

fof(f4938,plain,
    ( spl0_350
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f650,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).

fof(f4936,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f649,f4934]) ).

fof(f4934,plain,
    ( spl0_349
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f649,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).

fof(f4932,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f648,f4930]) ).

fof(f4930,plain,
    ( spl0_348
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f648,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).

fof(f4928,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f647,f4926]) ).

fof(f4926,plain,
    ( spl0_347
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f647,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).

fof(f4924,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f646,f4922]) ).

fof(f4922,plain,
    ( spl0_346
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f646,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).

fof(f4920,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f645,f4918]) ).

fof(f4918,plain,
    ( spl0_345
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f645,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).

fof(f4916,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f644,f4914]) ).

fof(f4914,plain,
    ( spl0_344
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Ocomm__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f644,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Ocomm__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).

fof(f4912,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f643,f4910]) ).

fof(f4910,plain,
    ( spl0_343
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oidom(X39)
        | class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f643,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oidom(X39)
      | class_Ring__and__Field_Ocomm__ring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).

fof(f4908,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f607,f4906]) ).

fof(f4906,plain,
    ( spl0_342
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f607,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).

fof(f4904,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f606,f4902]) ).

fof(f4902,plain,
    ( spl0_341
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f606,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

fof(f4900,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f605,f4898]) ).

fof(f4898,plain,
    ( spl0_340
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f605,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

fof(f4896,plain,
    spl0_339,
    inference(avatar_split_clause,[],[f604,f4894]) ).

fof(f4894,plain,
    ( spl0_339
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f604,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

fof(f4892,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f603,f4890]) ).

fof(f4890,plain,
    ( spl0_338
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f603,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

fof(f4888,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f601,f4886]) ).

fof(f4886,plain,
    ( spl0_337
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f601,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

fof(f4884,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f600,f4882]) ).

fof(f4882,plain,
    ( spl0_336
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f600,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

fof(f4880,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f599,f4878]) ).

fof(f4878,plain,
    ( spl0_335
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f599,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

fof(f4876,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f598,f4874]) ).

fof(f4874,plain,
    ( spl0_334
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f598,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

fof(f4872,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f597,f4870]) ).

fof(f4870,plain,
    ( spl0_333
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f597,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

fof(f4868,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f596,f4866]) ).

fof(f4866,plain,
    ( spl0_332
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f596,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

fof(f4864,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f595,f4862]) ).

fof(f4862,plain,
    ( spl0_331
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f595,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).

fof(f4860,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f592,f4858]) ).

fof(f4858,plain,
    ( spl0_330
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f592,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

fof(f4856,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f591,f4854]) ).

fof(f4854,plain,
    ( spl0_329
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f591,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

fof(f4852,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f586,f4850]) ).

fof(f4850,plain,
    ( spl0_328
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f586,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

fof(f4848,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f585,f4846]) ).

fof(f4846,plain,
    ( spl0_327
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
        | class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f585,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
      | class_Ring__and__Field_Ocomm__semiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).

fof(f4844,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f582,f4842]) ).

fof(f4842,plain,
    ( spl0_326
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f582,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

fof(f4840,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f581,f4838]) ).

fof(f4838,plain,
    ( spl0_325
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f581,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

fof(f4836,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f579,f4834]) ).

fof(f4834,plain,
    ( spl0_324
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f579,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

fof(f4832,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f578,f4830]) ).

fof(f4830,plain,
    ( spl0_323
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f578,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).

fof(f4828,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f577,f4826]) ).

fof(f4826,plain,
    ( spl0_322
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f577,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

fof(f4824,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f576,f4822]) ).

fof(f4822,plain,
    ( spl0_321
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f576,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

fof(f4820,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f575,f4818]) ).

fof(f4818,plain,
    ( spl0_320
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f575,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

fof(f4816,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f574,f4814]) ).

fof(f4814,plain,
    ( spl0_319
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f574,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

fof(f4812,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f570,f4810]) ).

fof(f4810,plain,
    ( spl0_318
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f570,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

fof(f4808,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f568,f4806]) ).

fof(f4806,plain,
    ( spl0_317
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f568,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

fof(f4804,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f565,f4802]) ).

fof(f4802,plain,
    ( spl0_316
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f565,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

fof(f4800,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f562,f4798]) ).

fof(f4798,plain,
    ( spl0_315
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f562,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

fof(f4796,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f561,f4794]) ).

fof(f4794,plain,
    ( spl0_314
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f561,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

fof(f4792,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f559,f4790]) ).

fof(f4790,plain,
    ( spl0_313
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f559,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

fof(f4788,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f558,f4786]) ).

fof(f4786,plain,
    ( spl0_312
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f558,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

fof(f4784,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f557,f4782]) ).

fof(f4782,plain,
    ( spl0_311
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f557,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

fof(f4780,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f554,f4778]) ).

fof(f4778,plain,
    ( spl0_310
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f554,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

fof(f4776,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f553,f4774]) ).

fof(f4774,plain,
    ( spl0_309
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f553,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

fof(f4772,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f551,f4770]) ).

fof(f4770,plain,
    ( spl0_308
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f551,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

fof(f4768,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f545,f4766]) ).

fof(f4766,plain,
    ( spl0_307
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f545,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

fof(f4764,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f544,f4762]) ).

fof(f4762,plain,
    ( spl0_306
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f544,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

fof(f4760,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f542,f4758]) ).

fof(f4758,plain,
    ( spl0_305
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f542,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

fof(f4756,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f541,f4754]) ).

fof(f4754,plain,
    ( spl0_304
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__semiring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f541,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

fof(f4752,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f534,f4750]) ).

fof(f4750,plain,
    ( spl0_303
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f534,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).

fof(f4748,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f533,f4746]) ).

fof(f4746,plain,
    ( spl0_302
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f533,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).

fof(f4744,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f531,f4742]) ).

fof(f4742,plain,
    ( spl0_301
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f531,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).

fof(f4740,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f530,f4738]) ).

fof(f4738,plain,
    ( spl0_300
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f530,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).

fof(f4736,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f529,f4734]) ).

fof(f4734,plain,
    ( spl0_299
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f529,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).

fof(f4732,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f527,f4730]) ).

fof(f4730,plain,
    ( spl0_298
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f527,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).

fof(f4728,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f526,f4726]) ).

fof(f4726,plain,
    ( spl0_297
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f526,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).

fof(f4724,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f525,f4722]) ).

fof(f4722,plain,
    ( spl0_296
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Oring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f525,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Oring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).

fof(f4720,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f524,f4718]) ).

fof(f4718,plain,
    ( spl0_295
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f524,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).

fof(f4716,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f523,f4714]) ).

fof(f4714,plain,
    ( spl0_294
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f523,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).

fof(f4712,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f522,f4710]) ).

fof(f4710,plain,
    ( spl0_293
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f522,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).

fof(f4708,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f521,f4706]) ).

fof(f4706,plain,
    ( spl0_292
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f521,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).

fof(f4704,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f520,f4702]) ).

fof(f4702,plain,
    ( spl0_291
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f520,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).

fof(f4700,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f519,f4698]) ).

fof(f4698,plain,
    ( spl0_290
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f519,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Ocomm__semiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).

fof(f4696,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f518,f4694]) ).

fof(f4694,plain,
    ( spl0_289
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f518,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).

fof(f4692,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f515,f4690]) ).

fof(f4690,plain,
    ( spl0_288
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f515,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).

fof(f4688,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f513,f4686]) ).

fof(f4686,plain,
    ( spl0_287
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f513,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).

fof(f4684,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f511,f4682]) ).

fof(f4682,plain,
    ( spl0_286
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f511,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).

fof(f4680,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f508,f4678]) ).

fof(f4678,plain,
    ( spl0_285
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f508,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).

fof(f4676,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f507,f4674]) ).

fof(f4674,plain,
    ( spl0_284
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f507,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).

fof(f4672,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f506,f4670]) ).

fof(f4670,plain,
    ( spl0_283
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
        | class_Ring__and__Field_Ocomm__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f506,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
      | class_Ring__and__Field_Ocomm__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).

fof(f4668,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f503,f4666]) ).

fof(f4666,plain,
    ( spl0_282
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f503,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).

fof(f4664,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f500,f4662]) ).

fof(f4662,plain,
    ( spl0_281
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f500,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).

fof(f4660,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f499,f4658]) ).

fof(f4658,plain,
    ( spl0_280
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f499,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).

fof(f4656,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f497,f4654]) ).

fof(f4654,plain,
    ( spl0_279
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f497,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).

fof(f4652,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f496,f4650]) ).

fof(f4650,plain,
    ( spl0_278
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f496,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).

fof(f4648,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f495,f4646]) ).

fof(f4646,plain,
    ( spl0_277
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f495,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).

fof(f4644,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f494,f4642]) ).

fof(f4642,plain,
    ( spl0_276
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f494,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).

fof(f4640,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f493,f4638]) ).

fof(f4638,plain,
    ( spl0_275
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f493,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).

fof(f4636,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f491,f4634]) ).

fof(f4634,plain,
    ( spl0_274
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f491,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).

fof(f4632,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f488,f4630]) ).

fof(f4630,plain,
    ( spl0_273
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f488,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).

fof(f4628,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f487,f4626]) ).

fof(f4626,plain,
    ( spl0_272
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f487,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).

fof(f4624,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f483,f4622]) ).

fof(f4622,plain,
    ( spl0_271
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f483,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

fof(f4620,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f481,f4618]) ).

fof(f4618,plain,
    ( spl0_270
  <=> ! [X39] :
        ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f481,axiom,
    ! [X39] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

fof(f4616,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f473,f4614]) ).

fof(f4614,plain,
    ( spl0_269
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f473,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).

fof(f4612,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f472,f4610]) ).

fof(f4610,plain,
    ( spl0_268
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f472,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).

fof(f4608,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f471,f4606]) ).

fof(f4606,plain,
    ( spl0_267
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f471,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).

fof(f4604,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f470,f4602]) ).

fof(f4602,plain,
    ( spl0_266
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f470,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).

fof(f4600,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f469,f4598]) ).

fof(f4598,plain,
    ( spl0_265
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f469,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).

fof(f4596,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f468,f4594]) ).

fof(f4594,plain,
    ( spl0_264
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f468,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).

fof(f4592,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f467,f4590]) ).

fof(f4590,plain,
    ( spl0_263
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f467,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).

fof(f4588,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f466,f4586]) ).

fof(f4586,plain,
    ( spl0_262
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f466,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).

fof(f4584,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f465,f4582]) ).

fof(f4582,plain,
    ( spl0_261
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f465,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Ocomm__semiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).

fof(f4580,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f464,f4578]) ).

fof(f4578,plain,
    ( spl0_260
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f464,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).

fof(f4576,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f463,f4574]) ).

fof(f4574,plain,
    ( spl0_259
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f463,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).

fof(f4572,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f462,f4570]) ).

fof(f4570,plain,
    ( spl0_258
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f462,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).

fof(f4568,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f461,f4566]) ).

fof(f4566,plain,
    ( spl0_257
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f461,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).

fof(f4564,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f460,f4562]) ).

fof(f4562,plain,
    ( spl0_256
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f460,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).

fof(f4560,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f459,f4558]) ).

fof(f4558,plain,
    ( spl0_255
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f459,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).

fof(f4556,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f458,f4554]) ).

fof(f4554,plain,
    ( spl0_254
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f458,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).

fof(f4552,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f457,f4550]) ).

fof(f4550,plain,
    ( spl0_253
  <=> ! [X39] :
        ( ~ class_Power_Orecpower(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f457,axiom,
    ! [X39] :
      ( ~ class_Power_Orecpower(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).

fof(f4548,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f454,f4546]) ).

fof(f4546,plain,
    ( spl0_252
  <=> ! [X39] :
        ( ~ class_Orderings_Oorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f454,axiom,
    ! [X39] :
      ( ~ class_Orderings_Oorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).

fof(f4544,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f453,f4542]) ).

fof(f4542,plain,
    ( spl0_251
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f453,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

fof(f4540,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f452,f4538]) ).

fof(f4538,plain,
    ( spl0_250
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f452,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).

fof(f4536,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f451,f4534]) ).

fof(f4534,plain,
    ( spl0_249
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f451,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).

fof(f4532,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f450,f4530]) ).

fof(f4530,plain,
    ( spl0_248
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f450,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).

fof(f4528,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f449,f4526]) ).

fof(f4526,plain,
    ( spl0_247
  <=> ! [X39] :
        ( ~ class_Orderings_Olinorder(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f449,axiom,
    ! [X39] :
      ( ~ class_Orderings_Olinorder(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).

fof(f4524,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f446,f4522]) ).

fof(f4522,plain,
    ( spl0_246
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f446,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

fof(f4520,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f445,f4518]) ).

fof(f4518,plain,
    ( spl0_245
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f445,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

fof(f4516,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f441,f4514]) ).

fof(f4514,plain,
    ( spl0_244
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f441,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

fof(f4512,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f440,f4510]) ).

fof(f4510,plain,
    ( spl0_243
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f440,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

fof(f4508,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f439,f4506]) ).

fof(f4506,plain,
    ( spl0_242
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f439,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

fof(f4504,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f436,f4502]) ).

fof(f4502,plain,
    ( spl0_241
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f436,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

fof(f4500,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f434,f4498]) ).

fof(f4498,plain,
    ( spl0_240
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f434,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

fof(f4496,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f433,f4494]) ).

fof(f4494,plain,
    ( spl0_239
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f433,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

fof(f4492,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f432,f4490]) ).

fof(f4490,plain,
    ( spl0_238
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f432,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

fof(f4488,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f431,f4486]) ).

fof(f4486,plain,
    ( spl0_237
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f431,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

fof(f4484,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f430,f4482]) ).

fof(f4482,plain,
    ( spl0_236
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f430,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

fof(f4480,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f426,f4478]) ).

fof(f4478,plain,
    ( spl0_235
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f426,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

fof(f4476,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f425,f4474]) ).

fof(f4474,plain,
    ( spl0_234
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f425,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

fof(f4472,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f424,f4470]) ).

fof(f4470,plain,
    ( spl0_233
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f424,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

fof(f4468,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f421,f4466]) ).

fof(f4466,plain,
    ( spl0_232
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f421,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).

fof(f4464,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f419,f4462]) ).

fof(f4462,plain,
    ( spl0_231
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f419,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).

fof(f4460,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f417,f4458]) ).

fof(f4458,plain,
    ( spl0_230
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f417,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).

fof(f4456,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f416,f4454]) ).

fof(f4454,plain,
    ( spl0_229
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f416,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

fof(f4452,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f415,f4450]) ).

fof(f4450,plain,
    ( spl0_228
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f415,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

fof(f4448,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f414,f4446]) ).

fof(f4446,plain,
    ( spl0_227
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f414,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

fof(f4444,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f413,f4442]) ).

fof(f4442,plain,
    ( spl0_226
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f413,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

fof(f4440,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f411,f4438]) ).

fof(f4438,plain,
    ( spl0_225
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f411,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).

fof(f4436,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f410,f4434]) ).

fof(f4434,plain,
    ( spl0_224
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Olinorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f410,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Olinorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

fof(f4432,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f407,f4430]) ).

fof(f4430,plain,
    ( spl0_223
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f407,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

fof(f4428,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f405,f4426]) ).

fof(f4426,plain,
    ( spl0_222
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f405,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

fof(f4424,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f404,f4422]) ).

fof(f4422,plain,
    ( spl0_221
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f404,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

fof(f4420,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f403,f4418]) ).

fof(f4418,plain,
    ( spl0_220
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f403,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

fof(f4416,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f402,f4414]) ).

fof(f4414,plain,
    ( spl0_219
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f402,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

fof(f4412,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f401,f4410]) ).

fof(f4410,plain,
    ( spl0_218
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f401,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

fof(f4408,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f400,f4406]) ).

fof(f4406,plain,
    ( spl0_217
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f400,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

fof(f4404,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f399,f4402]) ).

fof(f4402,plain,
    ( spl0_216
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f399,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

fof(f4400,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f398,f4398]) ).

fof(f4398,plain,
    ( spl0_215
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f398,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

fof(f4396,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f397,f4394]) ).

fof(f4394,plain,
    ( spl0_214
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f397,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

fof(f4392,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f394,f4390]) ).

fof(f4390,plain,
    ( spl0_213
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Omonoid__mult(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f394,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Omonoid__mult(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).

fof(f4388,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f393,f4386]) ).

fof(f4386,plain,
    ( spl0_212
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f393,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

fof(f4384,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f392,f4382]) ).

fof(f4382,plain,
    ( spl0_211
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f392,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

fof(f4380,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f391,f4378]) ).

fof(f4378,plain,
    ( spl0_210
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f391,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

fof(f4376,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f390,f4374]) ).

fof(f4374,plain,
    ( spl0_209
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f390,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

fof(f4372,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f389,f4370]) ).

fof(f4370,plain,
    ( spl0_208
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f389,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

fof(f4368,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f387,f4366]) ).

fof(f4366,plain,
    ( spl0_207
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f387,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).

fof(f4364,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f385,f4362]) ).

fof(f4362,plain,
    ( spl0_206
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f385,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

fof(f4360,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f384,f4358]) ).

fof(f4358,plain,
    ( spl0_205
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f384,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

fof(f4356,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f383,f4354]) ).

fof(f4354,plain,
    ( spl0_204
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f383,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

fof(f4352,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f382,f4350]) ).

fof(f4350,plain,
    ( spl0_203
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f382,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

fof(f4348,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f379,f4346]) ).

fof(f4346,plain,
    ( spl0_202
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f379,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).

fof(f4344,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f377,f4342]) ).

fof(f4342,plain,
    ( spl0_201
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f377,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).

fof(f4340,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f376,f4338]) ).

fof(f4338,plain,
    ( spl0_200
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f376,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).

fof(f4336,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f375,f4334]) ).

fof(f4334,plain,
    ( spl0_199
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f375,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

fof(f4332,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f374,f4330]) ).

fof(f4330,plain,
    ( spl0_198
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f374,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

fof(f4328,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f373,f4326]) ).

fof(f4326,plain,
    ( spl0_197
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f373,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

fof(f4324,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f372,f4322]) ).

fof(f4322,plain,
    ( spl0_196
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f372,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

fof(f4320,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f371,f4318]) ).

fof(f4318,plain,
    ( spl0_195
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f371,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

fof(f4316,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f370,f4314]) ).

fof(f4314,plain,
    ( spl0_194
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f370,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

fof(f4312,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f368,f4310]) ).

fof(f4310,plain,
    ( spl0_193
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f368,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).

fof(f4308,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f366,f4306]) ).

fof(f4306,plain,
    ( spl0_192
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f366,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

fof(f4304,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f365,f4302]) ).

fof(f4302,plain,
    ( spl0_191
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f365,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

fof(f4300,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f364,f4298]) ).

fof(f4298,plain,
    ( spl0_190
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f364,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

fof(f4296,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f363,f4294]) ).

fof(f4294,plain,
    ( spl0_189
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f363,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

fof(f4292,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f360,f4290]) ).

fof(f4290,plain,
    ( spl0_188
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f360,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).

fof(f4288,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f358,f4286]) ).

fof(f4286,plain,
    ( spl0_187
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f358,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).

fof(f4284,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f357,f4282]) ).

fof(f4282,plain,
    ( spl0_186
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f357,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).

fof(f4280,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f356,f4278]) ).

fof(f4278,plain,
    ( spl0_185
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f356,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

fof(f4276,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f355,f4274]) ).

fof(f4274,plain,
    ( spl0_184
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f355,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).

fof(f4272,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f354,f4270]) ).

fof(f4270,plain,
    ( spl0_183
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f354,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

fof(f4268,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f353,f4266]) ).

fof(f4266,plain,
    ( spl0_182
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f353,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

fof(f4264,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f352,f4262]) ).

fof(f4262,plain,
    ( spl0_181
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f352,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

fof(f4260,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f350,f4258]) ).

fof(f4258,plain,
    ( spl0_180
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f350,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).

fof(f4256,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f348,f4254]) ).

fof(f4254,plain,
    ( spl0_179
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f348,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).

fof(f4252,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f347,f4250]) ).

fof(f4250,plain,
    ( spl0_178
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f347,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

fof(f4248,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f346,f4246]) ).

fof(f4246,plain,
    ( spl0_177
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f346,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

fof(f4244,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f345,f4242]) ).

fof(f4242,plain,
    ( spl0_176
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f345,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

fof(f4240,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f344,f4238]) ).

fof(f4238,plain,
    ( spl0_175
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f344,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

fof(f4236,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f343,f4234]) ).

fof(f4234,plain,
    ( spl0_174
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f343,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

fof(f4232,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f340,f4230]) ).

fof(f4230,plain,
    ( spl0_173
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f340,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).

fof(f4228,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f338,f4226]) ).

fof(f4226,plain,
    ( spl0_172
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f338,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

fof(f4224,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f337,f4222]) ).

fof(f4222,plain,
    ( spl0_171
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
        | class_OrderedGroup_Olordered__ab__group(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f337,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
      | class_OrderedGroup_Olordered__ab__group(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

fof(f4220,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f336,f4218]) ).

fof(f4218,plain,
    ( spl0_170
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f336,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).

fof(f4216,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f335,f4214]) ).

fof(f4214,plain,
    ( spl0_169
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f335,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).

fof(f4212,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f334,f4210]) ).

fof(f4210,plain,
    ( spl0_168
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f334,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).

fof(f4208,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f333,f4206]) ).

fof(f4206,plain,
    ( spl0_167
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f333,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).

fof(f4204,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f332,f4202]) ).

fof(f4202,plain,
    ( spl0_166
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f332,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).

fof(f4200,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f330,f4198]) ).

fof(f4198,plain,
    ( spl0_165
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f330,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).

fof(f4196,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f328,f4194]) ).

fof(f4194,plain,
    ( spl0_164
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f328,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).

fof(f4192,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f327,f4190]) ).

fof(f4190,plain,
    ( spl0_163
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f327,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).

fof(f4188,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f326,f4186]) ).

fof(f4186,plain,
    ( spl0_162
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_LOrder_Olorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f326,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_LOrder_Olorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).

fof(f4184,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f323,f4182]) ).

fof(f4182,plain,
    ( spl0_161
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f323,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).

fof(f4180,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f321,f4178]) ).

fof(f4178,plain,
    ( spl0_160
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f321,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).

fof(f4176,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f320,f4174]) ).

fof(f4174,plain,
    ( spl0_159
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f320,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).

fof(f4172,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f319,f4170]) ).

fof(f4170,plain,
    ( spl0_158
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Olordered__ab__group(X39)
        | class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f319,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X39)
      | class_OrderedGroup_Opordered__ab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).

fof(f4168,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f318,f4166]) ).

fof(f4166,plain,
    ( spl0_157
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f318,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

fof(f4164,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f314,f4162]) ).

fof(f4162,plain,
    ( spl0_156
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f314,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

fof(f4160,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f307,f4158]) ).

fof(f4158,plain,
    ( spl0_155
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f307,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

fof(f4156,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f299,f4154]) ).

fof(f4154,plain,
    ( spl0_154
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oab__group__add(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f299,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oab__group__add(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).

fof(f4152,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f298,f4150]) ).

fof(f4150,plain,
    ( spl0_153
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oab__group__add(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f298,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oab__group__add(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).

fof(f4148,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f293,f4146]) ).

fof(f4146,plain,
    ( spl0_152
  <=> ! [X39] :
        ( ~ class_OrderedGroup_Oab__group__add(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f293,axiom,
    ! [X39] :
      ( ~ class_OrderedGroup_Oab__group__add(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).

fof(f4144,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f291,f4142]) ).

fof(f4142,plain,
    ( spl0_151
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f291,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_OrderedGroup_Ocomm__monoid__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).

fof(f4140,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f289,f4138]) ).

fof(f4138,plain,
    ( spl0_150
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f289,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).

fof(f4136,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f288,f4134]) ).

fof(f4134,plain,
    ( spl0_149
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Osemiring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f288,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Osemiring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).

fof(f4132,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f285,f4130]) ).

fof(f4130,plain,
    ( spl0_148
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Numeral_Onumber(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f285,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Numeral_Onumber(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).

fof(f4128,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f283,f4126]) ).

fof(f4126,plain,
    ( spl0_147
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f283,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Ocomm__ring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).

fof(f4124,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f282,f4122]) ).

fof(f4122,plain,
    ( spl0_146
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f282,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).

fof(f4120,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f281,f4118]) ).

fof(f4118,plain,
    ( spl0_145
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Oring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f281,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Oring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).

fof(f4116,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f280,f4114]) ).

fof(f4114,plain,
    ( spl0_144
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f280,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Osemiring__1__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).

fof(f4112,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f279,f4110]) ).

fof(f4110,plain,
    ( spl0_143
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f279,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).

fof(f4108,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f278,f4106]) ).

fof(f4106,plain,
    ( spl0_142
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Osemiring__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f278,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Osemiring__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).

fof(f4104,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f277,f4102]) ).

fof(f4102,plain,
    ( spl0_141
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f277,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_OrderedGroup_Ocomm__monoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).

fof(f4100,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f276,f4098]) ).

fof(f4098,plain,
    ( spl0_140
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_OrderedGroup_Omonoid__mult(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f276,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_OrderedGroup_Omonoid__mult(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).

fof(f4096,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f275,f4094]) ).

fof(f4094,plain,
    ( spl0_139
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f275,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).

fof(f4092,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f274,f4090]) ).

fof(f4090,plain,
    ( spl0_138
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_HOL_Oone(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f274,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_HOL_Oone(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).

fof(f4088,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f272,f4086]) ).

fof(f4086,plain,
    ( spl0_137
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Ocomm__ring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f272,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Ocomm__ring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).

fof(f4084,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f271,f4082]) ).

fof(f4082,plain,
    ( spl0_136
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f271,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).

fof(f4080,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f270,f4078]) ).

fof(f4078,plain,
    ( spl0_135
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Oring(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f270,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Oring(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).

fof(f4076,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f269,f4074]) ).

fof(f4074,plain,
    ( spl0_134
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f269,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Osemiring__0__cancel(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).

fof(f4072,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f268,f4070]) ).

fof(f4070,plain,
    ( spl0_133
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_OrderedGroup_Oab__group__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f268,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_OrderedGroup_Oab__group__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).

fof(f4068,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f267,f4066]) ).

fof(f4066,plain,
    ( spl0_132
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f267,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).

fof(f4064,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f266,f4062]) ).

fof(f4062,plain,
    ( spl0_131
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f266,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_OrderedGroup_Ocancel__semigroup__add(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).

fof(f4060,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f264,f4058]) ).

fof(f4058,plain,
    ( spl0_130
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f264,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Ocomm__semiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).

fof(f4056,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f263,f4054]) ).

fof(f4054,plain,
    ( spl0_129
  <=> ! [X39] :
        ( ~ class_Numeral_Onumber__ring(X39)
        | class_Ring__and__Field_Osemiring__0(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f263,axiom,
    ! [X39] :
      ( ~ class_Numeral_Onumber__ring(X39)
      | class_Ring__and__Field_Osemiring__0(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).

fof(f4052,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f260,f4050]) ).

fof(f4050,plain,
    ( spl0_128
  <=> ! [X39] :
        ( ~ class_LOrder_Omeet__semilorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f260,axiom,
    ! [X39] :
      ( ~ class_LOrder_Omeet__semilorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).

fof(f4048,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f259,f4046]) ).

fof(f4046,plain,
    ( spl0_127
  <=> ! [X39] :
        ( ~ class_LOrder_Omeet__semilorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f259,axiom,
    ! [X39] :
      ( ~ class_LOrder_Omeet__semilorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).

fof(f4044,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f258,f4042]) ).

fof(f4042,plain,
    ( spl0_126
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_LOrder_Ojoin__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f258,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_LOrder_Ojoin__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).

fof(f4040,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f257,f4038]) ).

fof(f4038,plain,
    ( spl0_125
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f257,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).

fof(f4036,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f256,f4034]) ).

fof(f4034,plain,
    ( spl0_124
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f256,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).

fof(f4032,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f255,f4030]) ).

fof(f4030,plain,
    ( spl0_123
  <=> ! [X39] :
        ( ~ class_LOrder_Olorder(X39)
        | class_LOrder_Omeet__semilorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f255,axiom,
    ! [X39] :
      ( ~ class_LOrder_Olorder(X39)
      | class_LOrder_Omeet__semilorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).

fof(f4028,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f254,f4026]) ).

fof(f4026,plain,
    ( spl0_122
  <=> ! [X39] :
        ( ~ class_LOrder_Ojoin__semilorder(X39)
        | class_Orderings_Oorder(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f254,axiom,
    ! [X39] :
      ( ~ class_LOrder_Ojoin__semilorder(X39)
      | class_Orderings_Oorder(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

fof(f4024,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f253,f4022]) ).

fof(f4022,plain,
    ( spl0_121
  <=> ! [X39] :
        ( ~ class_LOrder_Ojoin__semilorder(X39)
        | class_Orderings_Oord(X39) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f253,axiom,
    ! [X39] :
      ( ~ class_LOrder_Ojoin__semilorder(X39)
      | class_Orderings_Oord(X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).

fof(f4020,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f98,f4018]) ).

fof(f98,axiom,
    ! [X0,X1] : c_in(X0,c_UNIV,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).

fof(f4016,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f66,f4014]) ).

fof(f66,axiom,
    ! [X21] : ~ c_less(X21,X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

fof(f4012,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f64,f4010]) ).

fof(f64,axiom,
    ! [X21] : c_lessequals(c_0,X21,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

fof(f4008,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f40,f4006]) ).

fof(f4006,plain,
    ( spl0_117
  <=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f40,axiom,
    ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).

fof(f4004,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f39,f4002]) ).

fof(f4002,plain,
    ( spl0_116
  <=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f39,axiom,
    ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).

fof(f4000,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f23,f3998]) ).

fof(f3998,plain,
    ( spl0_115
  <=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f23,axiom,
    ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).

fof(f3996,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f2971,f3994]) ).

fof(f2971,axiom,
    ! [X24] : ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X24))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f3992,plain,
    ~ spl0_113,
    inference(avatar_split_clause,[],[f2904,f3989]) ).

fof(f3989,plain,
    ( spl0_113
  <=> c_Public_Okeymode_OSignature = c_Public_Okeymode_OEncryption ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f2904,axiom,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Odistinct__2_0) ).

fof(f3987,plain,
    ~ spl0_112,
    inference(avatar_split_clause,[],[f2733,f3984]) ).

fof(f3984,plain,
    ( spl0_112
  <=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f2733,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4_0) ).

fof(f3982,plain,
    ~ spl0_111,
    inference(avatar_split_clause,[],[f2629,f3979]) ).

fof(f3979,plain,
    ( spl0_111
  <=> c_emptyset = c_UNIV ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f2629,axiom,
    c_emptyset != c_UNIV,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).

fof(f3977,plain,
    ~ spl0_110,
    inference(avatar_split_clause,[],[f2310,f3974]) ).

fof(f3974,plain,
    ( spl0_110
  <=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f2310,axiom,
    ~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).

fof(f3972,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f2303,f3969]) ).

fof(f3969,plain,
    ( spl0_109
  <=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f2303,axiom,
    c_Parity_Oeven(c_0,tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).

fof(f3967,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f2290,f3964]) ).

fof(f3964,plain,
    ( spl0_108
  <=> c_Parity_Oeven(c_0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f2290,axiom,
    c_Parity_Oeven(c_0,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).

fof(f3962,plain,
    ~ spl0_107,
    inference(avatar_split_clause,[],[f2159,f3959]) ).

fof(f3959,plain,
    ( spl0_107
  <=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f2159,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).

fof(f3957,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f1706,f3955]) ).

fof(f3955,plain,
    ( spl0_106
  <=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1706,axiom,
    ! [X41] : c_List_Onull(c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).

fof(f3953,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f1551,f3951]) ).

fof(f3951,plain,
    ( spl0_105
  <=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f1551,axiom,
    ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).

fof(f3949,plain,
    ~ spl0_104,
    inference(avatar_split_clause,[],[f1370,f3946]) ).

fof(f1370,axiom,
    c_0 != c_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).

fof(f3944,plain,
    ~ spl0_103,
    inference(avatar_split_clause,[],[f1250,f3941]) ).

fof(f3941,plain,
    ( spl0_103
  <=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1250,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).

fof(f3939,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f249,f3937]) ).

fof(f3937,plain,
    ( spl0_102
  <=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f249,axiom,
    ! [X37] : class_Orderings_Oorder(tc_set(X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).

fof(f3935,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f248,f3933]) ).

fof(f3933,plain,
    ( spl0_101
  <=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f248,axiom,
    ! [X37] : class_Orderings_Oord(tc_set(X37)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).

fof(f3931,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f126,f3928]) ).

fof(f3928,plain,
    ( spl0_100
  <=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f126,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(f3926,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f124,f3923]) ).

fof(f3923,plain,
    ( spl0_99
  <=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f124,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(f3921,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f123,f3919]) ).

fof(f3919,plain,
    ( spl0_98
  <=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f123,axiom,
    ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

fof(f3917,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f244,f3914]) ).

fof(f3914,plain,
    ( spl0_97
  <=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f244,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).

fof(f3912,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f243,f3909]) ).

fof(f243,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).

fof(f3907,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f242,f3904]) ).

fof(f3904,plain,
    ( spl0_95
  <=> class_LOrder_Olorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f242,axiom,
    class_LOrder_Olorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).

fof(f3902,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f241,f3899]) ).

fof(f241,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).

fof(f3897,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f239,f3894]) ).

fof(f3894,plain,
    ( spl0_93
  <=> class_Numeral_Onumber(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f239,axiom,
    class_Numeral_Onumber(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).

fof(f3892,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f238,f3889]) ).

fof(f238,axiom,
    class_Power_Orecpower(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).

fof(f3887,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f236,f3884]) ).

fof(f3884,plain,
    ( spl0_91
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f236,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).

fof(f3882,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f235,f3879]) ).

fof(f3879,plain,
    ( spl0_90
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f235,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).

fof(f3877,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f234,f3874]) ).

fof(f3874,plain,
    ( spl0_89
  <=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f234,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).

fof(f3872,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f233,f3869]) ).

fof(f3869,plain,
    ( spl0_88
  <=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f233,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).

fof(f3867,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f232,f3864]) ).

fof(f232,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).

fof(f3862,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f231,f3859]) ).

fof(f3859,plain,
    ( spl0_86
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f231,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).

fof(f3857,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f230,f3854]) ).

fof(f3854,plain,
    ( spl0_85
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f230,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).

fof(f3852,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f229,f3849]) ).

fof(f3849,plain,
    ( spl0_84
  <=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f229,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).

fof(f3847,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f228,f3844]) ).

fof(f3844,plain,
    ( spl0_83
  <=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f228,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).

fof(f3842,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f227,f3839]) ).

fof(f3839,plain,
    ( spl0_82
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f227,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).

fof(f3837,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f226,f3834]) ).

fof(f3834,plain,
    ( spl0_81
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f226,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).

fof(f3832,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f225,f3829]) ).

fof(f3829,plain,
    ( spl0_80
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f225,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).

fof(f3827,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f224,f3824]) ).

fof(f224,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).

fof(f3822,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f223,f3819]) ).

fof(f3819,plain,
    ( spl0_78
  <=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f223,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).

fof(f3817,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f222,f3814]) ).

fof(f3814,plain,
    ( spl0_77
  <=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f222,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).

fof(f3812,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f221,f3809]) ).

fof(f221,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).

fof(f3807,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f220,f3804]) ).

fof(f3804,plain,
    ( spl0_75
  <=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f220,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).

fof(f3802,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f219,f3799]) ).

fof(f3799,plain,
    ( spl0_74
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f219,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).

fof(f3797,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f218,f3794]) ).

fof(f3794,plain,
    ( spl0_73
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f218,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).

fof(f3792,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f217,f3789]) ).

fof(f3789,plain,
    ( spl0_72
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f217,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).

fof(f3787,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f216,f3784]) ).

fof(f3784,plain,
    ( spl0_71
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f216,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).

fof(f3782,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f215,f3779]) ).

fof(f3779,plain,
    ( spl0_70
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f215,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).

fof(f3777,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f214,f3774]) ).

fof(f214,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).

fof(f3772,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f213,f3769]) ).

fof(f3769,plain,
    ( spl0_68
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f213,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).

fof(f3767,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f212,f3764]) ).

fof(f3764,plain,
    ( spl0_67
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f212,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).

fof(f3762,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f211,f3759]) ).

fof(f3759,plain,
    ( spl0_66
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f211,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).

fof(f3757,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f210,f3754]) ).

fof(f3754,plain,
    ( spl0_65
  <=> class_Orderings_Oord(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f210,axiom,
    class_Orderings_Oord(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).

fof(f3752,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f209,f3749]) ).

fof(f3749,plain,
    ( spl0_64
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f209,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).

fof(f3747,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f208,f3744]) ).

fof(f3744,plain,
    ( spl0_63
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f208,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).

fof(f3742,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f203,f3739]) ).

fof(f3739,plain,
    ( spl0_62
  <=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f203,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).

fof(f3737,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f198,f3734]) ).

fof(f3734,plain,
    ( spl0_61
  <=> class_HOL_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f198,axiom,
    class_HOL_Oone(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).

fof(f3732,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f195,f3729]) ).

fof(f3729,plain,
    ( spl0_60
  <=> class_Finite__Set_Ofinite(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f195,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).

fof(f3727,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f194,f3724]) ).

fof(f3724,plain,
    ( spl0_59
  <=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f194,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).

fof(f3722,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f189,f3719]) ).

fof(f189,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).

fof(f3717,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f186,f3714]) ).

fof(f186,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).

fof(f3712,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f184,f3709]) ).

fof(f3709,plain,
    ( spl0_56
  <=> class_Numeral_Onumber(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f184,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).

fof(f3707,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f183,f3704]) ).

fof(f183,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).

fof(f3702,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f182,f3699]) ).

fof(f3699,plain,
    ( spl0_54
  <=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f182,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).

fof(f3697,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f181,f3694]) ).

fof(f181,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).

fof(f3692,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f180,f3689]) ).

fof(f3689,plain,
    ( spl0_52
  <=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f180,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).

fof(f3687,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f178,f3684]) ).

fof(f3684,plain,
    ( spl0_51
  <=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f178,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).

fof(f3682,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f177,f3679]) ).

fof(f3679,plain,
    ( spl0_50
  <=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f177,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).

fof(f3677,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f176,f3674]) ).

fof(f3674,plain,
    ( spl0_49
  <=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f176,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).

fof(f3672,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f175,f3669]) ).

fof(f3669,plain,
    ( spl0_48
  <=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f175,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).

fof(f3667,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f174,f3664]) ).

fof(f3664,plain,
    ( spl0_47
  <=> class_Orderings_Oord(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f174,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).

fof(f3662,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f173,f3659]) ).

fof(f3659,plain,
    ( spl0_46
  <=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f173,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).

fof(f3657,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f172,f3654]) ).

fof(f172,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).

fof(f3652,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f171,f3649]) ).

fof(f171,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).

fof(f3647,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f170,f3644]) ).

fof(f3644,plain,
    ( spl0_43
  <=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f170,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).

fof(f3642,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f169,f3639]) ).

fof(f3639,plain,
    ( spl0_42
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f169,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).

fof(f3637,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f168,f3634]) ).

fof(f3634,plain,
    ( spl0_41
  <=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f168,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).

fof(f3632,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f167,f3629]) ).

fof(f3629,plain,
    ( spl0_40
  <=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f167,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).

fof(f3627,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f166,f3624]) ).

fof(f3624,plain,
    ( spl0_39
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f166,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).

fof(f3622,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f165,f3619]) ).

fof(f3619,plain,
    ( spl0_38
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f165,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).

fof(f3617,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f164,f3614]) ).

fof(f3614,plain,
    ( spl0_37
  <=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f164,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).

fof(f3612,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f162,f3609]) ).

fof(f3609,plain,
    ( spl0_36
  <=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f162,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).

fof(f3607,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f161,f3604]) ).

fof(f3604,plain,
    ( spl0_35
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f161,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).

fof(f3602,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f160,f3599]) ).

fof(f3599,plain,
    ( spl0_34
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f160,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).

fof(f3597,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f159,f3594]) ).

fof(f3594,plain,
    ( spl0_33
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f159,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).

fof(f3592,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f158,f3589]) ).

fof(f158,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).

fof(f3587,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f157,f3584]) ).

fof(f3584,plain,
    ( spl0_31
  <=> class_LOrder_Olorder(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f157,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).

fof(f3582,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f156,f3579]) ).

fof(f156,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).

fof(f3577,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f155,f3574]) ).

fof(f155,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).

fof(f3572,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f154,f3569]) ).

fof(f154,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).

fof(f3567,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f153,f3564]) ).

fof(f153,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).

fof(f3562,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f151,f3559]) ).

fof(f151,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).

fof(f3557,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f150,f3554]) ).

fof(f3554,plain,
    ( spl0_25
  <=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f150,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).

fof(f3552,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f149,f3549]) ).

fof(f3549,plain,
    ( spl0_24
  <=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f149,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).

fof(f3547,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f148,f3544]) ).

fof(f3544,plain,
    ( spl0_23
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f148,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).

fof(f3542,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f147,f3539]) ).

fof(f3539,plain,
    ( spl0_22
  <=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f147,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).

fof(f3537,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f146,f3534]) ).

fof(f3534,plain,
    ( spl0_21
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f146,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).

fof(f3532,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f145,f3529]) ).

fof(f145,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).

fof(f3527,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f144,f3524]) ).

fof(f3524,plain,
    ( spl0_19
  <=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f144,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).

fof(f3522,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f143,f3519]) ).

fof(f3519,plain,
    ( spl0_18
  <=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f143,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).

fof(f3517,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f142,f3514]) ).

fof(f3514,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f142,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).

fof(f3512,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f140,f3509]) ).

fof(f3509,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f140,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).

fof(f3507,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f139,f3504]) ).

fof(f3504,plain,
    ( spl0_15
  <=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f139,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).

fof(f3502,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f138,f3499]) ).

fof(f138,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).

fof(f3497,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f137,f3494]) ).

fof(f3494,plain,
    ( spl0_13
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f137,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).

fof(f3492,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f136,f3489]) ).

fof(f3489,plain,
    ( spl0_12
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f136,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).

fof(f3487,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f135,f3484]) ).

fof(f3484,plain,
    ( spl0_11
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f135,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).

fof(f3482,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f134,f3479]) ).

fof(f3479,plain,
    ( spl0_10
  <=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f134,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).

fof(f3477,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f133,f3474]) ).

fof(f133,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).

fof(f3472,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f132,f3469]) ).

fof(f3469,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f132,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).

fof(f3467,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f131,f3464]) ).

fof(f3464,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f131,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).

fof(f3462,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f130,f3459]) ).

fof(f3459,plain,
    ( spl0_6
  <=> class_HOL_Oone(tc_IntDef_Oint) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f130,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).

fof(f3457,plain,
    ~ spl0_5,
    inference(avatar_split_clause,[],[f2973,f3454]) ).

fof(f2973,axiom,
    ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

fof(f3452,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f2969,f3449]) ).

fof(f2969,axiom,
    c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f3447,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f2968,f3444]) ).

fof(f2968,axiom,
    ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f3442,plain,
    ~ spl0_2,
    inference(avatar_split_clause,[],[f2967,f3439]) ).

fof(f2967,axiom,
    ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f3437,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f3228,f3434]) ).

fof(f3228,plain,
    v_NAa != v_NA,
    inference(equality_resolution,[],[f2974]) ).

fof(f2974,axiom,
    ! [X24] :
      ( v_NAa != v_NA
      | c_Message_Omsg_OKey(v_K) != X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWV353-1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 04:32:48 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (15392)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (15439)WARNING: value z3 for option sas not known
% 0.22/0.48  % (15438)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.48  % (15437)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.48  % (15440)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.48  % (15439)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.48  % (15441)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.48  % (15442)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.48  % (15443)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.93/0.74  TRYING [1]
% 4.06/1.02  TRYING [2]
% 6.33/1.34  TRYING [1]
% 6.75/1.42  % (15441)First to succeed.
% 7.19/1.49  % (15441)Refutation found. Thanks to Tanya!
% 7.19/1.49  % SZS status Unsatisfiable for theBenchmark
% 7.19/1.49  % SZS output start Proof for theBenchmark
% See solution above
% 7.46/1.53  % (15441)------------------------------
% 7.46/1.53  % (15441)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 7.46/1.53  % (15441)Termination reason: Refutation
% 7.46/1.53  
% 7.46/1.53  % (15441)Memory used [KB]: 21561
% 7.46/1.53  % (15441)Time elapsed: 1.002 s
% 7.46/1.53  % (15441)Instructions burned: 2763 (million)
% 7.46/1.53  % (15441)------------------------------
% 7.46/1.53  % (15441)------------------------------
% 7.46/1.53  % (15392)Success in time 1.125 s
%------------------------------------------------------------------------------