TSTP Solution File: SWV347-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV347-1 : 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 : n009.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 16:45:31 EDT 2024
% Result : Unsatisfiable 11.17s 1.99s
% Output : Refutation 11.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4903
% Syntax : Number of formulae : 8929 (3077 unt; 0 def)
% Number of atoms : 20115 (3771 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 19447 (8261 ~;8526 |; 0 &)
% (2660 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 2731 (2729 usr;2661 prp; 0-3 aty)
% Number of functors : 280 ( 280 usr; 64 con; 0-18 aty)
% Number of variables : 12992 (12992 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34709,plain,
$false,
inference(avatar_sat_refutation,[],[f3438,f3443,f3448,f3453,f3458,f3463,f3468,f3473,f3478,f3483,f3488,f3493,f3498,f3503,f3508,f3513,f3518,f3523,f3528,f3533,f3538,f3543,f3548,f3553,f3558,f3563,f3568,f3573,f3578,f3583,f3588,f3593,f3598,f3603,f3608,f3613,f3618,f3623,f3628,f3633,f3638,f3643,f3648,f3653,f3658,f3663,f3668,f3673,f3678,f3683,f3688,f3693,f3698,f3703,f3708,f3713,f3718,f3723,f3728,f3733,f3738,f3743,f3748,f3753,f3758,f3763,f3768,f3773,f3778,f3783,f3788,f3793,f3798,f3803,f3808,f3813,f3818,f3823,f3828,f3833,f3838,f3843,f3848,f3853,f3858,f3863,f3868,f3873,f3878,f3883,f3888,f3893,f3898,f3903,f3908,f3913,f3918,f3923,f3928,f3932,f3937,f3942,f3946,f3950,f3955,f3960,f3964,f3968,f3973,f3978,f3983,f3988,f3993,f3998,f4003,f4007,f4011,f4015,f4019,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4123,f4127,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4167,f4171,f4175,f4179,f4183,f4187,f4191,f4195,f4199,f4203,f4207,f4211,f4215,f4219,f4223,f4227,f4231,f4235,f4239,f4243,f4247,f4251,f4255,f4259,f4263,f4267,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4327,f4331,f4335,f4339,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4383,f4387,f4391,f4395,f4399,f4403,f4407,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4555,f4559,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4595,f4599,f4603,f4607,f4611,f4615,f4619,f4623,f4627,f4631,f4635,f4639,f4643,f4647,f4651,f4655,f4659,f4663,f4667,f4671,f4675,f4679,f4683,f4687,f4691,f4695,f4699,f4703,f4707,f4711,f4715,f4719,f4723,f4727,f4731,f4735,f4739,f4743,f4747,f4751,f4755,f4759,f4763,f4767,f4771,f4775,f4779,f4783,f4787,f4791,f4795,f4799,f4803,f4807,f4811,f4815,f4819,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4863,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4899,f4903,f4907,f4911,f4915,f4919,f4923,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4967,f4971,f4975,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5135,f5139,f5143,f5147,f5151,f5155,f5159,f5163,f5167,f5171,f5175,f5179,f5183,f5187,f5191,f5195,f5199,f5203,f5207,f5211,f5215,f5219,f5223,f5227,f5231,f5235,f5239,f5243,f5247,f5251,f5255,f5259,f5263,f5267,f5271,f5275,f5279,f5283,f5287,f5291,f5295,f5299,f5303,f5307,f5311,f5315,f5319,f5323,f5327,f5331,f5335,f5339,f5343,f5347,f5351,f5355,f5359,f5363,f5367,f5371,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5419,f5423,f5427,f5431,f5435,f5439,f5443,f5447,f5451,f5455,f5459,f5463,f5467,f5471,f5475,f5479,f5483,f5487,f5491,f5495,f5499,f5503,f5507,f5511,f5515,f5519,f5523,f5527,f5531,f5535,f5539,f5543,f5547,f5551,f5555,f5559,f5563,f5567,f5571,f5575,f5579,f5583,f5587,f5591,f5595,f5599,f5603,f5607,f5611,f5615,f5619,f5623,f5627,f5631,f5635,f5639,f5643,f5647,f5651,f5655,f5659,f5663,f5667,f5671,f5675,f5679,f5683,f5687,f5691,f5695,f5699,f5703,f5707,f5711,f5715,f5719,f5723,f5727,f5731,f5735,f5739,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5783,f5787,f5791,f5795,f5799,f5803,f5807,f5811,f5815,f5819,f5823,f5827,f5831,f5835,f5839,f5843,f5847,f5851,f5855,f5859,f5863,f5867,f5871,f5875,f5879,f5883,f5887,f5891,f5895,f5899,f5903,f5907,f5911,f5915,f5919,f5923,f5927,f5931,f5935,f5939,f5943,f5947,f5951,f5955,f5959,f5963,f5967,f5971,f5975,f5979,f5983,f5987,f5991,f5995,f5999,f6003,f6007,f6011,f6015,f6019,f6023,f6027,f6031,f6035,f6039,f6043,f6047,f6051,f6055,f6059,f6063,f6067,f6071,f6075,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6107,f6111,f6115,f6119,f6123,f6127,f6131,f6136,f6141,f6146,f6150,f6154,f6158,f6163,f6167,f6172,f6176,f6180,f6184,f6189,f6194,f6199,f6204,f6209,f6214,f6219,f6223,f6228,f6995,f7000,f7004,f7008,f7012,f7016,f7020,f7024,f7028,f7032,f7036,f7040,f7045,f7050,f7055,f7059,f7063,f7067,f7072,f7076,f7080,f7084,f7088,f7092,f7096,f7100,f7105,f7110,f7115,f7120,f7125,f7130,f7135,f7140,f7145,f7150,f7155,f7160,f7165,f7170,f7175,f7180,f7184,f7188,f7192,f7196,f7200,f7204,f7209,f7214,f7219,f7223,f7227,f7231,f7235,f7239,f7243,f7248,f7253,f7257,f7262,f7267,f7271,f7275,f7279,f7283,f7287,f7291,f7295,f7299,f7304,f7309,f7313,f7318,f7323,f7327,f7332,f7336,f7341,f7352,f7357,f7363,f7369,f7374,f7378,f7382,f7386,f7390,f7394,f7398,f7402,f7406,f7410,f7414,f7419,f7423,f7427,f7431,f7435,f7439,f7443,f7447,f7451,f7455,f7459,f7463,f7467,f7471,f7475,f7479,f7483,f7487,f7491,f7495,f7499,f7503,f7507,f7511,f7515,f7519,f7523,f7527,f7531,f7535,f7539,f7543,f7547,f7551,f7555,f7559,f7563,f7568,f7572,f7576,f7580,f7584,f7588,f7592,f7596,f7600,f7604,f7608,f7612,f7616,f7620,f7624,f7628,f7632,f7636,f7640,f7644,f7648,f7652,f7656,f7660,f7664,f7668,f7672,f7676,f7680,f7684,f7688,f7692,f7696,f7700,f7704,f7709,f7713,f7718,f7722,f7727,f7731,f7745,f7749,f7753,f7757,f7761,f7765,f7769,f7773,f7777,f7781,f7785,f7789,f7793,f7797,f7801,f7805,f7809,f7813,f7817,f7821,f7825,f7829,f7833,f7837,f7841,f7845,f7849,f7853,f7857,f7861,f7865,f7869,f7873,f7877,f7881,f7885,f7889,f7893,f7897,f7901,f7905,f7909,f7913,f7917,f7921,f7925,f7929,f7933,f7937,f7941,f7945,f7949,f7953,f7957,f7961,f7965,f7969,f7973,f7977,f7981,f7985,f7989,f7993,f7997,f8001,f8005,f8009,f8013,f8017,f8021,f8026,f8030,f8035,f8039,f8043,f8047,f8067,f8108,f8118,f8127,f8132,f8142,f8146,f8150,f8154,f8158,f8162,f8166,f8170,f8174,f8178,f8182,f8187,f8191,f8195,f8199,f8204,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8240,f8244,f8248,f8252,f8256,f8260,f8264,f8268,f8277,f8281,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8325,f8329,f8333,f8337,f8341,f8345,f8349,f8353,f8357,f8361,f8365,f8369,f8373,f8377,f8381,f8385,f8389,f8393,f8397,f8402,f8406,f8410,f8414,f8418,f8422,f8426,f8430,f8434,f8438,f8442,f8447,f8451,f8455,f8460,f8464,f8468,f8472,f8476,f8480,f8484,f8488,f8493,f8497,f8501,f8505,f8509,f8513,f8517,f8521,f8525,f8529,f8534,f8538,f8542,f8546,f8550,f8554,f8558,f8675,f8696,f8701,f8705,f8709,f8713,f8717,f8721,f8725,f8729,f8733,f8740,f8744,f8748,f8752,f8756,f8760,f8764,f8768,f8772,f8776,f8780,f8784,f8788,f8792,f8796,f8800,f8804,f8808,f8812,f8816,f8820,f8827,f8831,f8835,f8839,f8843,f8847,f8851,f8855,f8859,f8863,f8867,f8871,f8875,f8879,f8883,f8887,f8891,f8895,f8899,f8903,f8907,f8912,f8916,f8920,f8924,f8928,f8932,f8936,f8940,f8944,f8948,f8953,f8957,f8961,f8965,f8969,f8973,f8977,f8981,f8985,f8989,f8993,f8997,f9001,f9005,f9009,f9013,f9017,f9021,f9025,f9029,f9033,f9038,f9042,f9046,f9050,f9054,f9058,f9062,f9066,f9070,f9074,f9078,f9082,f9086,f9090,f9094,f9098,f9102,f9106,f9122,f9164,f9223,f9256,f9295,f9325,f9352,f9356,f9360,f9364,f9368,f9372,f9376,f9380,f9384,f9388,f9392,f9396,f9400,f9404,f9408,f9412,f9416,f9420,f9424,f9428,f9433,f9437,f9441,f9445,f9449,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9486,f9490,f9494,f9498,f9502,f9506,f9510,f9514,f9518,f9522,f9526,f9530,f9534,f9538,f9542,f9546,f9550,f9554,f9558,f9562,f9566,f9570,f9574,f9578,f9582,f9586,f9590,f9594,f9598,f9602,f9607,f9611,f9615,f9619,f9623,f9627,f9631,f9635,f9639,f9643,f9647,f9651,f9655,f9659,f9663,f9667,f9671,f9675,f9679,f9683,f9687,f9691,f9695,f9699,f9703,f9708,f9712,f9716,f9721,f9728,f9732,f9737,f9741,f9745,f9749,f9753,f9757,f9802,f9834,f9870,f9924,f9948,f9961,f9981,f10003,f10018,f10022,f10026,f10030,f10034,f10038,f10042,f10046,f10051,f10055,f10059,f10063,f10067,f10071,f10075,f10079,f10083,f10087,f10091,f10095,f10099,f10103,f10107,f10111,f10115,f10119,f10123,f10127,f10131,f10135,f10139,f10143,f10147,f10151,f10155,f10159,f10163,f10167,f10171,f10175,f10179,f10183,f10187,f10191,f10195,f10199,f10203,f10207,f10211,f10215,f10219,f10223,f10227,f10231,f10235,f10239,f10243,f10247,f10251,f10255,f10259,f10263,f10267,f10271,f10275,f10279,f10283,f10287,f10291,f10295,f10299,f10303,f10307,f10311,f10315,f10320,f10328,f10332,f10336,f10340,f10344,f10348,f10352,f10356,f10390,f10397,f10447,f10661,f10774,f10778,f10782,f10786,f10790,f10794,f10798,f10802,f10806,f10810,f10814,f10818,f10822,f10826,f10830,f10834,f10838,f10842,f10846,f10850,f10854,f10858,f10862,f10866,f10870,f10878,f10882,f10886,f10890,f10894,f10898,f10903,f10908,f10912,f10916,f10920,f10924,f10928,f10932,f10936,f10940,f10944,f10948,f10952,f10956,f10961,f10965,f10969,f10973,f10977,f10981,f10985,f10989,f10993,f10997,f11001,f11005,f11009,f11013,f11017,f11021,f11025,f11029,f11033,f11037,f11041,f11045,f11049,f11053,f11057,f11061,f11065,f11069,f11073,f11077,f11081,f11085,f11089,f11093,f11097,f11101,f11105,f11109,f11113,f11117,f11121,f11128,f11132,f11136,f11140,f11144,f11148,f11152,f11156,f11160,f11164,f11168,f11172,f11176,f11180,f11184,f11188,f11192,f11196,f11200,f11204,f11212,f11216,f11220,f11224,f11228,f11232,f11236,f11240,f11244,f11248,f11253,f11257,f11261,f11265,f11269,f11273,f11277,f11281,f11285,f11289,f11293,f11297,f11301,f11305,f11309,f11313,f11317,f11321,f11325,f11329,f11333,f11337,f11341,f11345,f11349,f11353,f11390,f11658,f11889,f11978,f12270,f12402,f12406,f12410,f12414,f12418,f12422,f12426,f12430,f12434,f12438,f12442,f12446,f12450,f12454,f12458,f12462,f12466,f12470,f12474,f12478,f12482,f12486,f12490,f12494,f12498,f12502,f12506,f12510,f12514,f12518,f12522,f12528,f12532,f12536,f12540,f12544,f12548,f12552,f12556,f12560,f12564,f12572,f12576,f12580,f12584,f12588,f12592,f12596,f12600,f12604,f12608,f12617,f12621,f12625,f12629,f12633,f12637,f12641,f12645,f12649,f12653,f12658,f12662,f12666,f12670,f12674,f12678,f12682,f12686,f12690,f12694,f12698,f12707,f12711,f12715,f12719,f12723,f12727,f12731,f12735,f12739,f12743,f12748,f12752,f12756,f12760,f12764,f12768,f12772,f12776,f12780,f12784,f12799,f12803,f12807,f12811,f12815,f12819,f12823,f12827,f12831,f12835,f12845,f12849,f12853,f12857,f12862,f12869,f12873,f12877,f12881,f12891,f12899,f12903,f12908,f12940,f12944,f12948,f12952,f12960,f12964,f12968,f13137,f13570,f14017,f14171,f14290,f14294,f14298,f14302,f14306,f14310,f14314,f14318,f14322,f14326,f14330,f14334,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,f14497,f14501,f14505,f14509,f14513,f14517,f14521,f14525,f14529,f14533,f14537,f14541,f14545,f14549,f14553,f14558,f14562,f14566,f14570,f14574,f14578,f14582,f14586,f14590,f14594,f14598,f14602,f14606,f14610,f14614,f14618,f14623,f14632,f14636,f14640,f14644,f15484,f15602,f15701,f15705,f15709,f15713,f15717,f15721,f15725,f15729,f15733,f15737,f15741,f15746,f15750,f15754,f15758,f15762,f15766,f15770,f15774,f15778,f15782,f15786,f15791,f15795,f15799,f15803,f15807,f15811,f15815,f15819,f15823,f15827,f15831,f15835,f15839,f15843,f15847,f15851,f15855,f15859,f15863,f15867,f15871,f15884,f15888,f15892,f15896,f15900,f15904,f15908,f15912,f15916,f15920,f15924,f15928,f15932,f15936,f15940,f15944,f15948,f15953,f15977,f15982,f15986,f16004,f16009,f16029,f16033,f16037,f16041,f16045,f16049,f16053,f16057,f16061,f16065,f16069,f16073,f16095,f16276,f16593,f16834,f17002,f17055,f17059,f17063,f17067,f17071,f17075,f17079,f17083,f17087,f17091,f17095,f17099,f17103,f17107,f17111,f17115,f17119,f17123,f17127,f17131,f17135,f17139,f17144,f17148,f17152,f17156,f17160,f17217,f17221,f17225,f17229,f17233,f17237,f17241,f17245,f17249,f17253,f17272,f17276,f17280,f17284,f17288,f17292,f17296,f17300,f17304,f17308,f17312,f17316,f17320,f17324,f17328,f17332,f17336,f17340,f17344,f17348,f17352,f17356,f17360,f17364,f17368,f17372,f17376,f17380,f17385,f17413,f17418,f17422,f17480,f17485,f17580,f17585,f17684,f17689,f17726,f17730,f17735,f17753,f17758,f17766,f17771,f17779,f17787,f17791,f17797,f17803,f17807,f17811,f17817,f17823,f17827,f17831,f17835,f17839,f17845,f17878,f17882,f17896,f17932,f18107,f18302,f18603,f19080,f19185,f19189,f19193,f19197,f19201,f19205,f19209,f19213,f19217,f19221,f19225,f19229,f19233,f19237,f19241,f19254,f19258,f19262,f19266,f19270,f19274,f19278,f19282,f19286,f19290,f19303,f19307,f19311,f19315,f19319,f19323,f19327,f19331,f19335,f19339,f19344,f19348,f19352,f19356,f19360,f19364,f19368,f19372,f19376,f19380,f19384,f19399,f19403,f19407,f19411,f19415,f19419,f19423,f19427,f19431,f19435,f19440,f19444,f19450,f19476,f19482,f19567,f19572,f19597,f19609,f19613,f19618,f19623,f19628,f19633,f19638,f19643,f19647,f19651,f19655,f19659,f19664,f19686,f19690,f19694,f19698,f19703,f19707,f19712,f19717,f19723,f19728,f19734,f19739,f19759,f19763,f19768,f19777,f19781,f19785,f19789,f19793,f19906,f20012,f20306,f20442,f20861,f20865,f20874,f20878,f20882,f20886,f20890,f20894,f20900,f20906,f20910,f20914,f20918,f20922,f20926,f20930,f20934,f20938,f20942,f20946,f20950,f20954,f20958,f20962,f20966,f20970,f20974,f20978,f20982,f20986,f20990,f20994,f20998,f21002,f21006,f21010,f21014,f21018,f21022,f21026,f21030,f21034,f21038,f21042,f21057,f21061,f21065,f21071,f21388,f21403,f21407,f21907,f22233,f22381,f22385,f22389,f22393,f22397,f22402,f22406,f22410,f22415,f22419,f22423,f22427,f22431,f22435,f22439,f22443,f22447,f22451,f22455,f22459,f22469,f22473,f22531,f22567,f22571,f22892,f22979,f22983,f22987,f22991,f22995,f22999,f23003,f23007,f23011,f23015,f23019,f23023,f23027,f23031,f23035,f23039,f23043,f23047,f23051,f23055,f23059,f23063,f23068,f23073,f23079,f23100,f23128,f23141,f23145,f23149,f23154,f23175,f23180,f23224,f23228,f23232,f23237,f23544,f23587,f23591,f23665,f23696,f23700,f23704,f23708,f23712,f23716,f23720,f23724,f23748,f23752,f23756,f23760,f23764,f23768,f23772,f23776,f23780,f23784,f23806,f23810,f23814,f23818,f23822,f23826,f23830,f23834,f23838,f23842,f23846,f23850,f23854,f23858,f23862,f23866,f23870,f23874,f23878,f23882,f23886,f23890,f23894,f23898,f23902,f23906,f23910,f23914,f23918,f23922,f23926,f23930,f23934,f23938,f23942,f23946,f23950,f23954,f23958,f23962,f23966,f23970,f23974,f24020,f24024,f24031,f24051,f24058,f24081,f24085,f24089,f24094,f24098,f24104,f24169,f24173,f24177,f24181,f24185,f24189,f24193,f24213,f24218,f24245,f24251,f24324,f24630,f24634,f25236,f25240,f25244,f25248,f25252,f25264,f25268,f25272,f25276,f25280,f25284,f25288,f25292,f25296,f25300,f25308,f25312,f25316,f25320,f25324,f25328,f25332,f25336,f25340,f25344,f25348,f25378,f25387,f25391,f25395,f25399,f25403,f25709,f25999,f26122,f26126,f26130,f26134,f26138,f26147,f26151,f26155,f26159,f26163,f26167,f26171,f26175,f26179,f26183,f26188,f26192,f26196,f26200,f26204,f26208,f26212,f26216,f26221,f26246,f26254,f26304,f26308,f26312,f26317,f26767,f27107,f27111,f27115,f27119,f27123,f27127,f27131,f27136,f27141,f27145,f27173,f27177,f27181,f27185,f27189,f27193,f27197,f27203,f27209,f27291,f27295,f27299,f27303,f27307,f27312,f27322,f27326,f27365,f27406,f27410,f27860,f27925,f27929,f27933,f27937,f27941,f27945,f27949,f27953,f27957,f28125,f28129,f28133,f28137,f28141,f28145,f28149,f28153,f28157,f28161,f28165,f28169,f28173,f28177,f28181,f28185,f28189,f28575,f28579,f28584,f28588,f28592,f28596,f28601,f28738,f28764,f28768,f28772,f28776,f28780,f28784,f28788,f28792,f28796,f28800,f28805,f28809,f28813,f28817,f28821,f28825,f28829,f28833,f28837,f28841,f28845,f28849,f28853,f28857,f28861,f28865,f28871,f28879,f28885,f28893,f28897,f28903,f28919,f28925,f28974,f28980,f28993,f28998,f29002,f29723,f29727,f29744,f29748,f29752,f29756,f29760,f29764,f29769,f29849,f29853,f29857,f29861,f29865,f29869,f29873,f30161,f30165,f30169,f30276,f30280,f30284,f30288,f30292,f30296,f30300,f30306,f30334,f30466,f30470,f30474,f30482,f30486,f30624,f30628,f30632,f30637,f30642,f30675,f30689,f30694,f30717,f30721,f30725,f30729,f30774,f30778,f30782,f30786,f30790,f30794,f30798,f30802,f30949,f30954,f30958,f30962,f30990,f30994,f30998,f31002,f31006,f31011,f31016,f31021,f31106,f31110,f31114,f31118,f31131,f31143,f31147,f31151,f31157,f31184,f31222,f31229,f31268,f31272,f31278,f31303,f31351,f31355,f31375,f31381,f31397,f31401,f31405,f31409,f31449,f31453,f31457,f31461,f31598,f31605,f31649,f31653,f31657,f31661,f31675,f31709,f31713,f31717,f31721,f31725,f31741,f31784,f31788,f31792,f31845,f31849,f31870,f31886,f31909,f31913,f31955,f31959,f31982,f31995,f32016,f32020,f32074,f32096,f32109,f32142,f32151,f32155,f32167,f32198,f32202,f32206,f32210,f32214,f32219,f32224,f32232,f32244,f32248,f32252,f32256,f32260,f32264,f32268,f32272,f32279,f32284,f32289,f32346,f32350,f32354,f32718,f32780,f32784,f32796,f32800,f32804,f32808,f32812,f32817,f32821,f32825,f32834,f32839,f32844,f32848,f32852,f32856,f32860,f32865,f32869,f32873,f32877,f32881,f32897,f32904,f32914,f32925,f32943,f32947,f32957,f32961,f32965,f32970,f32975,f32979,f32983,f32987,f32991,f32995,f32999,f33003,f33007,f33012,f33017,f33022,f33026,f33030,f33034,f33038,f33042,f33046,f33050,f33054,f33058,f33065,f33069,f33073,f33077,f33081,f33085,f33089,f33093,f33097,f33101,f33106,f33110,f33114,f33157,f33162,f33166,f33170,f33174,f33178,f33270,f33277,f33474,f33796,f34165,f34284,f34311,f34315,f34342,f34354,f34363,f34375,f34379,f34383,f34388,f34392,f34396,f34400,f34404,f34408,f34412,f34416,f34421,f34425,f34430,f34434,f34438,f34442,f34446,f34450,f34454,f34458,f34462,f34466,f34470,f34476,f34480,f34485,f34489,f34493,f34497,f34501,f34505,f34509,f34514,f34520,f34553,f34558,f34562,f34566,f34570,f34574,f34586,f34590,f34611,f34615,f34620,f34624,f34628,f34632,f34636,f34647,f34668,f34673,f34677,f34682,f34686,f34694,f34699,f34703,f34707,f34708]) ).
fof(f34708,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_2612 ),
inference(avatar_split_clause,[],[f34591,f34427,f3450,f3435]) ).
fof(f3435,plain,
( spl0_1
<=> c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f3450,plain,
( spl0_4
<=> c_in(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f34427,plain,
( spl0_2612
<=> v_A = v_Aa ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2612])]) ).
fof(f34591,plain,
( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_4
| ~ spl0_2612 ),
inference(superposition,[],[f3452,f34429]) ).
fof(f34429,plain,
( v_A = v_Aa
| ~ spl0_2612 ),
inference(avatar_component_clause,[],[f34427]) ).
fof(f3452,plain,
( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3450]) ).
fof(f34707,plain,
( spl0_2660
| ~ spl0_836
| ~ spl0_1372 ),
inference(avatar_split_clause,[],[f11597,f10942,f7711,f34705]) ).
fof(f34705,plain,
( spl0_2660
<=> ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2660])]) ).
fof(f7711,plain,
( spl0_836
<=> ! [X41,X3] : c_append(c_List_Olist_ONil,X3,X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f10942,plain,
( spl0_1372
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f11597,plain,
( ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 )
| ~ spl0_836
| ~ spl0_1372 ),
inference(superposition,[],[f10943,f7712]) ).
fof(f7712,plain,
( ! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3
| ~ spl0_836 ),
inference(avatar_component_clause,[],[f7711]) ).
fof(f10943,plain,
( ! [X51,X1,X25,X23] :
( c_append(X23,X25,X1) != c_append(X23,X51,X1)
| X25 = X51 )
| ~ spl0_1372 ),
inference(avatar_component_clause,[],[f10942]) ).
fof(f34703,plain,
( spl0_2659
| ~ spl0_786
| ~ spl0_1366 ),
inference(avatar_split_clause,[],[f11572,f10918,f7509,f34701]) ).
fof(f34701,plain,
( spl0_2659
<=> ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2659])]) ).
fof(f7509,plain,
( spl0_786
<=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f10918,plain,
( spl0_1366
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f11572,plain,
( ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 )
| ~ spl0_786
| ~ spl0_1366 ),
inference(superposition,[],[f10919,f7510]) ).
fof(f7510,plain,
( ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23
| ~ spl0_786 ),
inference(avatar_component_clause,[],[f7509]) ).
fof(f10919,plain,
( ! [X51,X1,X25,X23] :
( c_append(X25,X23,X1) != c_append(X51,X23,X1)
| X25 = X51 )
| ~ spl0_1366 ),
inference(avatar_component_clause,[],[f10918]) ).
fof(f34699,plain,
( spl0_2658
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1325 ),
inference(avatar_split_clause,[],[f10770,f10388,f8897,f3725,f34696]) ).
fof(f34696,plain,
( spl0_2658
<=> c_uminus(c_1,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2658])]) ).
fof(f3725,plain,
( spl0_59
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f8897,plain,
( spl0_1075
<=> ! [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_1075])]) ).
fof(f10388,plain,
( spl0_1325
<=> ! [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_1325])]) ).
fof(f10770,plain,
( c_uminus(c_1,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1325 ),
inference(forward_demodulation,[],[f10769,f9261]) ).
fof(f9261,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1075 ),
inference(resolution,[],[f8898,f3727]) ).
fof(f3727,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f3725]) ).
fof(f8898,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
| ~ spl0_1075 ),
inference(avatar_component_clause,[],[f8897]) ).
fof(f10769,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1325 ),
inference(resolution,[],[f10389,f3727]) ).
fof(f10389,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1) )
| ~ spl0_1325 ),
inference(avatar_component_clause,[],[f10388]) ).
fof(f34694,plain,
( spl0_2657
| ~ spl0_874
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10756,f10338,f7875,f34692]) ).
fof(f34692,plain,
( spl0_2657
<=> ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_Nat_Osize(X0,tc_Message_Omsg),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2657])]) ).
fof(f7875,plain,
( spl0_874
<=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f10338,plain,
( spl0_1320
<=> ! [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_1320])]) ).
fof(f10756,plain,
( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_Nat_Osize(X0,tc_Message_Omsg),tc_nat)
| ~ spl0_874
| ~ spl0_1320 ),
inference(superposition,[],[f7876,f10339]) ).
fof(f10339,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_1320 ),
inference(avatar_component_clause,[],[f10338]) ).
fof(f7876,plain,
( ! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat)
| ~ spl0_874 ),
inference(avatar_component_clause,[],[f7875]) ).
fof(f34686,plain,
( spl0_106
| spl0_2656
| ~ spl0_1074
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10753,f10338,f8893,f34684,f3957]) ).
fof(f3957,plain,
( spl0_106
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f34684,plain,
( spl0_2656
<=> ! [X0] : c_0 != c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2656])]) ).
fof(f8893,plain,
( spl0_1074
<=> ! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f10753,plain,
( ! [X0] :
( c_0 != c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg)
| c_0 = c_1 )
| ~ spl0_1074
| ~ spl0_1320 ),
inference(superposition,[],[f8894,f10339]) ).
fof(f8894,plain,
( ! [X21,X15] :
( c_0 != c_plus(X15,X21,tc_nat)
| c_0 = X21 )
| ~ spl0_1074 ),
inference(avatar_component_clause,[],[f8893]) ).
fof(f34682,plain,
( spl0_2655
| ~ spl0_800
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1078
| ~ spl0_1317 ),
inference(avatar_split_clause,[],[f10725,f10326,f8910,f8032,f7706,f7565,f34679]) ).
fof(f34679,plain,
( spl0_2655
<=> c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2655])]) ).
fof(f7565,plain,
( spl0_800
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f7706,plain,
( spl0_835
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f8032,plain,
( spl0_913
<=> 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_913])]) ).
fof(f8910,plain,
( spl0_1078
<=> ! [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_1078])]) ).
fof(f10326,plain,
( spl0_1317
<=> ! [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_1317])]) ).
fof(f10725,plain,
( c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_800
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1078
| ~ spl0_1317 ),
inference(forward_demodulation,[],[f10724,f7567]) ).
fof(f7567,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f7565]) ).
fof(f10724,plain,
( c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1078
| ~ spl0_1317 ),
inference(forward_demodulation,[],[f10723,f8911]) ).
fof(f8911,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_1078 ),
inference(avatar_component_clause,[],[f8910]) ).
fof(f10723,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1317 ),
inference(forward_demodulation,[],[f10718,f8034]) ).
fof(f8034,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_913 ),
inference(avatar_component_clause,[],[f8032]) ).
fof(f10718,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0))
| ~ spl0_835
| ~ spl0_1317 ),
inference(superposition,[],[f10327,f7708]) ).
fof(f7708,plain,
( c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_835 ),
inference(avatar_component_clause,[],[f7706]) ).
fof(f10327,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)
| ~ spl0_1317 ),
inference(avatar_component_clause,[],[f10326]) ).
fof(f34677,plain,
( spl0_2654
| ~ spl0_78
| ~ spl0_1298 ),
inference(avatar_split_clause,[],[f10682,f10245,f3820,f34675]) ).
fof(f34675,plain,
( spl0_2654
<=> ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2654])]) ).
fof(f3820,plain,
( spl0_78
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f10245,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(f10682,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_78
| ~ spl0_1298 ),
inference(resolution,[],[f10246,f3822]) ).
fof(f3822,plain,
( class_Orderings_Oorder(tc_nat)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f3820]) ).
fof(f10246,plain,
( ! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) )
| ~ spl0_1298 ),
inference(avatar_component_clause,[],[f10245]) ).
fof(f34673,plain,
( spl0_2653
| ~ spl0_30
| ~ spl0_1298 ),
inference(avatar_split_clause,[],[f10681,f10245,f3580,f34671]) ).
fof(f34671,plain,
( spl0_2653
<=> ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2653])]) ).
fof(f3580,plain,
( spl0_30
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f10681,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_30
| ~ spl0_1298 ),
inference(resolution,[],[f10246,f3582]) ).
fof(f3582,plain,
( class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f3580]) ).
fof(f34668,plain,
( spl0_2652
| ~ spl0_737
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f10650,f10229,f7293,f34666]) ).
fof(f34666,plain,
( spl0_2652
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_UNIV = c_OrderedGroup_Opprt(c_UNIV,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2652])]) ).
fof(f7293,plain,
( spl0_737
<=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f10229,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(f10650,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_UNIV = c_OrderedGroup_Opprt(c_UNIV,tc_set(X0)) )
| ~ spl0_737
| ~ spl0_1294 ),
inference(resolution,[],[f10230,f7294]) ).
fof(f7294,plain,
( ! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1))
| ~ spl0_737 ),
inference(avatar_component_clause,[],[f7293]) ).
fof(f10230,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 )
| ~ spl0_1294 ),
inference(avatar_component_clause,[],[f10229]) ).
fof(f34647,plain,
( spl0_2651
| ~ spl0_811
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f10643,f10229,f7610,f34645]) ).
fof(f34645,plain,
( spl0_2651
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_1 = c_OrderedGroup_Opprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2651])]) ).
fof(f7610,plain,
( spl0_811
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f10643,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_1 = c_OrderedGroup_Opprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_811
| ~ spl0_1294 ),
inference(resolution,[],[f10230,f7611]) ).
fof(f7611,plain,
( ! [X1] :
( c_lessequals(c_0,c_1,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_811 ),
inference(avatar_component_clause,[],[f7610]) ).
fof(f34636,plain,
( spl0_2650
| ~ spl0_47
| ~ spl0_690
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f10641,f10229,f7082,f3665,f34634]) ).
fof(f34634,plain,
( spl0_2650
<=> ! [X0] : c_IntDef_Oint(X0) = c_OrderedGroup_Opprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2650])]) ).
fof(f3665,plain,
( spl0_47
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f7082,plain,
( spl0_690
<=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f10641,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_IntDef_Oint(X0) = c_OrderedGroup_Opprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_690
| ~ spl0_1294 ),
inference(resolution,[],[f10230,f7083]) ).
fof(f7083,plain,
( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_690 ),
inference(avatar_component_clause,[],[f7082]) ).
fof(f34632,plain,
( spl0_2649
| ~ spl0_978
| ~ spl0_1293 ),
inference(avatar_split_clause,[],[f10634,f10225,f8367,f34630]) ).
fof(f34630,plain,
( spl0_2649
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2649])]) ).
fof(f8367,plain,
( spl0_978
<=> ! [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_978])]) ).
fof(f10225,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(f10634,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0) )
| ~ spl0_978
| ~ spl0_1293 ),
inference(duplicate_literal_removal,[],[f10633]) ).
fof(f10633,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0) )
| ~ spl0_978
| ~ spl0_1293 ),
inference(resolution,[],[f10226,f8368]) ).
fof(f8368,plain,
( ! [X18,X1] :
( c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_978 ),
inference(avatar_component_clause,[],[f8367]) ).
fof(f10226,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) )
| ~ spl0_1293 ),
inference(avatar_component_clause,[],[f10225]) ).
fof(f34628,plain,
( spl0_2648
| ~ spl0_673
| ~ spl0_1293 ),
inference(avatar_split_clause,[],[f10628,f10225,f7010,f34626]) ).
fof(f34626,plain,
( spl0_2648
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Opprt(c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2648])]) ).
fof(f7010,plain,
( spl0_673
<=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f10628,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Opprt(c_emptyset,tc_set(X0)) )
| ~ spl0_673
| ~ spl0_1293 ),
inference(resolution,[],[f10226,f7011]) ).
fof(f7011,plain,
( ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1))
| ~ spl0_673 ),
inference(avatar_component_clause,[],[f7010]) ).
fof(f34624,plain,
( spl0_2647
| ~ spl0_673
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10611,f10221,f7010,f34622]) ).
fof(f34622,plain,
( spl0_2647
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_emptyset = c_OrderedGroup_Onprt(c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2647])]) ).
fof(f10221,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(f10611,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_emptyset = c_OrderedGroup_Onprt(c_emptyset,tc_set(X0)) )
| ~ spl0_673
| ~ spl0_1292 ),
inference(resolution,[],[f10222,f7011]) ).
fof(f10222,plain,
( ! [X3,X1] :
( ~ c_lessequals(X3,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 )
| ~ spl0_1292 ),
inference(avatar_component_clause,[],[f10221]) ).
fof(f34620,plain,
( spl0_2646
| ~ spl0_979
| ~ spl0_1290 ),
inference(avatar_split_clause,[],[f10602,f10213,f8371,f34618]) ).
fof(f34618,plain,
( spl0_2646
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2646])]) ).
fof(f8371,plain,
( spl0_979
<=> ! [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_979])]) ).
fof(f10213,plain,
( spl0_1290
<=> ! [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_1290])]) ).
fof(f10602,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0) )
| ~ spl0_979
| ~ spl0_1290 ),
inference(duplicate_literal_removal,[],[f10596]) ).
fof(f10596,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0) )
| ~ spl0_979
| ~ spl0_1290 ),
inference(resolution,[],[f10214,f8372]) ).
fof(f8372,plain,
( ! [X18,X1] :
( c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_979 ),
inference(avatar_component_clause,[],[f8371]) ).
fof(f10214,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_0,X0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) )
| ~ spl0_1290 ),
inference(avatar_component_clause,[],[f10213]) ).
fof(f34615,plain,
( spl0_2645
| ~ spl0_737
| ~ spl0_1290 ),
inference(avatar_split_clause,[],[f10599,f10213,f7293,f34613]) ).
fof(f34613,plain,
( spl0_2645
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Onprt(c_UNIV,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2645])]) ).
fof(f10599,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Onprt(c_UNIV,tc_set(X0)) )
| ~ spl0_737
| ~ spl0_1290 ),
inference(resolution,[],[f10214,f7294]) ).
fof(f34611,plain,
( spl0_2644
| ~ spl0_811
| ~ spl0_1290 ),
inference(avatar_split_clause,[],[f10592,f10213,f7610,f34609]) ).
fof(f34609,plain,
( spl0_2644
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2644])]) ).
fof(f10592,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_811
| ~ spl0_1290 ),
inference(resolution,[],[f10214,f7611]) ).
fof(f34590,plain,
( spl0_2640
| spl0_2643
| ~ spl0_894
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10583,f10209,f7955,f34588,f34577]) ).
fof(f34577,plain,
( spl0_2640
<=> ! [X1] : ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2640])]) ).
fof(f34588,plain,
( spl0_2643
<=> ! [X0] :
( c_0 != X0
| c_emptyset = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2643])]) ).
fof(f7955,plain,
( spl0_894
<=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f10209,plain,
( spl0_1289
<=> ! [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_1289])]) ).
fof(f10583,plain,
( ! [X0,X1] :
( c_0 != X0
| c_emptyset = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_894
| ~ spl0_1289 ),
inference(superposition,[],[f10210,f7956]) ).
fof(f7956,plain,
( ! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3
| ~ spl0_894 ),
inference(avatar_component_clause,[],[f7955]) ).
fof(f10210,plain,
( ! [X18,X1,X27] :
( c_0 != c_minus(X18,X27,X1)
| X18 = X27
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_1289 ),
inference(avatar_component_clause,[],[f10209]) ).
fof(f34586,plain,
( spl0_2640
| spl0_2641
| ~ spl0_2642
| ~ spl0_892
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10581,f10209,f7947,f34583,f34580,f34577]) ).
fof(f34580,plain,
( spl0_2641
<=> ! [X0] : c_UNIV = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2641])]) ).
fof(f34583,plain,
( spl0_2642
<=> c_0 = c_emptyset ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2642])]) ).
fof(f7947,plain,
( spl0_892
<=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f10581,plain,
( ! [X0,X1] :
( c_0 != c_emptyset
| c_UNIV = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_892
| ~ spl0_1289 ),
inference(superposition,[],[f10210,f7948]) ).
fof(f7948,plain,
( ! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1))
| ~ spl0_892 ),
inference(avatar_component_clause,[],[f7947]) ).
fof(f34574,plain,
( spl0_2639
| ~ spl0_737
| ~ spl0_1288 ),
inference(avatar_split_clause,[],[f10574,f10205,f7293,f34572]) ).
fof(f34572,plain,
( spl0_2639
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0))
| c_UNIV = c_HOL_Oabs(c_UNIV,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2639])]) ).
fof(f10205,plain,
( spl0_1288
<=> ! [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_1288])]) ).
fof(f10574,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0))
| c_UNIV = c_HOL_Oabs(c_UNIV,tc_set(X0)) )
| ~ spl0_737
| ~ spl0_1288 ),
inference(resolution,[],[f10206,f7294]) ).
fof(f10206,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X3,X1) = X3 )
| ~ spl0_1288 ),
inference(avatar_component_clause,[],[f10205]) ).
fof(f34570,plain,
( spl0_2638
| ~ spl0_811
| ~ spl0_1288 ),
inference(avatar_split_clause,[],[f10567,f10205,f7610,f34568]) ).
fof(f34568,plain,
( spl0_2638
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_1 = c_HOL_Oabs(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2638])]) ).
fof(f10567,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_1 = c_HOL_Oabs(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_811
| ~ spl0_1288 ),
inference(resolution,[],[f10206,f7611]) ).
fof(f34566,plain,
( spl0_2637
| ~ spl0_50
| ~ spl0_1287 ),
inference(avatar_split_clause,[],[f10560,f10201,f3680,f34564]) ).
fof(f34564,plain,
( spl0_2637
<=> ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2637])]) ).
fof(f3680,plain,
( spl0_50
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f10201,plain,
( spl0_1287
<=> ! [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_1287])]) ).
fof(f10560,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_50
| ~ spl0_1287 ),
inference(resolution,[],[f10202,f3682]) ).
fof(f3682,plain,
( class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f3680]) ).
fof(f10202,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) )
| ~ spl0_1287 ),
inference(avatar_component_clause,[],[f10201]) ).
fof(f34562,plain,
( spl0_2636
| ~ spl0_50
| ~ spl0_1285 ),
inference(avatar_split_clause,[],[f10554,f10193,f3680,f34560]) ).
fof(f34560,plain,
( spl0_2636
<=> ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2636])]) ).
fof(f10193,plain,
( spl0_1285
<=> ! [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_1285])]) ).
fof(f10554,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_50
| ~ spl0_1285 ),
inference(resolution,[],[f10194,f3682]) ).
fof(f10194,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) )
| ~ spl0_1285 ),
inference(avatar_component_clause,[],[f10193]) ).
fof(f34558,plain,
( spl0_2635
| ~ spl0_800
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1078
| ~ spl0_1283 ),
inference(avatar_split_clause,[],[f10545,f10185,f8910,f8032,f7706,f7565,f34555]) ).
fof(f34555,plain,
( spl0_2635
<=> c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2635])]) ).
fof(f10185,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(f10545,plain,
( c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin)
| ~ spl0_800
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1078
| ~ spl0_1283 ),
inference(forward_demodulation,[],[f10544,f7567]) ).
fof(f10544,plain,
( c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin)
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1078
| ~ spl0_1283 ),
inference(forward_demodulation,[],[f10543,f8911]) ).
fof(f10543,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OMin)
| ~ spl0_835
| ~ spl0_913
| ~ spl0_1283 ),
inference(forward_demodulation,[],[f10538,f8034]) ).
fof(f10538,plain,
( c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),c_Numeral_OMin)
| ~ spl0_835
| ~ spl0_1283 ),
inference(superposition,[],[f10186,f7708]) ).
fof(f10186,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,[],[f10185]) ).
fof(f34553,plain,
( spl0_2634
| ~ spl0_29
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10404,f10069,f3575,f34551]) ).
fof(f34551,plain,
( spl0_2634
<=> ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2634])]) ).
fof(f3575,plain,
( spl0_29
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f10069,plain,
( spl0_1254
<=> ! [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_1254])]) ).
fof(f10404,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_29
| ~ spl0_1254 ),
inference(resolution,[],[f10070,f3577]) ).
fof(f3577,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f3575]) ).
fof(f10070,plain,
( ! [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) )
| ~ spl0_1254 ),
inference(avatar_component_clause,[],[f10069]) ).
fof(f34520,plain,
( ~ spl0_57
| spl0_2633
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1246 ),
inference(avatar_split_clause,[],[f10386,f10036,f8897,f3725,f34517,f3715]) ).
fof(f3715,plain,
( spl0_57
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f34517,plain,
( spl0_2633
<=> c_1 = c_HOL_Oabs(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2633])]) ).
fof(f10036,plain,
( spl0_1246
<=> ! [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_1246])]) ).
fof(f10386,plain,
( c_1 = c_HOL_Oabs(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1246 ),
inference(forward_demodulation,[],[f10385,f9261]) ).
fof(f10385,plain,
( ~ class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1246 ),
inference(resolution,[],[f10037,f3727]) ).
fof(f10037,plain,
( ! [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) )
| ~ spl0_1246 ),
inference(avatar_component_clause,[],[f10036]) ).
fof(f34514,plain,
( ~ spl0_2632
| ~ spl0_648
| ~ spl0_1316 ),
inference(avatar_split_clause,[],[f10322,f10318,f6133,f34511]) ).
fof(f34511,plain,
( spl0_2632
<=> c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2632])]) ).
fof(f6133,plain,
( spl0_648
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f10318,plain,
( spl0_1316
<=> ! [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_1316])]) ).
fof(f10322,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_1316 ),
inference(superposition,[],[f10319,f6135]) ).
fof(f6135,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_648 ),
inference(avatar_component_clause,[],[f6133]) ).
fof(f10319,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_1316 ),
inference(avatar_component_clause,[],[f10318]) ).
fof(f34509,plain,
( spl0_2631
| ~ spl0_1091
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f9992,f9681,f8963,f34507]) ).
fof(f34507,plain,
( spl0_2631
<=> ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oparts(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2631])]) ).
fof(f8963,plain,
( spl0_1091
<=> ! [X13,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f9681,plain,
( spl0_1215
<=> ! [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_1215])]) ).
fof(f9992,plain,
( ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oparts(X0) )
| ~ spl0_1091
| ~ spl0_1215 ),
inference(superposition,[],[f8964,f9682]) ).
fof(f9682,plain,
( ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1215 ),
inference(avatar_component_clause,[],[f9681]) ).
fof(f8964,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_union(X12,X13,X1)
| c_emptyset = X12 )
| ~ spl0_1091 ),
inference(avatar_component_clause,[],[f8963]) ).
fof(f34505,plain,
( spl0_2630
| ~ spl0_1092
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f9991,f9681,f8967,f34503]) ).
fof(f34503,plain,
( spl0_2630
<=> ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2630])]) ).
fof(f8967,plain,
( spl0_1092
<=> ! [X13,X12,X1] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f9991,plain,
( ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) )
| ~ spl0_1092
| ~ spl0_1215 ),
inference(superposition,[],[f8968,f9682]) ).
fof(f8968,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_union(X12,X13,X1)
| c_emptyset = X13 )
| ~ spl0_1092 ),
inference(avatar_component_clause,[],[f8967]) ).
fof(f34501,plain,
( spl0_2629
| ~ spl0_1091
| ~ spl0_1214 ),
inference(avatar_split_clause,[],[f9986,f9677,f8963,f34499]) ).
fof(f34499,plain,
( spl0_2629
<=> ! [X0] :
( c_emptyset != c_Message_Oanalz(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oanalz(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2629])]) ).
fof(f9677,plain,
( spl0_1214
<=> ! [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_1214])]) ).
fof(f9986,plain,
( ! [X0] :
( c_emptyset != c_Message_Oanalz(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oanalz(X0) )
| ~ spl0_1091
| ~ spl0_1214 ),
inference(superposition,[],[f8964,f9678]) ).
fof(f9678,plain,
( ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1214 ),
inference(avatar_component_clause,[],[f9677]) ).
fof(f34497,plain,
( spl0_2628
| ~ spl0_1092
| ~ spl0_1214 ),
inference(avatar_split_clause,[],[f9985,f9677,f8967,f34495]) ).
fof(f34495,plain,
( spl0_2628
<=> ! [X0] :
( c_emptyset != c_Message_Oanalz(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2628])]) ).
fof(f9985,plain,
( ! [X0] :
( c_emptyset != c_Message_Oanalz(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) )
| ~ spl0_1092
| ~ spl0_1214 ),
inference(superposition,[],[f8968,f9678]) ).
fof(f34493,plain,
( spl0_2627
| ~ spl0_876
| ~ spl0_1191 ),
inference(avatar_split_clause,[],[f9943,f9584,f7883,f34491]) ).
fof(f34491,plain,
( spl0_2627
<=> ! [X0] :
( c_0 = X0
| c_0 = c_Nat_Opower(c_0,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2627])]) ).
fof(f7883,plain,
( spl0_876
<=> ! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f9584,plain,
( spl0_1191
<=> ! [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_1191])]) ).
fof(f9943,plain,
( ! [X0] :
( c_0 = X0
| c_0 = c_Nat_Opower(c_0,X0,tc_nat) )
| ~ spl0_876
| ~ spl0_1191 ),
inference(resolution,[],[f9585,f7884]) ).
fof(f7884,plain,
( ! [X21] :
( c_less(c_0,X21,tc_nat)
| c_0 = X21 )
| ~ spl0_876 ),
inference(avatar_component_clause,[],[f7883]) ).
fof(f9585,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat)
| c_0 = X21 )
| ~ spl0_1191 ),
inference(avatar_component_clause,[],[f9584]) ).
fof(f34489,plain,
( spl0_2626
| ~ spl0_871
| ~ spl0_1180 ),
inference(avatar_split_clause,[],[f9914,f9540,f7863,f34487]) ).
fof(f34487,plain,
( spl0_2626
<=> ! [X0,X1] : c_0 = c_minus(c_minus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2626])]) ).
fof(f7863,plain,
( spl0_871
<=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f9540,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(f9914,plain,
( ! [X0,X1] : c_0 = c_minus(c_minus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_871
| ~ spl0_1180 ),
inference(resolution,[],[f9541,f7864]) ).
fof(f7864,plain,
( ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_871 ),
inference(avatar_component_clause,[],[f7863]) ).
fof(f9541,plain,
( ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) )
| ~ spl0_1180 ),
inference(avatar_component_clause,[],[f9540]) ).
fof(f34485,plain,
( spl0_2625
| ~ spl0_851
| ~ spl0_1180 ),
inference(avatar_split_clause,[],[f9913,f9540,f7783,f34483]) ).
fof(f34483,plain,
( spl0_2625
<=> ! [X0,X1] : c_0 = c_minus(c_div(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2625])]) ).
fof(f7783,plain,
( spl0_851
<=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f9913,plain,
( ! [X0,X1] : c_0 = c_minus(c_div(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_851
| ~ spl0_1180 ),
inference(resolution,[],[f9541,f7784]) ).
fof(f7784,plain,
( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_851 ),
inference(avatar_component_clause,[],[f7783]) ).
fof(f34480,plain,
( spl0_2624
| ~ spl0_844
| ~ spl0_1166 ),
inference(avatar_split_clause,[],[f9874,f9484,f7755,f34478]) ).
fof(f34478,plain,
( spl0_2624
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2624])]) ).
fof(f7755,plain,
( spl0_844
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f9484,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(f9874,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_844
| ~ spl0_1166 ),
inference(resolution,[],[f9485,f7756]) ).
fof(f7756,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_844 ),
inference(avatar_component_clause,[],[f7755]) ).
fof(f9485,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,[],[f9484]) ).
fof(f34476,plain,
( spl0_2623
| ~ spl0_751
| ~ spl0_2598 ),
inference(avatar_split_clause,[],[f34364,f34361,f7366,f34473]) ).
fof(f34473,plain,
( spl0_2623
<=> v_B = v_Ba ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2623])]) ).
fof(f7366,plain,
( spl0_751
<=> 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_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f34361,plain,
( spl0_2598
<=> ! [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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_B = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2598])]) ).
fof(f34364,plain,
( v_B = v_Ba
| ~ spl0_751
| ~ spl0_2598 ),
inference(resolution,[],[f34362,f7368]) ).
fof(f7368,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_751 ),
inference(avatar_component_clause,[],[f7366]) ).
fof(f34362,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_B = X2 )
| ~ spl0_2598 ),
inference(avatar_component_clause,[],[f34361]) ).
fof(f34470,plain,
( spl0_2622
| ~ spl0_843
| ~ spl0_1166 ),
inference(avatar_split_clause,[],[f9873,f9484,f7751,f34468]) ).
fof(f34468,plain,
( spl0_2622
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2622])]) ).
fof(f7751,plain,
( spl0_843
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f9873,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_843
| ~ spl0_1166 ),
inference(resolution,[],[f9485,f7752]) ).
fof(f7752,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_843 ),
inference(avatar_component_clause,[],[f7751]) ).
fof(f34466,plain,
( spl0_2621
| ~ spl0_862
| ~ spl0_1164 ),
inference(avatar_split_clause,[],[f9864,f9475,f7827,f34464]) ).
fof(f34464,plain,
( spl0_2621
<=> ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2621])]) ).
fof(f7827,plain,
( spl0_862
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f9475,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(f9864,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_862
| ~ spl0_1164 ),
inference(resolution,[],[f9476,f7828]) ).
fof(f7828,plain,
( ! [X15] :
( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
| c_0 = X15 )
| ~ spl0_862 ),
inference(avatar_component_clause,[],[f7827]) ).
fof(f9476,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_1164 ),
inference(avatar_component_clause,[],[f9475]) ).
fof(f34462,plain,
( spl0_2620
| ~ spl0_665
| ~ spl0_1161 ),
inference(avatar_split_clause,[],[f9859,f9463,f6211,f34460]) ).
fof(f34460,plain,
( spl0_2620
<=> ! [X0] :
( ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| c_less(X0,c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2620])]) ).
fof(f6211,plain,
( spl0_665
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f9463,plain,
( spl0_1161
<=> ! [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_1161])]) ).
fof(f9859,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| c_less(X0,c_1,tc_IntDef_Oint) )
| ~ spl0_665
| ~ spl0_1161 ),
inference(superposition,[],[f9464,f6213]) ).
fof(f6213,plain,
( c_1 = c_IntDef_Onat(c_1)
| ~ spl0_665 ),
inference(avatar_component_clause,[],[f6211]) ).
fof(f9464,plain,
( ! [X48,X11] :
( ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
| c_less(X11,X48,tc_IntDef_Oint) )
| ~ spl0_1161 ),
inference(avatar_component_clause,[],[f9463]) ).
fof(f34458,plain,
( spl0_2619
| ~ spl0_689
| ~ spl0_1160 ),
inference(avatar_split_clause,[],[f9842,f9459,f7078,f34456]) ).
fof(f34456,plain,
( spl0_2619
<=> ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_0,X1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2619])]) ).
fof(f7078,plain,
( spl0_689
<=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f9459,plain,
( spl0_1160
<=> ! [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_1160])]) ).
fof(f9842,plain,
( ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_0,X1,tc_IntDef_Oint) )
| ~ spl0_689
| ~ spl0_1160 ),
inference(superposition,[],[f9460,f7079]) ).
fof(f7079,plain,
( ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3
| ~ spl0_689 ),
inference(avatar_component_clause,[],[f7078]) ).
fof(f9460,plain,
( ! [X48,X11] :
( ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
| c_less(c_0,X48,tc_IntDef_Oint) )
| ~ spl0_1160 ),
inference(avatar_component_clause,[],[f9459]) ).
fof(f34454,plain,
( spl0_2618
| ~ spl0_648
| ~ spl0_1159 ),
inference(avatar_split_clause,[],[f9839,f9455,f6133,f34452]) ).
fof(f34452,plain,
( spl0_2618
<=> ! [X0] :
( c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_less(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2618])]) ).
fof(f9455,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(f9839,plain,
( ! [X0] :
( c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_less(X0,c_1,tc_nat) )
| ~ spl0_648
| ~ spl0_1159 ),
inference(superposition,[],[f9456,f6135]) ).
fof(f9456,plain,
( ! [X21,X15] :
( c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ c_less(X15,X21,tc_nat) )
| ~ spl0_1159 ),
inference(avatar_component_clause,[],[f9455]) ).
fof(f34450,plain,
( spl0_2617
| ~ spl0_648
| ~ spl0_1158 ),
inference(avatar_split_clause,[],[f9828,f9451,f6133,f34448]) ).
fof(f34448,plain,
( spl0_2617
<=> ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_less(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2617])]) ).
fof(f9451,plain,
( spl0_1158
<=> ! [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_1158])]) ).
fof(f9828,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_less(X0,c_1,tc_nat) )
| ~ spl0_648
| ~ spl0_1158 ),
inference(superposition,[],[f9452,f6135]) ).
fof(f9452,plain,
( ! [X21,X15] :
( ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| c_less(X15,X21,tc_nat) )
| ~ spl0_1158 ),
inference(avatar_component_clause,[],[f9451]) ).
fof(f34446,plain,
( spl0_2616
| ~ spl0_649
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9825,f9447,f6138,f34444]) ).
fof(f34444,plain,
( spl0_2616
<=> ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2616])]) ).
fof(f6138,plain,
( spl0_649
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f9447,plain,
( spl0_1157
<=> ! [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_1157])]) ).
fof(f9825,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_649
| ~ spl0_1157 ),
inference(superposition,[],[f9448,f6140]) ).
fof(f6140,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f6138]) ).
fof(f9448,plain,
( ! [X21,X15] :
( c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1157 ),
inference(avatar_component_clause,[],[f9447]) ).
fof(f34442,plain,
( spl0_2615
| ~ spl0_648
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9824,f9447,f6133,f34440]) ).
fof(f34440,plain,
( spl0_2615
<=> ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2615])]) ).
fof(f9824,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_648
| ~ spl0_1157 ),
inference(superposition,[],[f9448,f6135]) ).
fof(f34438,plain,
( spl0_2614
| ~ spl0_648
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9822,f9447,f6133,f34436]) ).
fof(f34436,plain,
( spl0_2614
<=> ! [X0] :
( c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ c_lessequals(c_1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2614])]) ).
fof(f9822,plain,
( ! [X0] :
( c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_648
| ~ spl0_1157 ),
inference(superposition,[],[f9448,f6135]) ).
fof(f34434,plain,
( spl0_2613
| ~ spl0_649
| ~ spl0_1156 ),
inference(avatar_split_clause,[],[f9820,f9443,f6138,f34432]) ).
fof(f34432,plain,
( spl0_2613
<=> ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2613])]) ).
fof(f9443,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(f9820,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_649
| ~ spl0_1156 ),
inference(superposition,[],[f9444,f6140]) ).
fof(f9444,plain,
( ! [X21,X15] :
( ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1156 ),
inference(avatar_component_clause,[],[f9443]) ).
fof(f34430,plain,
( spl0_2612
| ~ spl0_751
| ~ spl0_2597 ),
inference(avatar_split_clause,[],[f34355,f34352,f7366,f34427]) ).
fof(f34352,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_A = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2597])]) ).
fof(f34355,plain,
( v_A = v_Aa
| ~ spl0_751
| ~ spl0_2597 ),
inference(resolution,[],[f34353,f7368]) ).
fof(f34353,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_A = X3 )
| ~ spl0_2597 ),
inference(avatar_component_clause,[],[f34352]) ).
fof(f34425,plain,
( spl0_2611
| ~ spl0_648
| ~ spl0_1156 ),
inference(avatar_split_clause,[],[f9819,f9443,f6133,f34423]) ).
fof(f34423,plain,
( spl0_2611
<=> ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_lessequals(X0,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2611])]) ).
fof(f9819,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_648
| ~ spl0_1156 ),
inference(superposition,[],[f9444,f6135]) ).
fof(f34421,plain,
( spl0_2610
| ~ spl0_648
| ~ spl0_1156 ),
inference(avatar_split_clause,[],[f9817,f9443,f6133,f34419]) ).
fof(f34419,plain,
( spl0_2610
<=> ! [X0] :
( ~ c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| c_lessequals(c_1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2610])]) ).
fof(f9817,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_648
| ~ spl0_1156 ),
inference(superposition,[],[f9444,f6135]) ).
fof(f34416,plain,
( spl0_106
| spl0_2609
| ~ spl0_648
| ~ spl0_1152 ),
inference(avatar_split_clause,[],[f9808,f9426,f6133,f34414,f3957]) ).
fof(f34414,plain,
( spl0_2609
<=> ! [X0] : c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2609])]) ).
fof(f9426,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(f9808,plain,
( ! [X0] :
( c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0)
| c_0 = c_1 )
| ~ spl0_648
| ~ spl0_1152 ),
inference(superposition,[],[f9427,f6135]) ).
fof(f9427,plain,
( ! [X21,X15] :
( c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15)
| c_0 = X21 )
| ~ spl0_1152 ),
inference(avatar_component_clause,[],[f9426]) ).
fof(f34412,plain,
( spl0_2608
| ~ spl0_876
| ~ spl0_1147 ),
inference(avatar_split_clause,[],[f9786,f9406,f7883,f34410]) ).
fof(f34410,plain,
( spl0_2608
<=> ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2608])]) ).
fof(f9406,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(f9786,plain,
( ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 )
| ~ spl0_876
| ~ spl0_1147 ),
inference(resolution,[],[f9407,f7884]) ).
fof(f9407,plain,
( ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) )
| ~ spl0_1147 ),
inference(avatar_component_clause,[],[f9406]) ).
fof(f34408,plain,
( spl0_2607
| ~ spl0_938
| ~ spl0_1136 ),
inference(avatar_split_clause,[],[f9765,f9362,f8206,f34406]) ).
fof(f34406,plain,
( spl0_2607
<=> ! [X0,X1] :
( c_0 = c_Nat_Osize(X0,tc_Datatype_Ooption(X1))
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2607])]) ).
fof(f8206,plain,
( spl0_938
<=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f9362,plain,
( spl0_1136
<=> ! [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_1136])]) ).
fof(f9765,plain,
( ! [X0,X1] :
( c_0 = c_Nat_Osize(X0,tc_Datatype_Ooption(X1))
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_938
| ~ spl0_1136 ),
inference(superposition,[],[f8207,f9363]) ).
fof(f9363,plain,
( ! [X0,X1] :
( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_1136 ),
inference(avatar_component_clause,[],[f9362]) ).
fof(f8207,plain,
( ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1))
| ~ spl0_938 ),
inference(avatar_component_clause,[],[f8206]) ).
fof(f34404,plain,
( spl0_2606
| ~ spl0_1000
| ~ spl0_1135 ),
inference(avatar_split_clause,[],[f9762,f9358,f8457,f34402]) ).
fof(f34402,plain,
( spl0_2606
<=> ! [X0] :
( ~ c_in(X0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2606])]) ).
fof(f8457,plain,
( spl0_1000
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f9358,plain,
( spl0_1135
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f9762,plain,
( ! [X0] :
( ~ c_in(X0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| c_0 = X0 )
| ~ spl0_1000
| ~ spl0_1135 ),
inference(superposition,[],[f9359,f8459]) ).
fof(f8459,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_1000 ),
inference(avatar_component_clause,[],[f8457]) ).
fof(f9359,plain,
( ! [X18,X1,X27] :
( ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1)
| X18 = X27 )
| ~ spl0_1135 ),
inference(avatar_component_clause,[],[f9358]) ).
fof(f34400,plain,
( spl0_2605
| ~ spl0_689
| ~ spl0_1126 ),
inference(avatar_split_clause,[],[f9345,f9104,f7078,f34398]) ).
fof(f34398,plain,
( spl0_2605
<=> ! [X0] :
( ~ c_less(c_1,X0,tc_nat)
| c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2605])]) ).
fof(f9104,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(f9345,plain,
( ! [X0] :
( ~ c_less(c_1,X0,tc_nat)
| c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_689
| ~ spl0_1126 ),
inference(superposition,[],[f9105,f7079]) ).
fof(f9105,plain,
( ! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) )
| ~ spl0_1126 ),
inference(avatar_component_clause,[],[f9104]) ).
fof(f34396,plain,
( spl0_2604
| ~ spl0_689
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f9339,f9100,f7078,f34394]) ).
fof(f34394,plain,
( spl0_2604
<=> ! [X0] :
( c_less(c_1,X0,tc_nat)
| ~ c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2604])]) ).
fof(f9100,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(f9339,plain,
( ! [X0] :
( c_less(c_1,X0,tc_nat)
| ~ c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_689
| ~ spl0_1125 ),
inference(superposition,[],[f9101,f7079]) ).
fof(f9101,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,[],[f9100]) ).
fof(f34392,plain,
( spl0_2603
| ~ spl0_914
| ~ spl0_1121 ),
inference(avatar_split_clause,[],[f9331,f9084,f8037,f34390]) ).
fof(f34390,plain,
( spl0_2603
<=> ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X0,c_Numeral_Obit_OB1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2603])]) ).
fof(f8037,plain,
( spl0_914
<=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f9084,plain,
( spl0_1121
<=> ! [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_1121])]) ).
fof(f9331,plain,
( ! [X0] : c_Numeral_OBit(X0,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X0,c_Numeral_Obit_OB1))
| ~ spl0_914
| ~ spl0_1121 ),
inference(superposition,[],[f9085,f8038]) ).
fof(f8038,plain,
( ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin)
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f8037]) ).
fof(f9085,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_1121 ),
inference(avatar_component_clause,[],[f9084]) ).
fof(f34388,plain,
( spl0_2602
| ~ spl0_751
| ~ spl0_2596 ),
inference(avatar_split_clause,[],[f34343,f34340,f7366,f34385]) ).
fof(f34385,plain,
( spl0_2602
<=> v_NAa = v_NA ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2602])]) ).
fof(f34340,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_NA = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2596])]) ).
fof(f34343,plain,
( v_NAa = v_NA
| ~ spl0_751
| ~ spl0_2596 ),
inference(resolution,[],[f34341,f7368]) ).
fof(f34341,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_NA = X4 )
| ~ spl0_2596 ),
inference(avatar_component_clause,[],[f34340]) ).
fof(f34383,plain,
( spl0_2601
| ~ spl0_1060
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f9219,f8841,f8837,f34381]) ).
fof(f34381,plain,
( spl0_2601
<=> ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2601])]) ).
fof(f8837,plain,
( spl0_1060
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f8841,plain,
( spl0_1061
<=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f9219,plain,
( ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) )
| ~ spl0_1060
| ~ spl0_1061 ),
inference(superposition,[],[f8838,f8842]) ).
fof(f8842,plain,
( ! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f8841]) ).
fof(f8838,plain,
( ! [X1,X23] :
( c_0 != c_Nat_Osize(X23,tc_List_Olist(X1))
| c_List_Olist_ONil = X23 )
| ~ spl0_1060 ),
inference(avatar_component_clause,[],[f8837]) ).
fof(f34379,plain,
( spl0_2600
| ~ spl0_857
| ~ spl0_1037 ),
inference(avatar_split_clause,[],[f9142,f8742,f7807,f34377]) ).
fof(f34377,plain,
( spl0_2600
<=> ! [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_2600])]) ).
fof(f7807,plain,
( spl0_857
<=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f8742,plain,
( spl0_1037
<=> ! [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_1037])]) ).
fof(f9142,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(X0) )
| ~ spl0_857
| ~ spl0_1037 ),
inference(superposition,[],[f8743,f7808]) ).
fof(f7808,plain,
( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f7807]) ).
fof(f8743,plain,
( ! [X48] :
( ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| c_0 = X48 )
| ~ spl0_1037 ),
inference(avatar_component_clause,[],[f8742]) ).
fof(f34375,plain,
( spl0_2599
| ~ spl0_832
| ~ spl0_1004 ),
inference(avatar_split_clause,[],[f8678,f8474,f7694,f34373]) ).
fof(f34373,plain,
( spl0_2599
<=> ! [X0,X1] :
( c_Public_OshrK(X0) != c_Message_OinvKey(X1)
| c_Public_OshrK(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2599])]) ).
fof(f7694,plain,
( spl0_832
<=> ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f8474,plain,
( spl0_1004
<=> ! [X92,X91] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f8678,plain,
( ! [X0,X1] :
( c_Public_OshrK(X0) != c_Message_OinvKey(X1)
| c_Public_OshrK(X0) = X1 )
| ~ spl0_832
| ~ spl0_1004 ),
inference(superposition,[],[f8475,f7695]) ).
fof(f7695,plain,
( ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12))
| ~ spl0_832 ),
inference(avatar_component_clause,[],[f7694]) ).
fof(f8475,plain,
( ! [X91,X92] :
( c_Message_OinvKey(X91) != c_Message_OinvKey(X92)
| X91 = X92 )
| ~ spl0_1004 ),
inference(avatar_component_clause,[],[f8474]) ).
fof(f34363,plain,
( spl0_2598
| spl0_7
| ~ spl0_5
| ~ spl0_752
| ~ spl0_2466 ),
inference(avatar_split_clause,[],[f31768,f31723,f7371,f3455,f3465,f34361]) ).
fof(f3465,plain,
( spl0_7
<=> c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f3455,plain,
( spl0_5
<=> c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f7371,plain,
( spl0_752
<=> 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_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f31723,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(f31768,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evs3,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_evs3)),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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_B = X2 )
| ~ spl0_752
| ~ spl0_2466 ),
inference(resolution,[],[f31724,f7373]) ).
fof(f7373,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_752 ),
inference(avatar_component_clause,[],[f7371]) ).
fof(f31724,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,[],[f31723]) ).
fof(f34354,plain,
( spl0_2597
| spl0_7
| ~ spl0_5
| ~ spl0_752
| ~ spl0_2465 ),
inference(avatar_split_clause,[],[f31755,f31719,f7371,f3455,f3465,f34352]) ).
fof(f31719,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(f31755,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evs3,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_evs3)),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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_A = X3 )
| ~ spl0_752
| ~ spl0_2465 ),
inference(resolution,[],[f31720,f7373]) ).
fof(f31720,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,[],[f31719]) ).
fof(f34342,plain,
( spl0_2596
| spl0_7
| ~ spl0_5
| ~ spl0_752
| ~ spl0_2464 ),
inference(avatar_split_clause,[],[f31742,f31715,f7371,f3455,f3465,f34340]) ).
fof(f31715,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(f31742,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(v_evs3,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_evs3)),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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| v_NA = X4 )
| ~ spl0_752
| ~ spl0_2464 ),
inference(resolution,[],[f31716,f7373]) ).
fof(f31716,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,[],[f31715]) ).
fof(f34315,plain,
( spl0_2595
| ~ spl0_2351
| ~ spl0_2561 ),
inference(avatar_split_clause,[],[f33606,f33024,f28891,f34313]) ).
fof(f34313,plain,
( spl0_2595
<=> ! [X0] : c_in(v_KAB,c_union(c_Message_OsymKeys,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2595])]) ).
fof(f28891,plain,
( spl0_2351
<=> ! [X0] :
( ~ c_lessequals(c_Message_OsymKeys,X0,tc_set(tc_nat))
| c_in(v_KAB,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2351])]) ).
fof(f33024,plain,
( spl0_2561
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2561])]) ).
fof(f33606,plain,
( ! [X0] : c_in(v_KAB,c_union(c_Message_OsymKeys,X0,tc_nat),tc_nat)
| ~ spl0_2351
| ~ spl0_2561 ),
inference(resolution,[],[f33025,f28892]) ).
fof(f28892,plain,
( ! [X0] :
( ~ c_lessequals(c_Message_OsymKeys,X0,tc_set(tc_nat))
| c_in(v_KAB,X0,tc_nat) )
| ~ spl0_2351 ),
inference(avatar_component_clause,[],[f28891]) ).
fof(f33025,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| ~ spl0_2561 ),
inference(avatar_component_clause,[],[f33024]) ).
fof(f34311,plain,
( spl0_2594
| ~ spl0_752
| ~ spl0_2013 ),
inference(avatar_split_clause,[],[f22052,f20976,f7371,f34309]) ).
fof(f34309,plain,
( spl0_2594
<=> ! [X0] : c_minus(X0,c_List_Oset(v_evs3,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_evs3,tc_Event_Oevent),tc_set(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2594])]) ).
fof(f20976,plain,
( spl0_2013
<=> ! [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_2013])]) ).
fof(f22052,plain,
( ! [X0] : c_minus(X0,c_List_Oset(v_evs3,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_evs3,tc_Event_Oevent),tc_set(tc_Event_Oevent))
| ~ spl0_752
| ~ spl0_2013 ),
inference(resolution,[],[f20977,f7373]) ).
fof(f20977,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_2013 ),
inference(avatar_component_clause,[],[f20976]) ).
fof(f34284,plain,
( spl0_2593
| ~ spl0_751
| ~ spl0_2013 ),
inference(avatar_split_clause,[],[f22053,f20976,f7366,f34282]) ).
fof(f34282,plain,
( spl0_2593
<=> ! [X0] : c_minus(X0,c_List_Oset(v_evs3,tc_Event_Oevent),tc_set(tc_Event_Oevent)) = c_minus(c_insert(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)))))),X0,tc_Event_Oevent),c_List_Oset(v_evs3,tc_Event_Oevent),tc_set(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2593])]) ).
fof(f22053,plain,
( ! [X0] : c_minus(X0,c_List_Oset(v_evs3,tc_Event_Oevent),tc_set(tc_Event_Oevent)) = c_minus(c_insert(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)))))),X0,tc_Event_Oevent),c_List_Oset(v_evs3,tc_Event_Oevent),tc_set(tc_Event_Oevent))
| ~ spl0_751
| ~ spl0_2013 ),
inference(resolution,[],[f20977,f7368]) ).
fof(f34165,plain,
( spl0_2592
| ~ spl0_2190
| ~ spl0_2561 ),
inference(avatar_split_clause,[],[f33605,f33024,f24628,f34163]) ).
fof(f34163,plain,
( spl0_2592
<=> ! [X0] : c_in(v_Aa,c_union(c_Event_Obad,X0,tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2592])]) ).
fof(f24628,plain,
( spl0_2190
<=> ! [X0] :
( ~ c_lessequals(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_in(v_Aa,X0,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f33605,plain,
( ! [X0] : c_in(v_Aa,c_union(c_Event_Obad,X0,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2190
| ~ spl0_2561 ),
inference(resolution,[],[f33025,f24629]) ).
fof(f24629,plain,
( ! [X0] :
( ~ c_lessequals(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_2190 ),
inference(avatar_component_clause,[],[f24628]) ).
fof(f33796,plain,
( spl0_2591
| ~ spl0_816
| ~ spl0_2590 ),
inference(avatar_split_clause,[],[f33578,f33472,f7630,f33794]) ).
fof(f33794,plain,
( spl0_2591
<=> ! [X0] : c_in(v_Aa,c_insert(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2591])]) ).
fof(f7630,plain,
( spl0_816
<=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f33472,plain,
( spl0_2590
<=> ! [X0,X1] : c_in(v_Aa,c_union(X1,c_insert(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2590])]) ).
fof(f33578,plain,
( ! [X0] : c_in(v_Aa,c_insert(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_816
| ~ spl0_2590 ),
inference(superposition,[],[f33473,f7631]) ).
fof(f7631,plain,
( ! [X3,X1] : c_union(X3,X3,X1) = X3
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f7630]) ).
fof(f33473,plain,
( ! [X0,X1] : c_in(v_Aa,c_union(X1,c_insert(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2590 ),
inference(avatar_component_clause,[],[f33472]) ).
fof(f33474,plain,
( spl0_2590
| ~ spl0_1762
| ~ spl0_2489 ),
inference(avatar_split_clause,[],[f32240,f32165,f16031,f33472]) ).
fof(f16031,plain,
( spl0_1762
<=> ! [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_1762])]) ).
fof(f32165,plain,
( spl0_2489
<=> ! [X0] : c_in(v_Aa,c_union(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).
fof(f32240,plain,
( ! [X0,X1] : c_in(v_Aa,c_union(X1,c_insert(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1762
| ~ spl0_2489 ),
inference(superposition,[],[f32166,f16032]) ).
fof(f16032,plain,
( ! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1)
| ~ spl0_1762 ),
inference(avatar_component_clause,[],[f16031]) ).
fof(f32166,plain,
( ! [X0] : c_in(v_Aa,c_union(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2489 ),
inference(avatar_component_clause,[],[f32165]) ).
fof(f33277,plain,
( ~ spl0_30
| ~ spl0_57
| ~ spl0_2582 ),
inference(avatar_split_clause,[],[f33158,f33112,f3715,f3580]) ).
fof(f33112,plain,
( spl0_2582
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2582])]) ).
fof(f33158,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_2582 ),
inference(resolution,[],[f33113,f3717]) ).
fof(f3717,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f3715]) ).
fof(f33113,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_2582 ),
inference(avatar_component_clause,[],[f33112]) ).
fof(f33270,plain,
( spl0_2589
| ~ spl0_16
| ~ spl0_1249
| ~ spl0_1915
| ~ spl0_2527 ),
inference(avatar_split_clause,[],[f32840,f32836,f19325,f10049,f3510,f33267]) ).
fof(f33267,plain,
( spl0_2589
<=> 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_2589])]) ).
fof(f3510,plain,
( spl0_16
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f10049,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(f19325,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(f32836,plain,
( spl0_2527
<=> 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_2527])]) ).
fof(f32840,plain,
( c_IntDef_Oneg(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_16
| ~ spl0_1249
| ~ spl0_1915
| ~ spl0_2527 ),
inference(forward_demodulation,[],[f32838,f20154]) ).
fof(f20154,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_16
| ~ spl0_1249
| ~ spl0_1915 ),
inference(forward_demodulation,[],[f20153,f10050]) ).
fof(f10050,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,[],[f10049]) ).
fof(f20153,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_16
| ~ spl0_1915 ),
inference(resolution,[],[f19326,f3512]) ).
fof(f3512,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f3510]) ).
fof(f19326,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,[],[f19325]) ).
fof(f32838,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2527 ),
inference(avatar_component_clause,[],[f32836]) ).
fof(f33178,plain,
( spl0_2588
| ~ spl0_657
| ~ spl0_2228 ),
inference(avatar_split_clause,[],[f26402,f26128,f6174,f33176]) ).
fof(f33176,plain,
( spl0_2588
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2588])]) ).
fof(f6174,plain,
( spl0_657
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f26128,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(f26402,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3)
| ~ spl0_657
| ~ spl0_2228 ),
inference(resolution,[],[f26129,f6175]) ).
fof(f6175,plain,
( ! [X1,X4] : ~ c_in(X4,c_emptyset,X1)
| ~ spl0_657 ),
inference(avatar_component_clause,[],[f6174]) ).
fof(f26129,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,[],[f26128]) ).
fof(f33174,plain,
( spl0_2587
| ~ spl0_59
| ~ spl0_947
| ~ spl0_1075
| ~ spl0_1992 ),
inference(avatar_split_clause,[],[f21399,f20888,f8897,f8242,f3725,f33172]) ).
fof(f33172,plain,
( spl0_2587
<=> ! [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_2587])]) ).
fof(f8242,plain,
( spl0_947
<=> ! [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_947])]) ).
fof(f20888,plain,
( spl0_1992
<=> ! [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_1992])]) ).
fof(f21399,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_59
| ~ spl0_947
| ~ spl0_1075
| ~ spl0_1992 ),
inference(forward_demodulation,[],[f21396,f9261]) ).
fof(f21396,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_947
| ~ spl0_1992 ),
inference(trivial_inequality_removal,[],[f21393]) ).
fof(f21393,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_947
| ~ spl0_1992 ),
inference(superposition,[],[f20889,f8243]) ).
fof(f8243,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_947 ),
inference(avatar_component_clause,[],[f8242]) ).
fof(f20889,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_1992 ),
inference(avatar_component_clause,[],[f20888]) ).
fof(f33170,plain,
( spl0_2586
| ~ spl0_875
| ~ spl0_1962 ),
inference(avatar_split_clause,[],[f20718,f19688,f7879,f33168]) ).
fof(f33168,plain,
( spl0_2586
<=> ! [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_2586])]) ).
fof(f7879,plain,
( spl0_875
<=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f19688,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(f20718,plain,
( ! [X0,X1] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_875
| ~ spl0_1962 ),
inference(superposition,[],[f7880,f19689]) ).
fof(f19689,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,[],[f19688]) ).
fof(f7880,plain,
( ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat)
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f7879]) ).
fof(f33166,plain,
( spl0_2585
| ~ spl0_790
| ~ spl0_1758 ),
inference(avatar_split_clause,[],[f15988,f15984,f7525,f33164]) ).
fof(f33164,plain,
( spl0_2585
<=> ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2585])]) ).
fof(f7525,plain,
( spl0_790
<=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f15984,plain,
( spl0_1758
<=> ! [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_1758])]) ).
fof(f15988,plain,
( ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat)
| ~ spl0_790
| ~ spl0_1758 ),
inference(superposition,[],[f15985,f7526]) ).
fof(f7526,plain,
( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
| ~ spl0_790 ),
inference(avatar_component_clause,[],[f7525]) ).
fof(f15985,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_1758 ),
inference(avatar_component_clause,[],[f15984]) ).
fof(f33162,plain,
( spl0_2584
| ~ spl0_121
| ~ spl0_1619 ),
inference(avatar_split_clause,[],[f14817,f14343,f4025,f33160]) ).
fof(f33160,plain,
( spl0_2584
<=> ! [X0] :
( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2584])]) ).
fof(f4025,plain,
( spl0_121
<=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f14343,plain,
( spl0_1619
<=> ! [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_1619])]) ).
fof(f14817,plain,
( ! [X0] :
( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) )
| ~ spl0_121
| ~ spl0_1619 ),
inference(resolution,[],[f14344,f4026]) ).
fof(f4026,plain,
( ! [X21] : ~ c_less(X21,X21,tc_nat)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f4025]) ).
fof(f14344,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_1619 ),
inference(avatar_component_clause,[],[f14343]) ).
fof(f33157,plain,
( spl0_2582
| spl0_2583
| ~ spl0_801
| ~ spl0_1618 ),
inference(avatar_split_clause,[],[f14802,f14339,f7570,f33155,f33112]) ).
fof(f33155,plain,
( spl0_2583
<=> ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2583])]) ).
fof(f7570,plain,
( spl0_801
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f14339,plain,
( spl0_1618
<=> ! [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_1618])]) ).
fof(f14802,plain,
( ! [X0,X1] :
( ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_801
| ~ spl0_1618 ),
inference(resolution,[],[f14340,f7571]) ).
fof(f7571,plain,
( ! [X0,X1] :
( ~ c_less(X0,X0,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_801 ),
inference(avatar_component_clause,[],[f7570]) ).
fof(f14340,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_1618 ),
inference(avatar_component_clause,[],[f14339]) ).
fof(f33114,plain,
( spl0_2582
| spl0_2508
| ~ spl0_753
| ~ spl0_1615 ),
inference(avatar_split_clause,[],[f14750,f14324,f7376,f32277,f33112]) ).
fof(f32277,plain,
( spl0_2508
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).
fof(f7376,plain,
( spl0_753
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f14324,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(f14750,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_753
| ~ spl0_1615 ),
inference(resolution,[],[f14325,f7377]) ).
fof(f7377,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_753 ),
inference(avatar_component_clause,[],[f7376]) ).
fof(f14325,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_1615 ),
inference(avatar_component_clause,[],[f14324]) ).
fof(f33110,plain,
( spl0_2581
| ~ spl0_773
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f14676,f14292,f7457,f33108]) ).
fof(f33108,plain,
( spl0_2581
<=> ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2581])]) ).
fof(f7457,plain,
( spl0_773
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f14292,plain,
( spl0_1607
<=> ! [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_1607])]) ).
fof(f14676,plain,
( ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0
| ~ spl0_773
| ~ spl0_1607 ),
inference(trivial_inequality_removal,[],[f14661]) ).
fof(f14661,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 )
| ~ spl0_773
| ~ spl0_1607 ),
inference(superposition,[],[f14293,f7458]) ).
fof(f7458,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint)
| ~ spl0_773 ),
inference(avatar_component_clause,[],[f7457]) ).
fof(f14293,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_1607 ),
inference(avatar_component_clause,[],[f14292]) ).
fof(f33106,plain,
( spl0_2580
| ~ spl0_1449
| ~ spl0_2533 ),
inference(avatar_split_clause,[],[f33059,f32862,f11259,f33103]) ).
fof(f33103,plain,
( spl0_2580
<=> c_in(c_Message_Omsg_OAgent(v_Ba),c_Event_Oused(v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2580])]) ).
fof(f11259,plain,
( spl0_1449
<=> ! [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_1449])]) ).
fof(f32862,plain,
( spl0_2533
<=> c_in(c_Message_Omsg_OAgent(v_Ba),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2533])]) ).
fof(f33059,plain,
( c_in(c_Message_Omsg_OAgent(v_Ba),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ spl0_1449
| ~ spl0_2533 ),
inference(resolution,[],[f32864,f11260]) ).
fof(f11260,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_1449 ),
inference(avatar_component_clause,[],[f11259]) ).
fof(f32864,plain,
( c_in(c_Message_Omsg_OAgent(v_Ba),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_2533 ),
inference(avatar_component_clause,[],[f32862]) ).
fof(f33101,plain,
( spl0_2579
| ~ spl0_772
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f14675,f14292,f7453,f33099]) ).
fof(f33099,plain,
( spl0_2579
<=> ! [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_2579])]) ).
fof(f7453,plain,
( spl0_772
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f14675,plain,
( ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0
| ~ spl0_772
| ~ spl0_1607 ),
inference(trivial_inequality_removal,[],[f14663]) ).
fof(f14663,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_772
| ~ spl0_1607 ),
inference(superposition,[],[f14293,f7454]) ).
fof(f7454,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint)
| ~ spl0_772 ),
inference(avatar_component_clause,[],[f7453]) ).
fof(f33097,plain,
( spl0_2578
| ~ spl0_774
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f14673,f14292,f7461,f33095]) ).
fof(f33095,plain,
( spl0_2578
<=> ! [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_2578])]) ).
fof(f7461,plain,
( spl0_774
<=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f14673,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint)
| ~ spl0_774
| ~ spl0_1607 ),
inference(trivial_inequality_removal,[],[f14665]) ).
fof(f14665,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_774
| ~ spl0_1607 ),
inference(superposition,[],[f14293,f7462]) ).
fof(f7462,plain,
( ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint)
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f7461]) ).
fof(f33093,plain,
( spl0_2577
| ~ spl0_761
| ~ spl0_1606 ),
inference(avatar_split_clause,[],[f14659,f14288,f7408,f33091]) ).
fof(f33091,plain,
( spl0_2577
<=> ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2577])]) ).
fof(f7408,plain,
( spl0_761
<=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f14288,plain,
( spl0_1606
<=> ! [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_1606])]) ).
fof(f14659,plain,
( ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0
| ~ spl0_761
| ~ spl0_1606 ),
inference(trivial_inequality_removal,[],[f14647]) ).
fof(f14647,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 )
| ~ spl0_761
| ~ spl0_1606 ),
inference(superposition,[],[f14289,f7409]) ).
fof(f7409,plain,
( ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat)
| ~ spl0_761 ),
inference(avatar_component_clause,[],[f7408]) ).
fof(f14289,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_1606 ),
inference(avatar_component_clause,[],[f14288]) ).
fof(f33089,plain,
( spl0_2576
| ~ spl0_838
| ~ spl0_1606 ),
inference(avatar_split_clause,[],[f14658,f14288,f7720,f33087]) ).
fof(f33087,plain,
( spl0_2576
<=> ! [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_2576])]) ).
fof(f7720,plain,
( spl0_838
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f14658,plain,
( ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0
| ~ spl0_838
| ~ spl0_1606 ),
inference(trivial_inequality_removal,[],[f14648]) ).
fof(f14648,plain,
( ! [X0] :
( c_0 != c_0
| c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0 )
| ~ spl0_838
| ~ spl0_1606 ),
inference(superposition,[],[f14289,f7721]) ).
fof(f7721,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat)
| ~ spl0_838 ),
inference(avatar_component_clause,[],[f7720]) ).
fof(f33085,plain,
( spl0_2575
| ~ spl0_760
| ~ spl0_1606 ),
inference(avatar_split_clause,[],[f14657,f14288,f7404,f33083]) ).
fof(f33083,plain,
( spl0_2575
<=> ! [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_2575])]) ).
fof(f7404,plain,
( spl0_760
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f14657,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat)
| ~ spl0_760
| ~ spl0_1606 ),
inference(trivial_inequality_removal,[],[f14649]) ).
fof(f14649,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat) )
| ~ spl0_760
| ~ spl0_1606 ),
inference(superposition,[],[f14289,f7405]) ).
fof(f7405,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat)
| ~ spl0_760 ),
inference(avatar_component_clause,[],[f7404]) ).
fof(f33081,plain,
( spl0_2574
| ~ spl0_814
| ~ spl0_1586 ),
inference(avatar_split_clause,[],[f14206,f12871,f7622,f33079]) ).
fof(f33079,plain,
( spl0_2574
<=> ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2574])]) ).
fof(f7622,plain,
( spl0_814
<=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f12871,plain,
( spl0_1586
<=> ! [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_1586])]) ).
fof(f14206,plain,
( ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_814
| ~ spl0_1586 ),
inference(superposition,[],[f12872,f7623]) ).
fof(f7623,plain,
( ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1)
| ~ spl0_814 ),
inference(avatar_component_clause,[],[f7622]) ).
fof(f12872,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_1586 ),
inference(avatar_component_clause,[],[f12871]) ).
fof(f33077,plain,
( spl0_2573
| ~ spl0_814
| ~ spl0_1585 ),
inference(avatar_split_clause,[],[f14198,f12867,f7622,f33075]) ).
fof(f33075,plain,
( spl0_2573
<=> ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2573])]) ).
fof(f12867,plain,
( spl0_1585
<=> ! [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_1585])]) ).
fof(f14198,plain,
( ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_814
| ~ spl0_1585 ),
inference(superposition,[],[f12868,f7623]) ).
fof(f12868,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_1585 ),
inference(avatar_component_clause,[],[f12867]) ).
fof(f33073,plain,
( spl0_2572
| ~ spl0_819
| ~ spl0_1574 ),
inference(avatar_split_clause,[],[f14146,f12813,f7642,f33071]) ).
fof(f33071,plain,
( spl0_2572
<=> ! [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_2572])]) ).
fof(f7642,plain,
( spl0_819
<=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f12813,plain,
( spl0_1574
<=> ! [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_1574])]) ).
fof(f14146,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1574 ),
inference(superposition,[],[f7643,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_1574 ),
inference(avatar_component_clause,[],[f12813]) ).
fof(f7643,plain,
( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7642]) ).
fof(f33069,plain,
( spl0_2571
| ~ spl0_819
| ~ spl0_1573 ),
inference(avatar_split_clause,[],[f14129,f12809,f7642,f33067]) ).
fof(f33067,plain,
( spl0_2571
<=> ! [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_2571])]) ).
fof(f12809,plain,
( spl0_1573
<=> ! [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_1573])]) ).
fof(f14129,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1573 ),
inference(superposition,[],[f7643,f12810]) ).
fof(f12810,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_1573 ),
inference(avatar_component_clause,[],[f12809]) ).
fof(f33065,plain,
( spl0_2570
| ~ spl0_819
| ~ spl0_1572 ),
inference(avatar_split_clause,[],[f14113,f12805,f7642,f33063]) ).
fof(f33063,plain,
( spl0_2570
<=> ! [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_2570])]) ).
fof(f12805,plain,
( spl0_1572
<=> ! [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_1572])]) ).
fof(f14113,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1572 ),
inference(superposition,[],[f7643,f12806]) ).
fof(f12806,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_1572 ),
inference(avatar_component_clause,[],[f12805]) ).
fof(f33058,plain,
( spl0_2569
| ~ spl0_819
| ~ spl0_1571 ),
inference(avatar_split_clause,[],[f14096,f12801,f7642,f33056]) ).
fof(f33056,plain,
( spl0_2569
<=> ! [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_2569])]) ).
fof(f12801,plain,
( spl0_1571
<=> ! [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_1571])]) ).
fof(f14096,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1571 ),
inference(superposition,[],[f7643,f12802]) ).
fof(f12802,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_1571 ),
inference(avatar_component_clause,[],[f12801]) ).
fof(f33054,plain,
( spl0_2568
| ~ spl0_819
| ~ spl0_1570 ),
inference(avatar_split_clause,[],[f14079,f12797,f7642,f33052]) ).
fof(f33052,plain,
( spl0_2568
<=> ! [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_2568])]) ).
fof(f12797,plain,
( spl0_1570
<=> ! [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_1570])]) ).
fof(f14079,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1570 ),
inference(superposition,[],[f7643,f12798]) ).
fof(f12798,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_1570 ),
inference(avatar_component_clause,[],[f12797]) ).
fof(f33050,plain,
( spl0_2567
| ~ spl0_819
| ~ spl0_1566 ),
inference(avatar_split_clause,[],[f14024,f12770,f7642,f33048]) ).
fof(f33048,plain,
( spl0_2567
<=> ! [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_2567])]) ).
fof(f12770,plain,
( spl0_1566
<=> ! [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_1566])]) ).
fof(f14024,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1566 ),
inference(superposition,[],[f7643,f12771]) ).
fof(f12771,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_1566 ),
inference(avatar_component_clause,[],[f12770]) ).
fof(f33046,plain,
( spl0_2566
| ~ spl0_819
| ~ spl0_1565 ),
inference(avatar_split_clause,[],[f14000,f12766,f7642,f33044]) ).
fof(f33044,plain,
( spl0_2566
<=> ! [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_2566])]) ).
fof(f12766,plain,
( spl0_1565
<=> ! [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_1565])]) ).
fof(f14000,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1565 ),
inference(superposition,[],[f7643,f12767]) ).
fof(f12767,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_1565 ),
inference(avatar_component_clause,[],[f12766]) ).
fof(f33042,plain,
( spl0_2565
| ~ spl0_819
| ~ spl0_1564 ),
inference(avatar_split_clause,[],[f13980,f12762,f7642,f33040]) ).
fof(f33040,plain,
( spl0_2565
<=> ! [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_2565])]) ).
fof(f12762,plain,
( spl0_1564
<=> ! [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_1564])]) ).
fof(f13980,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1564 ),
inference(superposition,[],[f7643,f12763]) ).
fof(f12763,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_1564 ),
inference(avatar_component_clause,[],[f12762]) ).
fof(f33038,plain,
( spl0_2564
| ~ spl0_819
| ~ spl0_1563 ),
inference(avatar_split_clause,[],[f13960,f12758,f7642,f33036]) ).
fof(f33036,plain,
( spl0_2564
<=> ! [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_2564])]) ).
fof(f12758,plain,
( spl0_1563
<=> ! [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_1563])]) ).
fof(f13960,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_819
| ~ spl0_1563 ),
inference(superposition,[],[f7643,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_1563 ),
inference(avatar_component_clause,[],[f12758]) ).
fof(f33034,plain,
( spl0_2563
| ~ spl0_674
| ~ spl0_1561 ),
inference(avatar_split_clause,[],[f13932,f12750,f7014,f33032]) ).
fof(f33032,plain,
( spl0_2563
<=> ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2563])]) ).
fof(f7014,plain,
( spl0_674
<=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f12750,plain,
( spl0_1561
<=> ! [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_1561])]) ).
fof(f13932,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2))
| ~ spl0_674
| ~ spl0_1561 ),
inference(resolution,[],[f12751,f7015]) ).
fof(f7015,plain,
( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f7014]) ).
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_1561 ),
inference(avatar_component_clause,[],[f12750]) ).
fof(f33030,plain,
( spl0_2562
| ~ spl0_674
| ~ spl0_1558 ),
inference(avatar_split_clause,[],[f13912,f12737,f7014,f33028]) ).
fof(f33028,plain,
( spl0_2562
<=> ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2562])]) ).
fof(f12737,plain,
( spl0_1558
<=> ! [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_1558])]) ).
fof(f13912,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| ~ spl0_674
| ~ spl0_1558 ),
inference(resolution,[],[f12738,f7015]) ).
fof(f12738,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| c_lessequals(X13,X32,tc_set(X1)) )
| ~ spl0_1558 ),
inference(avatar_component_clause,[],[f12737]) ).
fof(f33026,plain,
( spl0_2561
| ~ spl0_674
| ~ spl0_1557 ),
inference(avatar_split_clause,[],[f13896,f12733,f7014,f33024]) ).
fof(f12733,plain,
( spl0_1557
<=> ! [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_1557])]) ).
fof(f13896,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| ~ spl0_674
| ~ spl0_1557 ),
inference(resolution,[],[f12734,f7015]) ).
fof(f12734,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| c_lessequals(X12,X32,tc_set(X1)) )
| ~ spl0_1557 ),
inference(avatar_component_clause,[],[f12733]) ).
fof(f33022,plain,
( spl0_2560
| ~ spl0_1027
| ~ spl0_1543 ),
inference(avatar_split_clause,[],[f13777,f12672,f8699,f33020]) ).
fof(f33020,plain,
( spl0_2560
<=> ! [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_2560])]) ).
fof(f8699,plain,
( spl0_1027
<=> ! [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_1027])]) ).
fof(f12672,plain,
( spl0_1543
<=> ! [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_1543])]) ).
fof(f13777,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1027
| ~ spl0_1543 ),
inference(superposition,[],[f8700,f12673]) ).
fof(f12673,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_1543 ),
inference(avatar_component_clause,[],[f12672]) ).
fof(f8700,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat)
| ~ spl0_1027 ),
inference(avatar_component_clause,[],[f8699]) ).
fof(f33017,plain,
( spl0_2559
| ~ spl0_1028
| ~ spl0_1543 ),
inference(avatar_split_clause,[],[f13776,f12672,f8703,f33015]) ).
fof(f33015,plain,
( spl0_2559
<=> ! [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_2559])]) ).
fof(f8703,plain,
( spl0_1028
<=> ! [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_1028])]) ).
fof(f13776,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1028
| ~ spl0_1543 ),
inference(superposition,[],[f8704,f12673]) ).
fof(f8704,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat)
| ~ spl0_1028 ),
inference(avatar_component_clause,[],[f8703]) ).
fof(f33012,plain,
( spl0_2558
| ~ spl0_1027
| ~ spl0_1542 ),
inference(avatar_split_clause,[],[f13771,f12668,f8699,f33010]) ).
fof(f33010,plain,
( spl0_2558
<=> ! [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_2558])]) ).
fof(f12668,plain,
( spl0_1542
<=> ! [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_1542])]) ).
fof(f13771,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1027
| ~ spl0_1542 ),
inference(superposition,[],[f8700,f12669]) ).
fof(f12669,plain,
( ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3
| ~ spl0_1542 ),
inference(avatar_component_clause,[],[f12668]) ).
fof(f33007,plain,
( spl0_2557
| ~ spl0_1028
| ~ spl0_1542 ),
inference(avatar_split_clause,[],[f13770,f12668,f8703,f33005]) ).
fof(f33005,plain,
( spl0_2557
<=> ! [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_2557])]) ).
fof(f13770,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1028
| ~ spl0_1542 ),
inference(superposition,[],[f8704,f12669]) ).
fof(f33003,plain,
( spl0_2556
| ~ spl0_819
| ~ spl0_1506 ),
inference(avatar_split_clause,[],[f13241,f12512,f7642,f33001]) ).
fof(f33001,plain,
( spl0_2556
<=> ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2556])]) ).
fof(f12512,plain,
( spl0_1506
<=> ! [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_1506])]) ).
fof(f13241,plain,
( ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2)
| ~ spl0_819
| ~ spl0_1506 ),
inference(superposition,[],[f7643,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_1506 ),
inference(avatar_component_clause,[],[f12512]) ).
fof(f32999,plain,
( spl0_2555
| ~ spl0_781
| ~ spl0_1499 ),
inference(avatar_split_clause,[],[f13178,f12484,f7489,f32997]) ).
fof(f32997,plain,
( spl0_2555
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2555])]) ).
fof(f7489,plain,
( spl0_781
<=> ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f12484,plain,
( spl0_1499
<=> ! [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_1499])]) ).
fof(f13178,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 )
| ~ spl0_781
| ~ spl0_1499 ),
inference(superposition,[],[f7490,f12485]) ).
fof(f12485,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_1499 ),
inference(avatar_component_clause,[],[f12484]) ).
fof(f7490,plain,
( ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23
| ~ spl0_781 ),
inference(avatar_component_clause,[],[f7489]) ).
fof(f32995,plain,
( spl0_2554
| ~ spl0_1022
| ~ spl0_1492 ),
inference(avatar_split_clause,[],[f13116,f12456,f8548,f32993]) ).
fof(f32993,plain,
( spl0_2554
<=> ! [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_2554])]) ).
fof(f8548,plain,
( spl0_1022
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f12456,plain,
( spl0_1492
<=> ! [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_1492])]) ).
fof(f13116,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
| c_Divides_Oop_Advd(X1,X0,tc_nat) )
| ~ spl0_1022
| ~ spl0_1492 ),
inference(superposition,[],[f12457,f8549]) ).
fof(f8549,plain,
( ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat))
| ~ spl0_1022 ),
inference(avatar_component_clause,[],[f8548]) ).
fof(f12457,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_1492 ),
inference(avatar_component_clause,[],[f12456]) ).
fof(f32991,plain,
( spl0_2553
| ~ spl0_737
| ~ spl0_1483 ),
inference(avatar_split_clause,[],[f13006,f12420,f7293,f32989]) ).
fof(f32989,plain,
( spl0_2553
<=> ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2553])]) ).
fof(f12420,plain,
( spl0_1483
<=> ! [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_1483])]) ).
fof(f13006,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 )
| ~ spl0_737
| ~ spl0_1483 ),
inference(resolution,[],[f12421,f7294]) ).
fof(f12421,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13 )
| ~ spl0_1483 ),
inference(avatar_component_clause,[],[f12420]) ).
fof(f32987,plain,
( spl0_2552
| ~ spl0_673
| ~ spl0_1481 ),
inference(avatar_split_clause,[],[f12983,f12412,f7010,f32985]) ).
fof(f32985,plain,
( spl0_2552
<=> ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2552])]) ).
fof(f12412,plain,
( spl0_1481
<=> ! [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_1481])]) ).
fof(f12983,plain,
( ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) )
| ~ spl0_673
| ~ spl0_1481 ),
inference(resolution,[],[f12413,f7011]) ).
fof(f12413,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13
| c_less(X12,X13,tc_set(X1)) )
| ~ spl0_1481 ),
inference(avatar_component_clause,[],[f12412]) ).
fof(f32983,plain,
( spl0_2551
| ~ spl0_737
| ~ spl0_1481 ),
inference(avatar_split_clause,[],[f12974,f12412,f7293,f32981]) ).
fof(f32981,plain,
( spl0_2551
<=> ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2551])]) ).
fof(f12974,plain,
( ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) )
| ~ spl0_737
| ~ spl0_1481 ),
inference(resolution,[],[f12413,f7294]) ).
fof(f32979,plain,
( spl0_2550
| ~ spl0_789
| ~ spl0_872
| ~ spl0_1592 ),
inference(avatar_split_clause,[],[f12929,f12906,f7867,f7521,f32977]) ).
fof(f32977,plain,
( spl0_2550
<=> ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2550])]) ).
fof(f7521,plain,
( spl0_789
<=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f7867,plain,
( spl0_872
<=> ! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f12906,plain,
( spl0_1592
<=> ! [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_1592])]) ).
fof(f12929,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 )
| ~ spl0_789
| ~ spl0_872
| ~ spl0_1592 ),
inference(forward_demodulation,[],[f12916,f7522]) ).
fof(f7522,plain,
( ! [X3] : c_plus(X3,c_0,tc_nat) = X3
| ~ spl0_789 ),
inference(avatar_component_clause,[],[f7521]) ).
fof(f12916,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_plus(c_1,c_0,tc_nat))
| c_0 = X0 )
| ~ spl0_872
| ~ spl0_1592 ),
inference(resolution,[],[f12907,f7868]) ).
fof(f7868,plain,
( ! [X43] :
( ~ c_lessequals(X43,c_0,tc_nat)
| c_0 = X43 )
| ~ spl0_872 ),
inference(avatar_component_clause,[],[f7867]) ).
fof(f12907,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_1592 ),
inference(avatar_component_clause,[],[f12906]) ).
fof(f32975,plain,
( spl0_2549
| ~ spl0_1449
| ~ spl0_2522 ),
inference(avatar_split_clause,[],[f32915,f32814,f11259,f32972]) ).
fof(f32972,plain,
( spl0_2549
<=> c_in(c_Message_Omsg_OAgent(v_B),c_Event_Oused(v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2549])]) ).
fof(f32814,plain,
( spl0_2522
<=> c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).
fof(f32915,plain,
( c_in(c_Message_Omsg_OAgent(v_B),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ spl0_1449
| ~ spl0_2522 ),
inference(resolution,[],[f32816,f11260]) ).
fof(f32816,plain,
( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_2522 ),
inference(avatar_component_clause,[],[f32814]) ).
fof(f32970,plain,
( spl0_2548
| ~ spl0_789
| ~ spl0_1000
| ~ spl0_1589 ),
inference(avatar_split_clause,[],[f12895,f12889,f8457,f7521,f32967]) ).
fof(f32967,plain,
( spl0_2548
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2548])]) ).
fof(f12889,plain,
( spl0_1589
<=> ! [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_1589])]) ).
fof(f12895,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_789
| ~ spl0_1000
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f12892,f8459]) ).
fof(f12892,plain,
( c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_789
| ~ spl0_1589 ),
inference(superposition,[],[f12890,f7522]) ).
fof(f12890,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_1589 ),
inference(avatar_component_clause,[],[f12889]) ).
fof(f32965,plain,
( spl0_2547
| ~ spl0_926
| ~ spl0_1589 ),
inference(avatar_split_clause,[],[f12894,f12889,f8156,f32963]) ).
fof(f32963,plain,
( spl0_2547
<=> ! [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_2547])]) ).
fof(f8156,plain,
( spl0_926
<=> ! [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_926])]) ).
fof(f12894,plain,
( ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_926
| ~ spl0_1589 ),
inference(superposition,[],[f8157,f12890]) ).
fof(f8157,plain,
( ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f8156]) ).
fof(f32961,plain,
( spl0_2546
| ~ spl0_894
| ~ spl0_1429 ),
inference(avatar_split_clause,[],[f12004,f11174,f7955,f32959]) ).
fof(f32959,plain,
( spl0_2546
<=> ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2546])]) ).
fof(f11174,plain,
( spl0_1429
<=> ! [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_1429])]) ).
fof(f12004,plain,
( ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) )
| ~ spl0_894
| ~ spl0_1429 ),
inference(superposition,[],[f11175,f7956]) ).
fof(f11175,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_minus(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1429 ),
inference(avatar_component_clause,[],[f11174]) ).
fof(f32957,plain,
( spl0_2545
| ~ spl0_753
| ~ spl0_1421 ),
inference(avatar_split_clause,[],[f11973,f11142,f7376,f32955]) ).
fof(f32955,plain,
( spl0_2545
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2545])]) ).
fof(f11142,plain,
( spl0_1421
<=> ! [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_1421])]) ).
fof(f11973,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_753
| ~ spl0_1421 ),
inference(duplicate_literal_removal,[],[f11940]) ).
fof(f11940,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_753
| ~ spl0_1421 ),
inference(resolution,[],[f11143,f7377]) ).
fof(f11143,plain,
( ! [X1,X26,X16] :
( ~ c_lessequals(X26,X16,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) )
| ~ spl0_1421 ),
inference(avatar_component_clause,[],[f11142]) ).
fof(f32947,plain,
( spl0_2544
| ~ spl0_78
| ~ spl0_120
| ~ spl0_1421 ),
inference(avatar_split_clause,[],[f11946,f11142,f4021,f3820,f32945]) ).
fof(f32945,plain,
( spl0_2544
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2544])]) ).
fof(f4021,plain,
( spl0_120
<=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f11946,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) )
| ~ spl0_120
| ~ spl0_1421 ),
inference(resolution,[],[f11143,f4022]) ).
fof(f4022,plain,
( ! [X21] : c_lessequals(c_0,X21,tc_nat)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f4021]) ).
fof(f32943,plain,
( spl0_2543
| ~ spl0_753
| ~ spl0_1412 ),
inference(avatar_split_clause,[],[f11923,f11103,f7376,f32941]) ).
fof(f32941,plain,
( spl0_2543
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2543])]) ).
fof(f11103,plain,
( spl0_1412
<=> ! [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_1412])]) ).
fof(f11923,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_753
| ~ spl0_1412 ),
inference(duplicate_literal_removal,[],[f11890]) ).
fof(f11890,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_753
| ~ spl0_1412 ),
inference(resolution,[],[f11104,f7377]) ).
fof(f11104,plain,
( ! [X21,X1,X15] :
( ~ c_lessequals(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) )
| ~ spl0_1412 ),
inference(avatar_component_clause,[],[f11103]) ).
fof(f32925,plain,
( spl0_2542
| ~ spl0_78
| ~ spl0_120
| ~ spl0_1412 ),
inference(avatar_split_clause,[],[f11896,f11103,f4021,f3820,f32923]) ).
fof(f32923,plain,
( spl0_2542
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2542])]) ).
fof(f11896,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) )
| ~ spl0_120
| ~ spl0_1412 ),
inference(resolution,[],[f11104,f4022]) ).
fof(f32914,plain,
( spl0_2541
| ~ spl0_30
| ~ spl0_668
| ~ spl0_1411 ),
inference(avatar_split_clause,[],[f11866,f11099,f6225,f3580,f32911]) ).
fof(f32911,plain,
( spl0_2541
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2541])]) ).
fof(f6225,plain,
( spl0_668
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f11099,plain,
( spl0_1411
<=> ! [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_1411])]) ).
fof(f11866,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_668
| ~ spl0_1411 ),
inference(resolution,[],[f11100,f6227]) ).
fof(f6227,plain,
( c_less(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_668 ),
inference(avatar_component_clause,[],[f6225]) ).
fof(f11100,plain,
( ! [X21,X1,X15] :
( ~ c_less(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) )
| ~ spl0_1411 ),
inference(avatar_component_clause,[],[f11099]) ).
fof(f32904,plain,
( spl0_2540
| ~ spl0_78
| ~ spl0_654
| ~ spl0_1411 ),
inference(avatar_split_clause,[],[f11865,f11099,f6160,f3820,f32901]) ).
fof(f32901,plain,
( spl0_2540
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2540])]) ).
fof(f6160,plain,
( spl0_654
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f11865,plain,
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat)
| ~ spl0_654
| ~ spl0_1411 ),
inference(resolution,[],[f11100,f6162]) ).
fof(f6162,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_654 ),
inference(avatar_component_clause,[],[f6160]) ).
fof(f32897,plain,
( spl0_2538
| ~ spl0_2539
| ~ spl0_797
| ~ spl0_1322 ),
inference(avatar_split_clause,[],[f10766,f10346,f7553,f32894,f32891]) ).
fof(f32891,plain,
( spl0_2538
<=> ! [X0] : c_lessequals(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2538])]) ).
fof(f32894,plain,
( spl0_2539
<=> c_lessequals(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2539])]) ).
fof(f7553,plain,
( spl0_797
<=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f10346,plain,
( spl0_1322
<=> ! [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_1322])]) ).
fof(f10766,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_0,tc_nat)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_797
| ~ spl0_1322 ),
inference(superposition,[],[f10347,f7554]) ).
fof(f7554,plain,
( ! [X21] : c_0 = c_times(c_0,X21,tc_nat)
| ~ spl0_797 ),
inference(avatar_component_clause,[],[f7553]) ).
fof(f10347,plain,
( ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) )
| ~ spl0_1322 ),
inference(avatar_component_clause,[],[f10346]) ).
fof(f32881,plain,
( spl0_2537
| ~ spl0_47
| ~ spl0_690
| ~ spl0_1290 ),
inference(avatar_split_clause,[],[f10590,f10213,f7082,f3665,f32879]) ).
fof(f32879,plain,
( spl0_2537
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2537])]) ).
fof(f10590,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_690
| ~ spl0_1290 ),
inference(resolution,[],[f10214,f7083]) ).
fof(f32877,plain,
( spl0_2536
| ~ spl0_16
| ~ spl0_1188 ),
inference(avatar_split_clause,[],[f9940,f9572,f3510,f32875]) ).
fof(f32875,plain,
( spl0_2536
<=> ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2536])]) ).
fof(f9572,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(f9940,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_16
| ~ spl0_1188 ),
inference(resolution,[],[f9573,f3512]) ).
fof(f9573,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,[],[f9572]) ).
fof(f32873,plain,
( spl0_2535
| ~ spl0_16
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f9929,f9552,f3510,f32871]) ).
fof(f32871,plain,
( spl0_2535
<=> ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2535])]) ).
fof(f9552,plain,
( spl0_1183
<=> ! [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_1183])]) ).
fof(f9929,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint)
| ~ spl0_16
| ~ spl0_1183 ),
inference(resolution,[],[f9553,f3512]) ).
fof(f9553,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) )
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f9552]) ).
fof(f32869,plain,
( spl0_2534
| ~ spl0_16
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f9925,f9544,f3510,f32867]) ).
fof(f32867,plain,
( spl0_2534
<=> ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2534])]) ).
fof(f9544,plain,
( spl0_1181
<=> ! [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_1181])]) ).
fof(f9925,plain,
( ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_16
| ~ spl0_1181 ),
inference(resolution,[],[f9545,f3512]) ).
fof(f9545,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) )
| ~ spl0_1181 ),
inference(avatar_component_clause,[],[f9544]) ).
fof(f32865,plain,
( spl0_2533
| ~ spl0_1213
| ~ spl0_2511 ),
inference(avatar_split_clause,[],[f32713,f32343,f9673,f32862]) ).
fof(f9673,plain,
( spl0_1213
<=> ! [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_1213])]) ).
fof(f32343,plain,
( spl0_2511
<=> c_in(c_Message_Omsg_OAgent(v_Ba),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).
fof(f32713,plain,
( c_in(c_Message_Omsg_OAgent(v_Ba),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_1213
| ~ spl0_2511 ),
inference(resolution,[],[f32345,f9674]) ).
fof(f9674,plain,
( ! [X88,X86] :
( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) )
| ~ spl0_1213 ),
inference(avatar_component_clause,[],[f9673]) ).
fof(f32345,plain,
( c_in(c_Message_Omsg_OAgent(v_Ba),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_2511 ),
inference(avatar_component_clause,[],[f32343]) ).
fof(f32860,plain,
( spl0_2532
| ~ spl0_29
| ~ spl0_1155 ),
inference(avatar_split_clause,[],[f9815,f9439,f3575,f32858]) ).
fof(f32858,plain,
( spl0_2532
<=> ! [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_2532])]) ).
fof(f9439,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(f9815,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_29
| ~ spl0_1155 ),
inference(resolution,[],[f9440,f3577]) ).
fof(f9440,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,[],[f9439]) ).
fof(f32856,plain,
( spl0_2531
| ~ spl0_98
| ~ spl0_1150 ),
inference(avatar_split_clause,[],[f9806,f9418,f3920,f32854]) ).
fof(f32854,plain,
( spl0_2531
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).
fof(f3920,plain,
( spl0_98
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f9418,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(f9806,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_98
| ~ spl0_1150 ),
inference(resolution,[],[f9419,f3922]) ).
fof(f3922,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f3920]) ).
fof(f9419,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,[],[f9418]) ).
fof(f32852,plain,
( spl0_2530
| ~ spl0_34
| ~ spl0_1150 ),
inference(avatar_split_clause,[],[f9805,f9418,f3600,f32850]) ).
fof(f32850,plain,
( spl0_2530
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2530])]) ).
fof(f3600,plain,
( spl0_34
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f9805,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_34
| ~ spl0_1150 ),
inference(resolution,[],[f9419,f3602]) ).
fof(f3602,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f3600]) ).
fof(f32848,plain,
( spl0_2529
| ~ spl0_98
| ~ spl0_1149 ),
inference(avatar_split_clause,[],[f9804,f9414,f3920,f32846]) ).
fof(f32846,plain,
( spl0_2529
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2529])]) ).
fof(f9414,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(f9804,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_98
| ~ spl0_1149 ),
inference(resolution,[],[f9415,f3922]) ).
fof(f9415,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,[],[f9414]) ).
fof(f32844,plain,
( spl0_2528
| ~ spl0_34
| ~ spl0_1149 ),
inference(avatar_split_clause,[],[f9803,f9414,f3600,f32842]) ).
fof(f32842,plain,
( spl0_2528
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2528])]) ).
fof(f9803,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_34
| ~ spl0_1149 ),
inference(resolution,[],[f9415,f3602]) ).
fof(f32839,plain,
( spl0_2527
| ~ spl0_648
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f9722,f9719,f6133,f32836]) ).
fof(f9719,plain,
( spl0_1224
<=> ! [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_1224])]) ).
fof(f9722,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_1224 ),
inference(superposition,[],[f9720,f6135]) ).
fof(f9720,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(avatar_component_clause,[],[f9719]) ).
fof(f32834,plain,
( ~ spl0_2525
| spl0_2526
| ~ spl0_665
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f9341,f9100,f6211,f32831,f32827]) ).
fof(f32827,plain,
( spl0_2525
<=> c_less(c_1,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).
fof(f32831,plain,
( spl0_2526
<=> c_less(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).
fof(f9341,plain,
( c_less(c_1,c_1,tc_nat)
| ~ c_less(c_1,c_1,tc_IntDef_Oint)
| ~ spl0_665
| ~ spl0_1125 ),
inference(superposition,[],[f9101,f6213]) ).
fof(f32825,plain,
( spl0_2524
| ~ spl0_1001
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f9277,f8959,f8462,f32823]) ).
fof(f32823,plain,
( spl0_2524
<=> ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2524])]) ).
fof(f8462,plain,
( spl0_1001
<=> ! [X1,X3] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f8959,plain,
( spl0_1090
<=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f9277,plain,
( ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_1001
| ~ spl0_1090 ),
inference(superposition,[],[f8463,f8960]) ).
fof(f8960,plain,
( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
| ~ spl0_1090 ),
inference(avatar_component_clause,[],[f8959]) ).
fof(f8463,plain,
( ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3
| ~ spl0_1001 ),
inference(avatar_component_clause,[],[f8462]) ).
fof(f32821,plain,
( spl0_2523
| ~ spl0_871
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9248,f8885,f7863,f32819]) ).
fof(f32819,plain,
( spl0_2523
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2523])]) ).
fof(f8885,plain,
( spl0_1072
<=> ! [X43,X59] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f9248,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat))
| ~ spl0_871
| ~ spl0_1072 ),
inference(resolution,[],[f8886,f7864]) ).
fof(f8886,plain,
( ! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) )
| ~ spl0_1072 ),
inference(avatar_component_clause,[],[f8885]) ).
fof(f32817,plain,
( spl0_2522
| ~ spl0_1213
| ~ spl0_2509 ),
inference(avatar_split_clause,[],[f32617,f32281,f9673,f32814]) ).
fof(f32281,plain,
( spl0_2509
<=> c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).
fof(f32617,plain,
( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_1213
| ~ spl0_2509 ),
inference(resolution,[],[f32283,f9674]) ).
fof(f32283,plain,
( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_2509 ),
inference(avatar_component_clause,[],[f32281]) ).
fof(f32812,plain,
( spl0_2521
| ~ spl0_851
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9247,f8885,f7783,f32810]) ).
fof(f32810,plain,
( spl0_2521
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2521])]) ).
fof(f9247,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat))
| ~ spl0_851
| ~ spl0_1072 ),
inference(resolution,[],[f8886,f7784]) ).
fof(f32808,plain,
( spl0_2520
| ~ spl0_1001
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9224,f8845,f8462,f32806]) ).
fof(f32806,plain,
( spl0_2520
<=> ! [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_2520])]) ).
fof(f8845,plain,
( spl0_1062
<=> ! [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_1062])]) ).
fof(f9224,plain,
( ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_1001
| ~ spl0_1062 ),
inference(superposition,[],[f8463,f8846]) ).
fof(f8846,plain,
( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f8845]) ).
fof(f32804,plain,
( spl0_2519
| ~ spl0_857
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f9190,f8782,f7807,f32802]) ).
fof(f32802,plain,
( spl0_2519
<=> ! [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_2519])]) ).
fof(f8782,plain,
( spl0_1047
<=> ! [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_1047])]) ).
fof(f9190,plain,
( ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_857
| ~ spl0_1047 ),
inference(superposition,[],[f8783,f7808]) ).
fof(f8783,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_1047 ),
inference(avatar_component_clause,[],[f8782]) ).
fof(f32800,plain,
( spl0_2518
| ~ spl0_876
| ~ spl0_1042 ),
inference(avatar_split_clause,[],[f9168,f8762,f7883,f32798]) ).
fof(f32798,plain,
( spl0_2518
<=> ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).
fof(f8762,plain,
( spl0_1042
<=> ! [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_1042])]) ).
fof(f9168,plain,
( ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) )
| ~ spl0_876
| ~ spl0_1042 ),
inference(resolution,[],[f8763,f7884]) ).
fof(f8763,plain,
( ! [X48] :
( ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat)
| c_less(c_0,X48,tc_IntDef_Oint) )
| ~ spl0_1042 ),
inference(avatar_component_clause,[],[f8762]) ).
fof(f32796,plain,
( spl0_2517
| ~ spl0_741
| ~ spl0_1004 ),
inference(avatar_split_clause,[],[f8677,f8474,f7311,f32794]) ).
fof(f32794,plain,
( spl0_2517
<=> ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).
fof(f7311,plain,
( spl0_741
<=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f8677,plain,
( ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 )
| ~ spl0_741
| ~ spl0_1004 ),
inference(superposition,[],[f8475,f7312]) ).
fof(f7312,plain,
( ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3
| ~ spl0_741 ),
inference(avatar_component_clause,[],[f7311]) ).
fof(f32784,plain,
( spl0_2516
| ~ spl0_47
| ~ spl0_944
| ~ spl0_978 ),
inference(avatar_split_clause,[],[f8637,f8367,f8230,f3665,f32782]) ).
fof(f32782,plain,
( spl0_2516
<=> ! [X0] : c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).
fof(f8230,plain,
( spl0_944
<=> ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f8637,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) )
| ~ spl0_944
| ~ spl0_978 ),
inference(resolution,[],[f8368,f8231]) ).
fof(f8231,plain,
( ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) )
| ~ spl0_944 ),
inference(avatar_component_clause,[],[f8230]) ).
fof(f32780,plain,
( spl0_2515
| ~ spl0_866
| ~ spl0_950 ),
inference(avatar_split_clause,[],[f8586,f8254,f7843,f32778]) ).
fof(f32778,plain,
( spl0_2515
<=> ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2515])]) ).
fof(f7843,plain,
( spl0_866
<=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f8254,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(f8586,plain,
( ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) )
| ~ spl0_866
| ~ spl0_950 ),
inference(superposition,[],[f8255,f7844]) ).
fof(f7844,plain,
( ! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3
| ~ spl0_866 ),
inference(avatar_component_clause,[],[f7843]) ).
fof(f8255,plain,
( ! [X1,X23] :
( c_List_Olist_ONil != c_List_Orev(X23,X1)
| c_List_Olist_ONil = X23 )
| ~ spl0_950 ),
inference(avatar_component_clause,[],[f8254]) ).
fof(f32718,plain,
( spl0_2514
| ~ spl0_116
| ~ spl0_2045 ),
inference(avatar_split_clause,[],[f22540,f22404,f4005,f32716]) ).
fof(f32716,plain,
( spl0_2514
<=> ! [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_evs3,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_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2514])]) ).
fof(f4005,plain,
( spl0_116
<=> ! [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_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f22404,plain,
( spl0_2045
<=> ! [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_2045])]) ).
fof(f22540,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_evs3,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_116
| ~ spl0_2045 ),
inference(resolution,[],[f22405,f4006]) ).
fof(f4006,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f4005]) ).
fof(f22405,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_2045 ),
inference(avatar_component_clause,[],[f22404]) ).
fof(f32354,plain,
( spl0_2513
| ~ spl0_122
| ~ spl0_1890 ),
inference(avatar_split_clause,[],[f19875,f19207,f4029,f32352]) ).
fof(f32352,plain,
( spl0_2513
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2513])]) ).
fof(f4029,plain,
( spl0_122
<=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f19207,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(f19875,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
| ~ spl0_122
| ~ spl0_1890 ),
inference(resolution,[],[f19208,f4030]) ).
fof(f4030,plain,
( ! [X0,X1] : c_in(X0,c_UNIV,X1)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f4029]) ).
fof(f19208,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,[],[f19207]) ).
fof(f32350,plain,
( spl0_2512
| ~ spl0_122
| ~ spl0_1886 ),
inference(avatar_split_clause,[],[f19822,f19191,f4029,f32348]) ).
fof(f32348,plain,
( spl0_2512
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).
fof(f19191,plain,
( spl0_1886
<=> ! [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_1886])]) ).
fof(f19822,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
| ~ spl0_122
| ~ spl0_1886 ),
inference(resolution,[],[f19192,f4030]) ).
fof(f19192,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_1886 ),
inference(avatar_component_clause,[],[f19191]) ).
fof(f32346,plain,
( spl0_2511
| ~ spl0_1456
| ~ spl0_2486 ),
inference(avatar_split_clause,[],[f32143,f32139,f11287,f32343]) ).
fof(f11287,plain,
( spl0_1456
<=> ! [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_1456])]) ).
fof(f32139,plain,
( spl0_2486
<=> c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).
fof(f32143,plain,
( c_in(c_Message_Omsg_OAgent(v_Ba),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_1456
| ~ spl0_2486 ),
inference(resolution,[],[f32141,f11288]) ).
fof(f11288,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_1456 ),
inference(avatar_component_clause,[],[f11287]) ).
fof(f32141,plain,
( c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_2486 ),
inference(avatar_component_clause,[],[f32139]) ).
fof(f32289,plain,
( spl0_2510
| ~ spl0_654
| ~ spl0_791
| ~ spl0_1622 ),
inference(avatar_split_clause,[],[f14870,f14355,f7529,f6160,f32286]) ).
fof(f32286,plain,
( spl0_2510
<=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2510])]) ).
fof(f7529,plain,
( spl0_791
<=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f14355,plain,
( spl0_1622
<=> ! [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_1622])]) ).
fof(f14870,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_654
| ~ spl0_791
| ~ spl0_1622 ),
inference(forward_demodulation,[],[f14852,f7530]) ).
fof(f7530,plain,
( ! [X15] : c_0 = c_minus(X15,X15,tc_nat)
| ~ spl0_791 ),
inference(avatar_component_clause,[],[f7529]) ).
fof(f14852,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_654
| ~ spl0_1622 ),
inference(resolution,[],[f14356,f6162]) ).
fof(f14356,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_1622 ),
inference(avatar_component_clause,[],[f14355]) ).
fof(f32284,plain,
( spl0_2509
| ~ spl0_1456
| ~ spl0_2483 ),
inference(avatar_split_clause,[],[f32097,f32071,f11287,f32281]) ).
fof(f32071,plain,
( spl0_2483
<=> 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_evs3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).
fof(f32097,plain,
( c_in(c_Message_Omsg_OAgent(v_B),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ spl0_1456
| ~ spl0_2483 ),
inference(resolution,[],[f32073,f11288]) ).
fof(f32073,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_evs3)),tc_Message_Omsg)
| ~ spl0_2483 ),
inference(avatar_component_clause,[],[f32071]) ).
fof(f32279,plain,
( spl0_2507
| spl0_2508
| ~ spl0_674
| ~ spl0_1615 ),
inference(avatar_split_clause,[],[f14751,f14324,f7014,f32277,f32274]) ).
fof(f32274,plain,
( spl0_2507
<=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).
fof(f14751,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
| ~ spl0_674
| ~ spl0_1615 ),
inference(resolution,[],[f14325,f7015]) ).
fof(f32272,plain,
( spl0_2506
| ~ spl0_851
| ~ spl0_1597 ),
inference(avatar_split_clause,[],[f14272,f12958,f7783,f32270]) ).
fof(f32270,plain,
( spl0_2506
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f12958,plain,
( spl0_1597
<=> ! [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_1597])]) ).
fof(f14272,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_851
| ~ spl0_1597 ),
inference(superposition,[],[f7784,f12959]) ).
fof(f12959,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_1597 ),
inference(avatar_component_clause,[],[f12958]) ).
fof(f32268,plain,
( spl0_2505
| ~ spl0_1242
| ~ spl0_1542 ),
inference(avatar_split_clause,[],[f13767,f12668,f10020,f32266]) ).
fof(f32266,plain,
( spl0_2505
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).
fof(f10020,plain,
( spl0_1242
<=> ! [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_1242])]) ).
fof(f13767,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1242
| ~ spl0_1542 ),
inference(superposition,[],[f10021,f12669]) ).
fof(f10021,plain,
( ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2))
| ~ spl0_1242 ),
inference(avatar_component_clause,[],[f10020]) ).
fof(f32264,plain,
( spl0_2504
| ~ spl0_798
| ~ spl0_822
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10761,f10338,f7654,f7557,f32262]) ).
fof(f32262,plain,
( spl0_2504
<=> ! [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_2504])]) ).
fof(f7557,plain,
( spl0_798
<=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f7654,plain,
( spl0_822
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f10761,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_798
| ~ spl0_822
| ~ spl0_1320 ),
inference(forward_demodulation,[],[f10750,f7558]) ).
fof(f7558,plain,
( ! [X3] : c_plus(c_0,X3,tc_nat) = X3
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f7557]) ).
fof(f10750,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_822
| ~ spl0_1320 ),
inference(superposition,[],[f10339,f7655]) ).
fof(f7655,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg)
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f7654]) ).
fof(f32260,plain,
( spl0_2503
| ~ spl0_798
| ~ spl0_823
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10760,f10338,f7658,f7557,f32258]) ).
fof(f32258,plain,
( spl0_2503
<=> ! [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_2503])]) ).
fof(f7658,plain,
( spl0_823
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f10760,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_798
| ~ spl0_823
| ~ spl0_1320 ),
inference(forward_demodulation,[],[f10749,f7558]) ).
fof(f10749,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_823
| ~ spl0_1320 ),
inference(superposition,[],[f10339,f7659]) ).
fof(f7659,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg)
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f7658]) ).
fof(f32256,plain,
( spl0_2502
| ~ spl0_798
| ~ spl0_824
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10759,f10338,f7662,f7557,f32254]) ).
fof(f32254,plain,
( spl0_2502
<=> ! [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_2502])]) ).
fof(f7662,plain,
( spl0_824
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f10759,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_798
| ~ spl0_824
| ~ spl0_1320 ),
inference(forward_demodulation,[],[f10748,f7558]) ).
fof(f10748,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_824
| ~ spl0_1320 ),
inference(superposition,[],[f10339,f7663]) ).
fof(f7663,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg)
| ~ spl0_824 ),
inference(avatar_component_clause,[],[f7662]) ).
fof(f32252,plain,
( spl0_2501
| ~ spl0_798
| ~ spl0_821
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10757,f10338,f7650,f7557,f32250]) ).
fof(f32250,plain,
( spl0_2501
<=> ! [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_2501])]) ).
fof(f7650,plain,
( spl0_821
<=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f10757,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
| ~ spl0_798
| ~ spl0_821
| ~ spl0_1320 ),
inference(forward_demodulation,[],[f10746,f7558]) ).
fof(f10746,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_821
| ~ spl0_1320 ),
inference(superposition,[],[f10339,f7651]) ).
fof(f7651,plain,
( ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg)
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f7650]) ).
fof(f32248,plain,
( spl0_2500
| ~ spl0_875
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10755,f10338,f7879,f32246]) ).
fof(f32246,plain,
( spl0_2500
<=> ! [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_2500])]) ).
fof(f10755,plain,
( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_875
| ~ spl0_1320 ),
inference(superposition,[],[f7880,f10339]) ).
fof(f32244,plain,
( spl0_2499
| ~ spl0_649
| ~ spl0_1207
| ~ spl0_1319 ),
inference(avatar_split_clause,[],[f10745,f10334,f9649,f6138,f32242]) ).
fof(f32242,plain,
( spl0_2499
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f9649,plain,
( spl0_1207
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f10334,plain,
( spl0_1319
<=> ! [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_1319])]) ).
fof(f10745,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_1207
| ~ spl0_1319 ),
inference(forward_demodulation,[],[f10742,f9650]) ).
fof(f9650,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1207 ),
inference(avatar_component_clause,[],[f9649]) ).
fof(f10742,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_649
| ~ spl0_1319 ),
inference(superposition,[],[f10335,f6140]) ).
fof(f10335,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_1319 ),
inference(avatar_component_clause,[],[f10334]) ).
fof(f32232,plain,
( spl0_2497
| ~ spl0_2498
| ~ spl0_120
| ~ spl0_1288 ),
inference(avatar_split_clause,[],[f10561,f10205,f4021,f32229,f32226]) ).
fof(f32226,plain,
( spl0_2497
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2497])]) ).
fof(f32229,plain,
( spl0_2498
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).
fof(f10561,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_120
| ~ spl0_1288 ),
inference(resolution,[],[f10206,f4022]) ).
fof(f32224,plain,
( spl0_2496
| ~ spl0_719
| ~ spl0_745
| ~ spl0_913
| ~ spl0_1283 ),
inference(avatar_split_clause,[],[f10542,f10185,f8032,f7329,f7216,f32221]) ).
fof(f32221,plain,
( spl0_2496
<=> 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_2496])]) ).
fof(f7216,plain,
( spl0_719
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f7329,plain,
( spl0_745
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f10542,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_719
| ~ spl0_745
| ~ spl0_913
| ~ spl0_1283 ),
inference(forward_demodulation,[],[f10541,f7218]) ).
fof(f7218,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_719 ),
inference(avatar_component_clause,[],[f7216]) ).
fof(f10541,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_745
| ~ spl0_913
| ~ spl0_1283 ),
inference(forward_demodulation,[],[f10537,f8034]) ).
fof(f10537,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_745
| ~ spl0_1283 ),
inference(superposition,[],[f10186,f7331]) ).
fof(f7331,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_745 ),
inference(avatar_component_clause,[],[f7329]) ).
fof(f32219,plain,
( spl0_2495
| ~ spl0_654
| ~ spl0_1263 ),
inference(avatar_split_clause,[],[f10452,f10105,f6160,f32216]) ).
fof(f32216,plain,
( spl0_2495
<=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2495])]) ).
fof(f10105,plain,
( spl0_1263
<=> ! [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_1263])]) ).
fof(f10452,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_654
| ~ spl0_1263 ),
inference(resolution,[],[f10106,f6162]) ).
fof(f10106,plain,
( ! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 )
| ~ spl0_1263 ),
inference(avatar_component_clause,[],[f10105]) ).
fof(f32214,plain,
( spl0_2494
| ~ spl0_799
| ~ spl0_1179 ),
inference(avatar_split_clause,[],[f9903,f9536,f7561,f32212]) ).
fof(f32212,plain,
( spl0_2494
<=> ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).
fof(f7561,plain,
( spl0_799
<=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f9536,plain,
( spl0_1179
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f9903,plain,
( ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_799
| ~ spl0_1179 ),
inference(superposition,[],[f9537,f7562]) ).
fof(f7562,plain,
( ! [X3] : c_minus(X3,c_0,tc_nat) = X3
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7561]) ).
fof(f9537,plain,
( ! [X21,X15] :
( c_0 != c_minus(X15,X21,tc_nat)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1179 ),
inference(avatar_component_clause,[],[f9536]) ).
fof(f32210,plain,
( spl0_2493
| ~ spl0_1021
| ~ spl0_1103 ),
inference(avatar_split_clause,[],[f9303,f9011,f8544,f32208]) ).
fof(f32208,plain,
( spl0_2493
<=> ! [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_2493])]) ).
fof(f8544,plain,
( spl0_1021
<=> ! [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_1021])]) ).
fof(f9011,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(f9303,plain,
( ! [X0,X1] : ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oknows(X1,c_List_Olist_ONil),tc_Message_Omsg)
| ~ spl0_1021
| ~ spl0_1103 ),
inference(resolution,[],[f9012,f8545]) ).
fof(f8545,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_1021 ),
inference(avatar_component_clause,[],[f8544]) ).
fof(f9012,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,[],[f9011]) ).
fof(f32206,plain,
( spl0_2492
| ~ spl0_897
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f9278,f8959,f7967,f32204]) ).
fof(f32204,plain,
( spl0_2492
<=> ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2492])]) ).
fof(f7967,plain,
( spl0_897
<=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f9278,plain,
( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_897
| ~ spl0_1090 ),
inference(superposition,[],[f7968,f8960]) ).
fof(f7968,plain,
( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_897 ),
inference(avatar_component_clause,[],[f7967]) ).
fof(f32202,plain,
( spl0_2491
| ~ spl0_16
| ~ spl0_1079 ),
inference(avatar_split_clause,[],[f9269,f8914,f3510,f32200]) ).
fof(f32200,plain,
( spl0_2491
<=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2491])]) ).
fof(f8914,plain,
( spl0_1079
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f9269,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_16
| ~ spl0_1079 ),
inference(resolution,[],[f8915,f3512]) ).
fof(f8915,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 )
| ~ spl0_1079 ),
inference(avatar_component_clause,[],[f8914]) ).
fof(f32198,plain,
( spl0_2490
| ~ spl0_59
| ~ spl0_1075 ),
inference(avatar_split_clause,[],[f9261,f8897,f3725,f32195]) ).
fof(f32195,plain,
( spl0_2490
<=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).
fof(f32167,plain,
( spl0_2489
| ~ spl0_897
| ~ spl0_2461 ),
inference(avatar_split_clause,[],[f32075,f31673,f7967,f32165]) ).
fof(f31673,plain,
( spl0_2461
<=> ! [X0,X1] :
( c_in(X1,c_union(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).
fof(f32075,plain,
( ! [X0] : c_in(v_Aa,c_union(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_897
| ~ spl0_2461 ),
inference(resolution,[],[f31674,f7968]) ).
fof(f31674,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent)
| c_in(X1,c_union(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_2461 ),
inference(avatar_component_clause,[],[f31673]) ).
fof(f32155,plain,
( spl0_2488
| ~ spl0_116
| ~ spl0_2011 ),
inference(avatar_split_clause,[],[f21828,f20968,f4005,f32153]) ).
fof(f32153,plain,
( spl0_2488
<=> ! [X0,X1] : c_minus(c_List_Oset(v_evs3,tc_Event_Oevent),X0,tc_set(tc_Event_Oevent)) = c_minus(c_List_Oset(v_evs3,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_2488])]) ).
fof(f20968,plain,
( spl0_2011
<=> ! [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_2011])]) ).
fof(f21828,plain,
( ! [X0,X1] : c_minus(c_List_Oset(v_evs3,tc_Event_Oevent),X0,tc_set(tc_Event_Oevent)) = c_minus(c_List_Oset(v_evs3,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_116
| ~ spl0_2011 ),
inference(resolution,[],[f20969,f4006]) ).
fof(f20969,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_2011 ),
inference(avatar_component_clause,[],[f20968]) ).
fof(f32151,plain,
( spl0_2487
| ~ spl0_752
| ~ spl0_1798 ),
inference(avatar_split_clause,[],[f18211,f17129,f7371,f32148]) ).
fof(f32148,plain,
( spl0_2487
<=> 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_evs3,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evs3,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2487])]) ).
fof(f17129,plain,
( spl0_1798
<=> ! [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_1798])]) ).
fof(f18211,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_evs3,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oremdups(v_evs3,tc_Event_Oevent)
| ~ spl0_752
| ~ spl0_1798 ),
inference(resolution,[],[f17130,f7373]) ).
fof(f17130,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_1798 ),
inference(avatar_component_clause,[],[f17129]) ).
fof(f32142,plain,
( ~ spl0_5
| spl0_2486
| ~ spl0_751
| ~ spl0_2084 ),
inference(avatar_split_clause,[],[f23566,f23053,f7366,f32139,f3455]) ).
fof(f23053,plain,
( spl0_2084
<=> ! [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_2084])]) ).
fof(f23566,plain,
( c_in(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_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ spl0_751
| ~ spl0_2084 ),
inference(resolution,[],[f23054,f7368]) ).
fof(f23054,plain,
( ! [X86,X102,X13] :
( ~ c_in(c_Event_Oevent_OGets(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)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ spl0_2084 ),
inference(avatar_component_clause,[],[f23053]) ).
fof(f32109,plain,
( spl0_2485
| spl0_7
| ~ spl0_2011 ),
inference(avatar_split_clause,[],[f21893,f20968,f3465,f32107]) ).
fof(f32107,plain,
( spl0_2485
<=> ! [X0] : c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),c_insert(c_Message_Omsg_ONonce(v_NB),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2485])]) ).
fof(f21893,plain,
( ! [X0] : c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),c_insert(c_Message_Omsg_ONonce(v_NB),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| spl0_7
| ~ spl0_2011 ),
inference(resolution,[],[f20969,f3467]) ).
fof(f3467,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| spl0_7 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f32096,plain,
( spl0_2484
| ~ spl0_116
| ~ spl0_1996 ),
inference(avatar_split_clause,[],[f21505,f20908,f4005,f32094]) ).
fof(f32094,plain,
( spl0_2484
<=> ! [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_evs3,tc_Event_Oevent) = c_List_Olist__inter(X1,v_evs3,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2484])]) ).
fof(f20908,plain,
( spl0_1996
<=> ! [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_1996])]) ).
fof(f21505,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_evs3,tc_Event_Oevent) = c_List_Olist__inter(X1,v_evs3,tc_Event_Oevent)
| ~ spl0_116
| ~ spl0_1996 ),
inference(resolution,[],[f20909,f4006]) ).
fof(f20909,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_1996 ),
inference(avatar_component_clause,[],[f20908]) ).
fof(f32074,plain,
( spl0_2483
| ~ spl0_752
| ~ spl0_1841 ),
inference(avatar_split_clause,[],[f19011,f17370,f7371,f32071]) ).
fof(f17370,plain,
( spl0_1841
<=> ! [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_1841])]) ).
fof(f19011,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_evs3)),tc_Message_Omsg)
| ~ spl0_752
| ~ spl0_1841 ),
inference(resolution,[],[f17371,f7373]) ).
fof(f17371,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_1841 ),
inference(avatar_component_clause,[],[f17370]) ).
fof(f32020,plain,
( spl0_2482
| ~ spl0_5
| ~ spl0_2013 ),
inference(avatar_split_clause,[],[f22056,f20976,f3455,f32018]) ).
fof(f32018,plain,
( spl0_2482
<=> ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evs3,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_2482])]) ).
fof(f22056,plain,
( ! [X0] : c_minus(X0,c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent))) = c_minus(c_insert(v_evs3,X0,tc_List_Olist(tc_Event_Oevent)),c_Yahalom_Oyahalom,tc_set(tc_List_Olist(tc_Event_Oevent)))
| ~ spl0_5
| ~ spl0_2013 ),
inference(resolution,[],[f20977,f3457]) ).
fof(f3457,plain,
( c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f3455]) ).
fof(f32016,plain,
( spl0_2481
| spl0_6
| ~ spl0_2011 ),
inference(avatar_split_clause,[],[f21884,f20968,f3460,f32014]) ).
fof(f32014,plain,
( spl0_2481
<=> ! [X0] : c_minus(c_Event_Oused(v_evs3),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Event_Oused(v_evs3),c_insert(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2481])]) ).
fof(f3460,plain,
( spl0_6
<=> c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f21884,plain,
( ! [X0] : c_minus(c_Event_Oused(v_evs3),X0,tc_set(tc_Message_Omsg)) = c_minus(c_Event_Oused(v_evs3),c_insert(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| spl0_6
| ~ spl0_2011 ),
inference(resolution,[],[f20969,f3462]) ).
fof(f3462,plain,
( ~ c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(v_evs3),tc_Message_Omsg)
| spl0_6 ),
inference(avatar_component_clause,[],[f3460]) ).
fof(f31995,plain,
( spl0_2480
| ~ spl0_4
| ~ spl0_2053 ),
inference(avatar_split_clause,[],[f22813,f22437,f3450,f31993]) ).
fof(f31993,plain,
( spl0_2480
<=> ! [X0,X1] : c_insert(X0,c_Event_Oknows(c_Message_Oagent_OSpy,X1),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_Aa,X0),X1,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2480])]) ).
fof(f22437,plain,
( spl0_2053
<=> ! [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_2053])]) ).
fof(f22813,plain,
( ! [X0,X1] : c_insert(X0,c_Event_Oknows(c_Message_Oagent_OSpy,X1),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_Aa,X0),X1,tc_Event_Oevent))
| ~ spl0_4
| ~ spl0_2053 ),
inference(resolution,[],[f22438,f3452]) ).
fof(f22438,plain,
( ! [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) )
| ~ spl0_2053 ),
inference(avatar_component_clause,[],[f22437]) ).
fof(f31982,plain,
spl0_2479,
inference(avatar_split_clause,[],[f6,f31980]) ).
fof(f31980,plain,
( spl0_2479
<=> ! [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_2479])]) ).
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(f31959,plain,
( spl0_2478
| ~ spl0_1305
| ~ spl0_2284 ),
inference(avatar_split_clause,[],[f27874,f27363,f10273,f31957]) ).
fof(f31957,plain,
( spl0_2478
<=> ! [X0,X1] :
( c_in(X1,c_union(c_Message_OsymKeys,X0,tc_nat),tc_nat)
| ~ c_in(X1,c_insert(v_KAB,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).
fof(f10273,plain,
( spl0_1305
<=> ! [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_1305])]) ).
fof(f27363,plain,
( spl0_2284
<=> ! [X0] : c_union(c_Message_OsymKeys,c_insert(v_KAB,X0,tc_nat),tc_nat) = c_union(c_Message_OsymKeys,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).
fof(f27874,plain,
( ! [X0,X1] :
( c_in(X1,c_union(c_Message_OsymKeys,X0,tc_nat),tc_nat)
| ~ c_in(X1,c_insert(v_KAB,X0,tc_nat),tc_nat) )
| ~ spl0_1305
| ~ spl0_2284 ),
inference(superposition,[],[f10274,f27364]) ).
fof(f27364,plain,
( ! [X0] : c_union(c_Message_OsymKeys,c_insert(v_KAB,X0,tc_nat),tc_nat) = c_union(c_Message_OsymKeys,X0,tc_nat)
| ~ spl0_2284 ),
inference(avatar_component_clause,[],[f27363]) ).
fof(f10274,plain,
( ! [X1,X4,X12,X13] :
( c_in(X4,c_union(X12,X13,X1),X1)
| ~ c_in(X4,X13,X1) )
| ~ spl0_1305 ),
inference(avatar_component_clause,[],[f10273]) ).
fof(f31955,plain,
spl0_2477,
inference(avatar_split_clause,[],[f10,f31953]) ).
fof(f31953,plain,
( spl0_2477
<=> ! [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_2477])]) ).
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(f31913,plain,
spl0_2476,
inference(avatar_split_clause,[],[f9,f31911]) ).
fof(f31911,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_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_2476])]) ).
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(f31909,plain,
spl0_2475,
inference(avatar_split_clause,[],[f8,f31907]) ).
fof(f31907,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_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_2475])]) ).
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(f31886,plain,
spl0_2474,
inference(avatar_split_clause,[],[f7,f31884]) ).
fof(f31884,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_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_2474])]) ).
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(f31870,plain,
spl0_2473,
inference(avatar_split_clause,[],[f2959,f31868]) ).
fof(f31868,plain,
( spl0_2473
<=> ! [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_2473])]) ).
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(f31849,plain,
( spl0_2472
| ~ spl0_1304
| ~ spl0_2276 ),
inference(avatar_split_clause,[],[f27566,f27289,f10269,f31847]) ).
fof(f31847,plain,
( spl0_2472
<=> ! [X0,X1] :
( c_in(X1,c_union(X0,c_Message_OsymKeys,tc_nat),tc_nat)
| ~ c_in(X1,c_insert(v_KAB,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).
fof(f10269,plain,
( spl0_1304
<=> ! [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_1304])]) ).
fof(f27289,plain,
( spl0_2276
<=> ! [X0] : c_union(c_insert(v_KAB,X0,tc_nat),c_Message_OsymKeys,tc_nat) = c_union(X0,c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).
fof(f27566,plain,
( ! [X0,X1] :
( c_in(X1,c_union(X0,c_Message_OsymKeys,tc_nat),tc_nat)
| ~ c_in(X1,c_insert(v_KAB,X0,tc_nat),tc_nat) )
| ~ spl0_1304
| ~ spl0_2276 ),
inference(superposition,[],[f10270,f27290]) ).
fof(f27290,plain,
( ! [X0] : c_union(c_insert(v_KAB,X0,tc_nat),c_Message_OsymKeys,tc_nat) = c_union(X0,c_Message_OsymKeys,tc_nat)
| ~ spl0_2276 ),
inference(avatar_component_clause,[],[f27289]) ).
fof(f10270,plain,
( ! [X1,X4,X12,X13] :
( c_in(X4,c_union(X12,X13,X1),X1)
| ~ c_in(X4,X12,X1) )
| ~ spl0_1304 ),
inference(avatar_component_clause,[],[f10269]) ).
fof(f31845,plain,
spl0_2471,
inference(avatar_split_clause,[],[f3,f31843]) ).
fof(f31843,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(f31792,plain,
spl0_2470,
inference(avatar_split_clause,[],[f2962,f31790]) ).
fof(f31790,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(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(f31788,plain,
spl0_2469,
inference(avatar_split_clause,[],[f2961,f31786]) ).
fof(f31786,plain,
( spl0_2469
<=> ! [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_2469])]) ).
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(f31784,plain,
spl0_2468,
inference(avatar_split_clause,[],[f2941,f31782]) ).
fof(f31782,plain,
( spl0_2468
<=> ! [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_2468])]) ).
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(f31741,plain,
( spl0_2467
| ~ spl0_1305
| ~ spl0_2105 ),
inference(avatar_split_clause,[],[f23791,f23663,f10273,f31739]) ).
fof(f31739,plain,
( spl0_2467
<=> ! [X0,X1] :
( c_in(X1,c_union(c_Event_Obad,X0,tc_Message_Oagent),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2467])]) ).
fof(f23663,plain,
( spl0_2105
<=> ! [X0] : c_union(c_Event_Obad,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) = c_union(c_Event_Obad,X0,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f23791,plain,
( ! [X0,X1] :
( c_in(X1,c_union(c_Event_Obad,X0,tc_Message_Oagent),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_1305
| ~ spl0_2105 ),
inference(superposition,[],[f10274,f23664]) ).
fof(f23664,plain,
( ! [X0] : c_union(c_Event_Obad,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) = c_union(c_Event_Obad,X0,tc_Message_Oagent)
| ~ spl0_2105 ),
inference(avatar_component_clause,[],[f23663]) ).
fof(f31725,plain,
spl0_2466,
inference(avatar_split_clause,[],[f2958,f31723]) ).
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(f31721,plain,
spl0_2465,
inference(avatar_split_clause,[],[f2957,f31719]) ).
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(f31717,plain,
spl0_2464,
inference(avatar_split_clause,[],[f2956,f31715]) ).
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(f31713,plain,
spl0_2463,
inference(avatar_split_clause,[],[f12,f31711]) ).
fof(f31711,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(f31709,plain,
spl0_2462,
inference(avatar_split_clause,[],[f11,f31707]) ).
fof(f31707,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(f31675,plain,
( spl0_2461
| ~ spl0_1304
| ~ spl0_2102 ),
inference(avatar_split_clause,[],[f23732,f23542,f10269,f31673]) ).
fof(f23542,plain,
( spl0_2102
<=> ! [X0] : c_union(c_insert(v_Aa,X0,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) = c_union(X0,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f23732,plain,
( ! [X0,X1] :
( c_in(X1,c_union(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent)
| ~ c_in(X1,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_1304
| ~ spl0_2102 ),
inference(superposition,[],[f10270,f23543]) ).
fof(f23543,plain,
( ! [X0] : c_union(c_insert(v_Aa,X0,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) = c_union(X0,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_2102 ),
inference(avatar_component_clause,[],[f23542]) ).
fof(f31661,plain,
spl0_2460,
inference(avatar_split_clause,[],[f2966,f31659]) ).
fof(f31659,plain,
( spl0_2460
<=> ! [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_2460])]) ).
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(f31657,plain,
spl0_2459,
inference(avatar_split_clause,[],[f2965,f31655]) ).
fof(f31655,plain,
( spl0_2459
<=> ! [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_2459])]) ).
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(f31653,plain,
spl0_2458,
inference(avatar_split_clause,[],[f2964,f31651]) ).
fof(f31651,plain,
( spl0_2458
<=> ! [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_2458])]) ).
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(f31649,plain,
spl0_2457,
inference(avatar_split_clause,[],[f2963,f31647]) ).
fof(f31647,plain,
( spl0_2457
<=> ! [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_2457])]) ).
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(f31605,plain,
( spl0_2456
| ~ spl0_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1812
| ~ spl0_1813
| ~ spl0_2455 ),
inference(avatar_split_clause,[],[f31601,f31596,f17243,f17239,f14600,f10185,f8910,f7565,f3725,f31603]) ).
fof(f31603,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(f14600,plain,
( spl0_1683
<=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f17239,plain,
( spl0_1812
<=> ! [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_1812])]) ).
fof(f17243,plain,
( spl0_1813
<=> ! [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_1813])]) ).
fof(f31596,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(f31601,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_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1812
| ~ spl0_1813
| ~ spl0_2455 ),
inference(forward_demodulation,[],[f31600,f18409]) ).
fof(f18409,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_59
| ~ spl0_1812 ),
inference(resolution,[],[f17240,f3727]) ).
fof(f17240,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_1812 ),
inference(avatar_component_clause,[],[f17239]) ).
fof(f31600,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_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1813
| ~ spl0_2455 ),
inference(forward_demodulation,[],[f31599,f15398]) ).
fof(f15398,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_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683 ),
inference(forward_demodulation,[],[f15397,f7567]) ).
fof(f15397,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_1078
| ~ spl0_1283
| ~ spl0_1683 ),
inference(forward_demodulation,[],[f15396,f8911]) ).
fof(f15396,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_1683 ),
inference(superposition,[],[f10186,f14601]) ).
fof(f14601,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_1683 ),
inference(avatar_component_clause,[],[f14600]) ).
fof(f31599,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_59
| ~ spl0_1813
| ~ spl0_2455 ),
inference(forward_demodulation,[],[f31597,f18410]) ).
fof(f18410,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_59
| ~ spl0_1813 ),
inference(resolution,[],[f17244,f3727]) ).
fof(f17244,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_1813 ),
inference(avatar_component_clause,[],[f17243]) ).
fof(f31597,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,[],[f31596]) ).
fof(f31598,plain,
spl0_2455,
inference(avatar_split_clause,[],[f3411,f31596]) ).
fof(f3411,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,[],[f3410,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(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_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,[],[f3409,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(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_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(f31461,plain,
spl0_2454,
inference(avatar_split_clause,[],[f1620,f31459]) ).
fof(f31459,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(f31457,plain,
spl0_2453,
inference(avatar_split_clause,[],[f1501,f31455]) ).
fof(f31455,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(f31453,plain,
spl0_2452,
inference(avatar_split_clause,[],[f5,f31451]) ).
fof(f31451,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(f31449,plain,
spl0_2451,
inference(avatar_split_clause,[],[f4,f31447]) ).
fof(f31447,plain,
( spl0_2451
<=> ! [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_2451])]) ).
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(f31409,plain,
spl0_2450,
inference(avatar_split_clause,[],[f1503,f31407]) ).
fof(f31407,plain,
( spl0_2450
<=> ! [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_2450])]) ).
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(f31405,plain,
( spl0_2449
| ~ spl0_1587
| ~ spl0_2418 ),
inference(avatar_split_clause,[],[f31311,f30960,f12875,f31403]) ).
fof(f31403,plain,
( spl0_2449
<=> ! [X0] : ~ c_in(v_KAB,c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2449])]) ).
fof(f12875,plain,
( spl0_1587
<=> ! [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_1587])]) ).
fof(f30960,plain,
( spl0_2418
<=> ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_Message_OsymKeys,tc_nat),X0,tc_nat,tc_nat)
| ~ c_in(v_KAB,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2418])]) ).
fof(f31311,plain,
( ! [X0] : ~ c_in(v_KAB,c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),tc_nat)
| ~ spl0_1587
| ~ spl0_2418 ),
inference(trivial_inequality_removal,[],[f31308]) ).
fof(f31308,plain,
( ! [X0] :
( c_emptyset != c_emptyset
| ~ c_in(v_KAB,c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),tc_nat) )
| ~ spl0_1587
| ~ spl0_2418 ),
inference(superposition,[],[f30961,f12876]) ).
fof(f12876,plain,
( ! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1)
| ~ spl0_1587 ),
inference(avatar_component_clause,[],[f12875]) ).
fof(f30961,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_Message_OsymKeys,tc_nat),X0,tc_nat,tc_nat)
| ~ c_in(v_KAB,X0,tc_nat) )
| ~ spl0_2418 ),
inference(avatar_component_clause,[],[f30960]) ).
fof(f31401,plain,
spl0_2448,
inference(avatar_split_clause,[],[f1369,f31399]) ).
fof(f31399,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(f31397,plain,
spl0_2447,
inference(avatar_split_clause,[],[f1368,f31395]) ).
fof(f31395,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(f31381,plain,
( spl0_2446
| ~ spl0_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1813
| ~ spl0_2445 ),
inference(avatar_split_clause,[],[f31377,f31373,f17243,f14600,f10185,f8910,f7565,f3725,f31379]) ).
fof(f31379,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(f31373,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(f31377,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_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1813
| ~ spl0_2445 ),
inference(forward_demodulation,[],[f31376,f15398]) ).
fof(f31376,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_59
| ~ spl0_1813
| ~ spl0_2445 ),
inference(forward_demodulation,[],[f31374,f18410]) ).
fof(f31374,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,[],[f31373]) ).
fof(f31375,plain,
spl0_2445,
inference(avatar_split_clause,[],[f3405,f31373]) ).
fof(f3405,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,[],[f3404,f2156]) ).
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_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,[],[f3403,f2154]) ).
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_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(f31355,plain,
spl0_2444,
inference(avatar_split_clause,[],[f2960,f31353]) ).
fof(f31353,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(f31351,plain,
spl0_2443,
inference(avatar_split_clause,[],[f2955,f31349]) ).
fof(f31349,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(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(f31303,plain,
spl0_2442,
inference(avatar_split_clause,[],[f1791,f31301]) ).
fof(f31301,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(f31278,plain,
( spl0_2441
| ~ spl0_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1813
| ~ spl0_2440 ),
inference(avatar_split_clause,[],[f31274,f31270,f17243,f14600,f10185,f8910,f7565,f3725,f31276]) ).
fof(f31276,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(f31270,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(f31274,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_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1813
| ~ spl0_2440 ),
inference(forward_demodulation,[],[f31273,f15398]) ).
fof(f31273,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_59
| ~ spl0_1813
| ~ spl0_2440 ),
inference(forward_demodulation,[],[f31271,f18410]) ).
fof(f31271,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,[],[f31270]) ).
fof(f31272,plain,
spl0_2440,
inference(avatar_split_clause,[],[f3408,f31270]) ).
fof(f3408,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,[],[f3407,f2156]) ).
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_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,[],[f3406,f2154]) ).
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_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(f31268,plain,
spl0_2439,
inference(avatar_split_clause,[],[f2948,f31266]) ).
fof(f31266,plain,
( spl0_2439
<=> ! [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_2439])]) ).
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(f31229,plain,
( spl0_2438
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1812
| ~ spl0_2437 ),
inference(avatar_split_clause,[],[f31225,f31220,f17239,f8897,f3725,f31227]) ).
fof(f31227,plain,
( spl0_2438
<=> ! [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_2438])]) ).
fof(f31220,plain,
( spl0_2437
<=> ! [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_2437])]) ).
fof(f31225,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_59
| ~ spl0_1075
| ~ spl0_1812
| ~ spl0_2437 ),
inference(forward_demodulation,[],[f31224,f9261]) ).
fof(f31224,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_59
| ~ spl0_1812
| ~ spl0_2437 ),
inference(forward_demodulation,[],[f31223,f18409]) ).
fof(f31223,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_59
| ~ spl0_1812
| ~ spl0_2437 ),
inference(forward_demodulation,[],[f31221,f18409]) ).
fof(f31221,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_2437 ),
inference(avatar_component_clause,[],[f31220]) ).
fof(f31222,plain,
spl0_2437,
inference(avatar_split_clause,[],[f1451,f31220]) ).
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(f31184,plain,
spl0_2436,
inference(avatar_split_clause,[],[f1504,f31182]) ).
fof(f31182,plain,
( spl0_2436
<=> ! [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_2436])]) ).
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(f31157,plain,
( spl0_2435
| ~ spl0_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1813
| ~ spl0_2434 ),
inference(avatar_split_clause,[],[f31153,f31149,f17243,f14600,f10185,f8910,f7565,f3725,f31155]) ).
fof(f31155,plain,
( spl0_2435
<=> ! [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_2435])]) ).
fof(f31149,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_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_2434])]) ).
fof(f31153,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_59
| ~ spl0_800
| ~ spl0_1078
| ~ spl0_1283
| ~ spl0_1683
| ~ spl0_1813
| ~ spl0_2434 ),
inference(forward_demodulation,[],[f31152,f15398]) ).
fof(f31152,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_59
| ~ spl0_1813
| ~ spl0_2434 ),
inference(forward_demodulation,[],[f31150,f18410]) ).
fof(f31150,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_2434 ),
inference(avatar_component_clause,[],[f31149]) ).
fof(f31151,plain,
spl0_2434,
inference(avatar_split_clause,[],[f3402,f31149]) ).
fof(f3402,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,[],[f3401,f2156]) ).
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_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,[],[f3400,f2154]) ).
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_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(f31147,plain,
spl0_2433,
inference(avatar_split_clause,[],[f54,f31145]) ).
fof(f31145,plain,
( spl0_2433
<=> ! [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_2433])]) ).
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(f31143,plain,
spl0_2432,
inference(avatar_split_clause,[],[f51,f31141]) ).
fof(f31141,plain,
( spl0_2432
<=> ! [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_2432])]) ).
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(f31131,plain,
( ~ spl0_2431
| ~ spl0_1464
| ~ spl0_2414 ),
inference(avatar_split_clause,[],[f31027,f30800,f11319,f31128]) ).
fof(f31128,plain,
( spl0_2431
<=> c_in(v_KAB,c_uminus(c_Message_OsymKeys,tc_set(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2431])]) ).
fof(f11319,plain,
( spl0_1464
<=> ! [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_1464])]) ).
fof(f30800,plain,
( spl0_2414
<=> ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,tc_nat),c_Message_OsymKeys,tc_nat,tc_nat)
| ~ c_in(v_KAB,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2414])]) ).
fof(f31027,plain,
( ~ c_in(v_KAB,c_uminus(c_Message_OsymKeys,tc_set(tc_nat)),tc_nat)
| ~ spl0_1464
| ~ spl0_2414 ),
inference(trivial_inequality_removal,[],[f31026]) ).
fof(f31026,plain,
( c_emptyset != c_emptyset
| ~ c_in(v_KAB,c_uminus(c_Message_OsymKeys,tc_set(tc_nat)),tc_nat)
| ~ spl0_1464
| ~ spl0_2414 ),
inference(superposition,[],[f30801,f11320]) ).
fof(f11320,plain,
( ! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1)
| ~ spl0_1464 ),
inference(avatar_component_clause,[],[f11319]) ).
fof(f30801,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,tc_nat),c_Message_OsymKeys,tc_nat,tc_nat)
| ~ c_in(v_KAB,X0,tc_nat) )
| ~ spl0_2414 ),
inference(avatar_component_clause,[],[f30800]) ).
fof(f31118,plain,
( spl0_2430
| ~ spl0_1194
| ~ spl0_1543
| ~ spl0_2426 ),
inference(avatar_split_clause,[],[f31022,f31019,f12672,f9596,f31116]) ).
fof(f31116,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(f9596,plain,
( spl0_1194
<=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f31019,plain,
( spl0_2426
<=> ! [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_2426])]) ).
fof(f31022,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_1194
| ~ spl0_1543
| ~ spl0_2426 ),
inference(forward_demodulation,[],[f31020,f13772]) ).
fof(f13772,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1194
| ~ spl0_1543 ),
inference(superposition,[],[f9597,f12673]) ).
fof(f9597,plain,
( ! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3
| ~ spl0_1194 ),
inference(avatar_component_clause,[],[f9596]) ).
fof(f31020,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_2426 ),
inference(avatar_component_clause,[],[f31019]) ).
fof(f31114,plain,
( spl0_2429
| ~ spl0_1193
| ~ spl0_1543
| ~ spl0_2425 ),
inference(avatar_split_clause,[],[f31017,f31014,f12672,f9592,f31112]) ).
fof(f31112,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(f9592,plain,
( spl0_1193
<=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f31014,plain,
( spl0_2425
<=> ! [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_2425])]) ).
fof(f31017,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_1193
| ~ spl0_1543
| ~ spl0_2425 ),
inference(forward_demodulation,[],[f31015,f13773]) ).
fof(f13773,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1193
| ~ spl0_1543 ),
inference(superposition,[],[f9593,f12673]) ).
fof(f9593,plain,
( ! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3
| ~ spl0_1193 ),
inference(avatar_component_clause,[],[f9592]) ).
fof(f31015,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_2425 ),
inference(avatar_component_clause,[],[f31014]) ).
fof(f31110,plain,
( spl0_2428
| ~ spl0_1194
| ~ spl0_1543
| ~ spl0_2424 ),
inference(avatar_split_clause,[],[f31012,f31009,f12672,f9596,f31108]) ).
fof(f31108,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(f31009,plain,
( spl0_2424
<=> ! [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_2424])]) ).
fof(f31012,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_1194
| ~ spl0_1543
| ~ spl0_2424 ),
inference(forward_demodulation,[],[f31010,f13772]) ).
fof(f31010,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_2424 ),
inference(avatar_component_clause,[],[f31009]) ).
fof(f31106,plain,
( spl0_2427
| ~ spl0_1193
| ~ spl0_1543
| ~ spl0_2423 ),
inference(avatar_split_clause,[],[f31007,f31004,f12672,f9592,f31104]) ).
fof(f31104,plain,
( spl0_2427
<=> ! [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_2427])]) ).
fof(f31004,plain,
( spl0_2423
<=> ! [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_2423])]) ).
fof(f31007,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_1193
| ~ spl0_1543
| ~ spl0_2423 ),
inference(forward_demodulation,[],[f31005,f13773]) ).
fof(f31005,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_2423 ),
inference(avatar_component_clause,[],[f31004]) ).
fof(f31021,plain,
spl0_2426,
inference(avatar_split_clause,[],[f3399,f31019]) ).
fof(f3399,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(f31016,plain,
spl0_2425,
inference(avatar_split_clause,[],[f3398,f31014]) ).
fof(f3398,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(f31011,plain,
spl0_2424,
inference(avatar_split_clause,[],[f3397,f31009]) ).
fof(f3397,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(f31006,plain,
spl0_2423,
inference(avatar_split_clause,[],[f3396,f31004]) ).
fof(f3396,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(f31002,plain,
spl0_2422,
inference(avatar_split_clause,[],[f1622,f31000]) ).
fof(f31000,plain,
( spl0_2422
<=> ! [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_2422])]) ).
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(f30998,plain,
spl0_2421,
inference(avatar_split_clause,[],[f1505,f30996]) ).
fof(f30996,plain,
( spl0_2421
<=> ! [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_2421])]) ).
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(f30994,plain,
spl0_2420,
inference(avatar_split_clause,[],[f1188,f30992]) ).
fof(f30992,plain,
( spl0_2420
<=> ! [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_2420])]) ).
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(f30990,plain,
spl0_2419,
inference(avatar_split_clause,[],[f1187,f30988]) ).
fof(f30988,plain,
( spl0_2419
<=> ! [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_2419])]) ).
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(f30962,plain,
( spl0_2418
| ~ spl0_1867
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f28751,f28581,f17805,f30960]) ).
fof(f17805,plain,
( spl0_1867
<=> ! [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_1867])]) ).
fof(f28581,plain,
( spl0_2316
<=> c_Message_OsymKeys = c_insert(v_KAB,c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2316])]) ).
fof(f28751,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_Message_OsymKeys,tc_nat),X0,tc_nat,tc_nat)
| ~ c_in(v_KAB,X0,tc_nat) )
| ~ spl0_1867
| ~ spl0_2316 ),
inference(superposition,[],[f17806,f28583]) ).
fof(f28583,plain,
( c_Message_OsymKeys = c_insert(v_KAB,c_Message_OsymKeys,tc_nat)
| ~ spl0_2316 ),
inference(avatar_component_clause,[],[f28581]) ).
fof(f17806,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_1867 ),
inference(avatar_component_clause,[],[f17805]) ).
fof(f30958,plain,
( spl0_2417
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_2415 ),
inference(avatar_split_clause,[],[f30950,f30947,f8897,f3725,f30956]) ).
fof(f30956,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(f30947,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(f30950,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_59
| ~ spl0_1075
| ~ spl0_2415 ),
inference(forward_demodulation,[],[f30948,f9261]) ).
fof(f30948,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,[],[f30947]) ).
fof(f30954,plain,
spl0_2416,
inference(avatar_split_clause,[],[f1705,f30952]) ).
fof(f30952,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(f30949,plain,
spl0_2415,
inference(avatar_split_clause,[],[f1449,f30947]) ).
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(f30802,plain,
( spl0_2414
| ~ spl0_1866
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f28750,f28581,f17801,f30800]) ).
fof(f17801,plain,
( spl0_1866
<=> ! [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_1866])]) ).
fof(f28750,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,tc_nat),c_Message_OsymKeys,tc_nat,tc_nat)
| ~ c_in(v_KAB,X0,tc_nat) )
| ~ spl0_1866
| ~ spl0_2316 ),
inference(superposition,[],[f17802,f28583]) ).
fof(f17802,plain,
( ! [X1,X27,X12,X13] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1)
| ~ c_in(X27,X12,X1) )
| ~ spl0_1866 ),
inference(avatar_component_clause,[],[f17801]) ).
fof(f30798,plain,
spl0_2413,
inference(avatar_split_clause,[],[f1619,f30796]) ).
fof(f30796,plain,
( spl0_2413
<=> ! [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_2413])]) ).
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(f30794,plain,
spl0_2412,
inference(avatar_split_clause,[],[f1500,f30792]) ).
fof(f30792,plain,
( spl0_2412
<=> ! [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_2412])]) ).
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(f30790,plain,
spl0_2411,
inference(avatar_split_clause,[],[f1383,f30788]) ).
fof(f30788,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(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(f30786,plain,
spl0_2410,
inference(avatar_split_clause,[],[f1382,f30784]) ).
fof(f30784,plain,
( spl0_2410
<=> ! [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_2410])]) ).
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(f30782,plain,
spl0_2409,
inference(avatar_split_clause,[],[f85,f30780]) ).
fof(f30780,plain,
( spl0_2409
<=> ! [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_2409])]) ).
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(f30778,plain,
spl0_2408,
inference(avatar_split_clause,[],[f53,f30776]) ).
fof(f30776,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(f30774,plain,
spl0_2407,
inference(avatar_split_clause,[],[f50,f30772]) ).
fof(f30772,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(f30729,plain,
( spl0_2406
| ~ spl0_1194
| ~ spl0_1543
| ~ spl0_2401 ),
inference(avatar_split_clause,[],[f30690,f30687,f12672,f9596,f30727]) ).
fof(f30727,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(f30687,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(f30690,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_1194
| ~ spl0_1543
| ~ spl0_2401 ),
inference(forward_demodulation,[],[f30688,f13772]) ).
fof(f30688,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,[],[f30687]) ).
fof(f30725,plain,
( spl0_2405
| ~ spl0_1194
| ~ spl0_1543
| ~ spl0_2400 ),
inference(avatar_split_clause,[],[f30643,f30640,f12672,f9596,f30723]) ).
fof(f30723,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(f30640,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(f30643,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_1194
| ~ spl0_1543
| ~ spl0_2400 ),
inference(forward_demodulation,[],[f30641,f13772]) ).
fof(f30641,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,[],[f30640]) ).
fof(f30721,plain,
( spl0_2404
| ~ spl0_1193
| ~ spl0_1543
| ~ spl0_2399 ),
inference(avatar_split_clause,[],[f30638,f30635,f12672,f9592,f30719]) ).
fof(f30719,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(f30635,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(f30638,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_1193
| ~ spl0_1543
| ~ spl0_2399 ),
inference(forward_demodulation,[],[f30636,f13773]) ).
fof(f30636,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,[],[f30635]) ).
fof(f30717,plain,
( spl0_2403
| ~ spl0_1193
| ~ spl0_1543
| ~ spl0_2398 ),
inference(avatar_split_clause,[],[f30633,f30630,f12672,f9592,f30715]) ).
fof(f30715,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(f30630,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(f30633,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_1193
| ~ spl0_1543
| ~ spl0_2398 ),
inference(forward_demodulation,[],[f30631,f13773]) ).
fof(f30631,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,[],[f30630]) ).
fof(f30694,plain,
spl0_2402,
inference(avatar_split_clause,[],[f1502,f30692]) ).
fof(f30692,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(f30689,plain,
spl0_2401,
inference(avatar_split_clause,[],[f1448,f30687]) ).
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(f30675,plain,
( ~ spl0_819
| ~ spl0_2393 ),
inference(avatar_contradiction_clause,[],[f30674]) ).
fof(f30674,plain,
( $false
| ~ spl0_819
| ~ spl0_2393 ),
inference(trivial_inequality_removal,[],[f30653]) ).
fof(f30653,plain,
( c_emptyset != c_emptyset
| ~ spl0_819
| ~ spl0_2393 ),
inference(superposition,[],[f7643,f30478]) ).
fof(f30478,plain,
( c_emptyset = c_insert(v_KAB,c_emptyset,tc_nat)
| ~ spl0_2393 ),
inference(avatar_component_clause,[],[f30476]) ).
fof(f30476,plain,
( spl0_2393
<=> c_emptyset = c_insert(v_KAB,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2393])]) ).
fof(f30642,plain,
spl0_2400,
inference(avatar_split_clause,[],[f1444,f30640]) ).
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(f30637,plain,
spl0_2399,
inference(avatar_split_clause,[],[f1438,f30635]) ).
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(f30632,plain,
spl0_2398,
inference(avatar_split_clause,[],[f1434,f30630]) ).
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(f30628,plain,
spl0_2397,
inference(avatar_split_clause,[],[f55,f30626]) ).
fof(f30626,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(f30624,plain,
spl0_2396,
inference(avatar_split_clause,[],[f52,f30622]) ).
fof(f30622,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(f30486,plain,
spl0_2395,
inference(avatar_split_clause,[],[f1470,f30484]) ).
fof(f30484,plain,
( spl0_2395
<=> ! [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_2395])]) ).
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(f30482,plain,
( spl0_2393
| spl0_2394
| ~ spl0_1448
| ~ spl0_2310 ),
inference(avatar_split_clause,[],[f30330,f28175,f11255,f30480,f30476]) ).
fof(f30480,plain,
( spl0_2394
<=> ! [X0] : c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).
fof(f11255,plain,
( spl0_1448
<=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f28175,plain,
( spl0_2310
<=> ! [X0] :
( c_emptyset != c_union(c_Message_OsymKeys,X0,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).
fof(f30330,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat)
| c_emptyset = c_insert(v_KAB,c_emptyset,tc_nat) )
| ~ spl0_1448
| ~ spl0_2310 ),
inference(inner_rewriting,[],[f30328]) ).
fof(f30328,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat)
| c_emptyset = c_insert(v_KAB,c_union(X0,c_Message_OsymKeys,tc_nat),tc_nat) )
| ~ spl0_1448
| ~ spl0_2310 ),
inference(superposition,[],[f28176,f11256]) ).
fof(f11256,plain,
( ! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1)
| ~ spl0_1448 ),
inference(avatar_component_clause,[],[f11255]) ).
fof(f28176,plain,
( ! [X0] :
( c_emptyset != c_union(c_Message_OsymKeys,X0,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) )
| ~ spl0_2310 ),
inference(avatar_component_clause,[],[f28175]) ).
fof(f30474,plain,
spl0_2392,
inference(avatar_split_clause,[],[f83,f30472]) ).
fof(f30472,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__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_2392])]) ).
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(f30470,plain,
spl0_2391,
inference(avatar_split_clause,[],[f82,f30468]) ).
fof(f30468,plain,
( spl0_2391
<=> ! [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_2391])]) ).
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(f30466,plain,
spl0_2390,
inference(avatar_split_clause,[],[f20,f30464]) ).
fof(f30464,plain,
( spl0_2390
<=> ! [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_2390])]) ).
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(f30334,plain,
spl0_2389,
inference(avatar_split_clause,[],[f3303,f30332]) ).
fof(f30332,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(f3303,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,[],[f3302,f2156]) ).
fof(f3302,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,[],[f3301,f3048]) ).
fof(f3048,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(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_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,[],[f3103,f3265]) ).
fof(f3265,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,[],[f3264,f2156]) ).
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_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3263,f2154]) ).
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_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3069,f2156]) ).
fof(f3069,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(f3103,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(f30306,plain,
( spl0_2388
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2387 ),
inference(avatar_split_clause,[],[f30302,f30298,f21069,f11323,f10967,f7078,f6133,f30304]) ).
fof(f30304,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(f10967,plain,
( spl0_1378
<=> ! [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_1378])]) ).
fof(f11323,plain,
( spl0_1465
<=> ! [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_1465])]) ).
fof(f21069,plain,
( spl0_2033
<=> ! [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_2033])]) ).
fof(f30298,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(f30302,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2387 ),
inference(forward_demodulation,[],[f30301,f21070]) ).
fof(f21070,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_2033 ),
inference(avatar_component_clause,[],[f21069]) ).
fof(f30301,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2387 ),
inference(forward_demodulation,[],[f30299,f12324]) ).
fof(f12324,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465 ),
inference(forward_demodulation,[],[f12323,f7079]) ).
fof(f12323,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465 ),
inference(forward_demodulation,[],[f12285,f11631]) ).
fof(f11631,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_648
| ~ spl0_1378 ),
inference(superposition,[],[f10968,f6135]) ).
fof(f10968,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_1378 ),
inference(avatar_component_clause,[],[f10967]) ).
fof(f12285,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_689
| ~ spl0_1465 ),
inference(superposition,[],[f7079,f11324]) ).
fof(f11324,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_1465 ),
inference(avatar_component_clause,[],[f11323]) ).
fof(f30299,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,[],[f30298]) ).
fof(f30300,plain,
spl0_2387,
inference(avatar_split_clause,[],[f3300,f30298]) ).
fof(f3300,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,[],[f3299,f2156]) ).
fof(f3299,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,[],[f3298,f3048]) ).
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_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,[],[f3102,f3265]) ).
fof(f3102,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(f30296,plain,
spl0_2386,
inference(avatar_split_clause,[],[f3186,f30294]) ).
fof(f30294,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(f3186,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(f30292,plain,
spl0_2385,
inference(avatar_split_clause,[],[f3185,f30290]) ).
fof(f30290,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(f3185,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(f30288,plain,
spl0_2384,
inference(avatar_split_clause,[],[f1621,f30286]) ).
fof(f30286,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(f30284,plain,
spl0_2383,
inference(avatar_split_clause,[],[f1460,f30282]) ).
fof(f30282,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(f30280,plain,
spl0_2382,
inference(avatar_split_clause,[],[f19,f30278]) ).
fof(f30278,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(f30276,plain,
spl0_2381,
inference(avatar_split_clause,[],[f18,f30274]) ).
fof(f30274,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(f30169,plain,
spl0_2380,
inference(avatar_split_clause,[],[f3230,f30167]) ).
fof(f30167,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(f3230,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,f2837]) ).
fof(f2837,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_OMPair__eq__HPair_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(f30165,plain,
spl0_2379,
inference(avatar_split_clause,[],[f3155,f30163]) ).
fof(f30163,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(f3155,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(f30161,plain,
spl0_2378,
inference(avatar_split_clause,[],[f17,f30159]) ).
fof(f30159,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(f29873,plain,
spl0_2377,
inference(avatar_split_clause,[],[f3099,f29871]) ).
fof(f29871,plain,
( spl0_2377
<=> ! [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_2377])]) ).
fof(f3099,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(f29869,plain,
spl0_2376,
inference(avatar_split_clause,[],[f1998,f29867]) ).
fof(f29867,plain,
( spl0_2376
<=> ! [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_2376])]) ).
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(f29865,plain,
spl0_2375,
inference(avatar_split_clause,[],[f1992,f29863]) ).
fof(f29863,plain,
( spl0_2375
<=> ! [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_2375])]) ).
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(f29861,plain,
spl0_2374,
inference(avatar_split_clause,[],[f1986,f29859]) ).
fof(f29859,plain,
( spl0_2374
<=> ! [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_2374])]) ).
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(f29857,plain,
spl0_2373,
inference(avatar_split_clause,[],[f1980,f29855]) ).
fof(f29855,plain,
( spl0_2373
<=> ! [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_2373])]) ).
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(f29853,plain,
spl0_2372,
inference(avatar_split_clause,[],[f115,f29851]) ).
fof(f29851,plain,
( spl0_2372
<=> ! [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_2372])]) ).
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(f29849,plain,
spl0_2371,
inference(avatar_split_clause,[],[f84,f29847]) ).
fof(f29847,plain,
( spl0_2371
<=> ! [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_2371])]) ).
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(f29769,plain,
( spl0_2370
| ~ spl0_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2369 ),
inference(avatar_split_clause,[],[f29765,f29762,f21069,f7557,f7521,f29767]) ).
fof(f29767,plain,
( spl0_2370
<=> ! [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_2370])]) ).
fof(f29762,plain,
( spl0_2369
<=> ! [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_2369])]) ).
fof(f29765,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_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2369 ),
inference(forward_demodulation,[],[f29763,f21152]) ).
fof(f21152,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_789
| ~ spl0_798
| ~ spl0_2033 ),
inference(forward_demodulation,[],[f21073,f7522]) ).
fof(f21073,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_798
| ~ spl0_2033 ),
inference(superposition,[],[f21070,f7558]) ).
fof(f29763,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_2369 ),
inference(avatar_component_clause,[],[f29762]) ).
fof(f29764,plain,
spl0_2369,
inference(avatar_split_clause,[],[f3393,f29762]) ).
fof(f3393,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,[],[f3392,f2156]) ).
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_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,[],[f3391,f2154]) ).
fof(f3391,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(f29760,plain,
spl0_2368,
inference(avatar_split_clause,[],[f3173,f29758]) ).
fof(f29758,plain,
( spl0_2368
<=> ! [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_2368])]) ).
fof(f3173,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(f29756,plain,
spl0_2367,
inference(avatar_split_clause,[],[f3172,f29754]) ).
fof(f29754,plain,
( spl0_2367
<=> ! [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_2367])]) ).
fof(f3172,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(f29752,plain,
spl0_2366,
inference(avatar_split_clause,[],[f3070,f29750]) ).
fof(f29750,plain,
( spl0_2366
<=> ! [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_2366])]) ).
fof(f3070,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(f29748,plain,
spl0_2365,
inference(avatar_split_clause,[],[f16,f29746]) ).
fof(f29746,plain,
( spl0_2365
<=> ! [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_2365])]) ).
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(f29744,plain,
( spl0_2363
| ~ spl0_2364
| ~ spl0_1000
| ~ spl0_2359 ),
inference(avatar_split_clause,[],[f29604,f28996,f8457,f29741,f29737]) ).
fof(f29737,plain,
( spl0_2363
<=> c_0 = v_KAB ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2363])]) ).
fof(f29741,plain,
( spl0_2364
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_Message_OsymKeys ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f28996,plain,
( spl0_2359
<=> ! [X0] :
( c_Message_OsymKeys != c_insert(X0,c_emptyset,tc_nat)
| v_KAB = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2359])]) ).
fof(f29604,plain,
( c_SetInterval_OatMost(c_0,tc_nat) != c_Message_OsymKeys
| c_0 = v_KAB
| ~ spl0_1000
| ~ spl0_2359 ),
inference(superposition,[],[f28997,f8459]) ).
fof(f28997,plain,
( ! [X0] :
( c_Message_OsymKeys != c_insert(X0,c_emptyset,tc_nat)
| v_KAB = X0 )
| ~ spl0_2359 ),
inference(avatar_component_clause,[],[f28996]) ).
fof(f29727,plain,
( spl0_2362
| ~ spl0_1194
| ~ spl0_1543
| ~ spl0_2360 ),
inference(avatar_split_clause,[],[f29003,f29000,f12672,f9596,f29725]) ).
fof(f29725,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(f29000,plain,
( spl0_2360
<=> ! [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_2360])]) ).
fof(f29003,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_1194
| ~ spl0_1543
| ~ spl0_2360 ),
inference(forward_demodulation,[],[f29001,f13772]) ).
fof(f29001,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_2360 ),
inference(avatar_component_clause,[],[f29000]) ).
fof(f29723,plain,
( spl0_2361
| ~ spl0_1193
| ~ spl0_1543
| ~ spl0_2358 ),
inference(avatar_split_clause,[],[f28994,f28991,f12672,f9592,f29721]) ).
fof(f29721,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(f28991,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(f28994,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_1193
| ~ spl0_1543
| ~ spl0_2358 ),
inference(forward_demodulation,[],[f28992,f13773]) ).
fof(f28992,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,[],[f28991]) ).
fof(f29002,plain,
spl0_2360,
inference(avatar_split_clause,[],[f3350,f29000]) ).
fof(f3350,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(f28998,plain,
( spl0_2359
| ~ spl0_1441
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f28744,f28581,f11226,f28996]) ).
fof(f11226,plain,
( spl0_1441
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f28744,plain,
( ! [X0] :
( c_Message_OsymKeys != c_insert(X0,c_emptyset,tc_nat)
| v_KAB = X0 )
| ~ spl0_1441
| ~ spl0_2316 ),
inference(superposition,[],[f11227,f28583]) ).
fof(f11227,plain,
( ! [X18,X1,X27,X12] :
( c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1)
| X18 = X27 )
| ~ spl0_1441 ),
inference(avatar_component_clause,[],[f11226]) ).
fof(f28993,plain,
spl0_2358,
inference(avatar_split_clause,[],[f3349,f28991]) ).
fof(f3349,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(f28980,plain,
( spl0_2357
| ~ spl0_648
| ~ spl0_689
| ~ spl0_789
| ~ spl0_798
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2356 ),
inference(avatar_split_clause,[],[f28976,f28972,f21069,f11323,f10967,f7557,f7521,f7078,f6133,f28978]) ).
fof(f28978,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(f28972,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(f28976,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_648
| ~ spl0_689
| ~ spl0_789
| ~ spl0_798
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2356 ),
inference(forward_demodulation,[],[f28975,f12324]) ).
fof(f28975,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_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2356 ),
inference(forward_demodulation,[],[f28973,f21152]) ).
fof(f28973,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,[],[f28972]) ).
fof(f28974,plain,
spl0_2356,
inference(avatar_split_clause,[],[f3297,f28972]) ).
fof(f3297,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,[],[f3296,f3265]) ).
fof(f3296,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,[],[f3295,f2156]) ).
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_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,[],[f3294,f2154]) ).
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_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,[],[f3101,f2156]) ).
fof(f3101,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(f28925,plain,
( spl0_2355
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2354 ),
inference(avatar_split_clause,[],[f28921,f28917,f21069,f11323,f10967,f7078,f6133,f28923]) ).
fof(f28923,plain,
( spl0_2355
<=> ! [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_2355])]) ).
fof(f28917,plain,
( spl0_2354
<=> ! [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_2354])]) ).
fof(f28921,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2354 ),
inference(forward_demodulation,[],[f28920,f21070]) ).
fof(f28920,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2354 ),
inference(forward_demodulation,[],[f28918,f12324]) ).
fof(f28918,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_2354 ),
inference(avatar_component_clause,[],[f28917]) ).
fof(f28919,plain,
spl0_2354,
inference(avatar_split_clause,[],[f3287,f28917]) ).
fof(f3287,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,[],[f3286,f2156]) ).
fof(f3286,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,[],[f3285,f3048]) ).
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_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,[],[f3094,f3265]) ).
fof(f3094,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(f28903,plain,
( spl0_2353
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2352 ),
inference(avatar_split_clause,[],[f28899,f28895,f21069,f11323,f10967,f7078,f6133,f28901]) ).
fof(f28901,plain,
( spl0_2353
<=> ! [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_2353])]) ).
fof(f28895,plain,
( spl0_2352
<=> ! [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_2352])]) ).
fof(f28899,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2352 ),
inference(forward_demodulation,[],[f28898,f21070]) ).
fof(f28898,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2352 ),
inference(forward_demodulation,[],[f28896,f12324]) ).
fof(f28896,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_2352 ),
inference(avatar_component_clause,[],[f28895]) ).
fof(f28897,plain,
spl0_2352,
inference(avatar_split_clause,[],[f3284,f28895]) ).
fof(f3284,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,[],[f3283,f2156]) ).
fof(f3283,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,[],[f3282,f3048]) ).
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_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,[],[f3093,f3265]) ).
fof(f3093,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(f28893,plain,
( spl0_2351
| ~ spl0_1440
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f28743,f28581,f11222,f28891]) ).
fof(f11222,plain,
( spl0_1440
<=> ! [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_1440])]) ).
fof(f28743,plain,
( ! [X0] :
( ~ c_lessequals(c_Message_OsymKeys,X0,tc_set(tc_nat))
| c_in(v_KAB,X0,tc_nat) )
| ~ spl0_1440
| ~ spl0_2316 ),
inference(superposition,[],[f11223,f28583]) ).
fof(f11223,plain,
( ! [X0,X1,X12,X13] :
( ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1))
| c_in(X0,X13,X1) )
| ~ spl0_1440 ),
inference(avatar_component_clause,[],[f11222]) ).
fof(f28885,plain,
( spl0_2350
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2349 ),
inference(avatar_split_clause,[],[f28881,f28877,f21069,f11323,f10967,f7078,f6133,f28883]) ).
fof(f28883,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_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_2350])]) ).
fof(f28877,plain,
( spl0_2349
<=> ! [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_2349])]) ).
fof(f28881,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2349 ),
inference(forward_demodulation,[],[f28880,f12324]) ).
fof(f28880,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_2033
| ~ spl0_2349 ),
inference(forward_demodulation,[],[f28878,f21070]) ).
fof(f28878,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_2349 ),
inference(avatar_component_clause,[],[f28877]) ).
fof(f28879,plain,
spl0_2349,
inference(avatar_split_clause,[],[f3281,f28877]) ).
fof(f3281,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,[],[f3092,f3265]) ).
fof(f3092,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(f28871,plain,
( spl0_2348
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2347 ),
inference(avatar_split_clause,[],[f28867,f28863,f21069,f11323,f10967,f7078,f6133,f28869]) ).
fof(f28869,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_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_2348])]) ).
fof(f28863,plain,
( spl0_2347
<=> ! [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_2347])]) ).
fof(f28867,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2033
| ~ spl0_2347 ),
inference(forward_demodulation,[],[f28866,f12324]) ).
fof(f28866,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_2033
| ~ spl0_2347 ),
inference(forward_demodulation,[],[f28864,f21070]) ).
fof(f28864,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_2347 ),
inference(avatar_component_clause,[],[f28863]) ).
fof(f28865,plain,
spl0_2347,
inference(avatar_split_clause,[],[f3280,f28863]) ).
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,[],[f3091,f3265]) ).
fof(f3091,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(f28861,plain,
spl0_2346,
inference(avatar_split_clause,[],[f2951,f28859]) ).
fof(f28859,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(f28857,plain,
spl0_2345,
inference(avatar_split_clause,[],[f2003,f28855]) ).
fof(f28855,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(f28853,plain,
spl0_2344,
inference(avatar_split_clause,[],[f2002,f28851]) ).
fof(f28851,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(f28849,plain,
spl0_2343,
inference(avatar_split_clause,[],[f2000,f28847]) ).
fof(f28847,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(f28845,plain,
spl0_2342,
inference(avatar_split_clause,[],[f1999,f28843]) ).
fof(f28843,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(f28841,plain,
spl0_2341,
inference(avatar_split_clause,[],[f1997,f28839]) ).
fof(f28839,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(f28837,plain,
spl0_2340,
inference(avatar_split_clause,[],[f1996,f28835]) ).
fof(f28835,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(f28833,plain,
spl0_2339,
inference(avatar_split_clause,[],[f1994,f28831]) ).
fof(f28831,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(f28829,plain,
spl0_2338,
inference(avatar_split_clause,[],[f1993,f28827]) ).
fof(f28827,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(f28825,plain,
spl0_2337,
inference(avatar_split_clause,[],[f1991,f28823]) ).
fof(f28823,plain,
( spl0_2337
<=> ! [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_2337])]) ).
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(f28821,plain,
spl0_2336,
inference(avatar_split_clause,[],[f1990,f28819]) ).
fof(f28819,plain,
( spl0_2336
<=> ! [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_2336])]) ).
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(f28817,plain,
spl0_2335,
inference(avatar_split_clause,[],[f1988,f28815]) ).
fof(f28815,plain,
( spl0_2335
<=> ! [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_2335])]) ).
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(f28813,plain,
spl0_2334,
inference(avatar_split_clause,[],[f1987,f28811]) ).
fof(f28811,plain,
( spl0_2334
<=> ! [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_2334])]) ).
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(f28809,plain,
spl0_2333,
inference(avatar_split_clause,[],[f1985,f28807]) ).
fof(f28807,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_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_2333])]) ).
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(f28805,plain,
( ~ spl0_2332
| ~ spl0_819
| ~ spl0_2316 ),
inference(avatar_split_clause,[],[f28739,f28581,f7642,f28802]) ).
fof(f28802,plain,
( spl0_2332
<=> c_emptyset = c_Message_OsymKeys ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2332])]) ).
fof(f28739,plain,
( c_emptyset != c_Message_OsymKeys
| ~ spl0_819
| ~ spl0_2316 ),
inference(superposition,[],[f7643,f28583]) ).
fof(f28800,plain,
spl0_2331,
inference(avatar_split_clause,[],[f1984,f28798]) ).
fof(f28798,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(f28796,plain,
spl0_2330,
inference(avatar_split_clause,[],[f1982,f28794]) ).
fof(f28794,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(f28792,plain,
spl0_2329,
inference(avatar_split_clause,[],[f1981,f28790]) ).
fof(f28790,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(f28788,plain,
spl0_2328,
inference(avatar_split_clause,[],[f1979,f28786]) ).
fof(f28786,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(f28784,plain,
spl0_2327,
inference(avatar_split_clause,[],[f1978,f28782]) ).
fof(f28782,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(f28780,plain,
spl0_2326,
inference(avatar_split_clause,[],[f1948,f28778]) ).
fof(f28778,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(f28776,plain,
spl0_2325,
inference(avatar_split_clause,[],[f1947,f28774]) ).
fof(f28774,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(f28772,plain,
spl0_2324,
inference(avatar_split_clause,[],[f1862,f28770]) ).
fof(f28770,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(f28768,plain,
spl0_2323,
inference(avatar_split_clause,[],[f117,f28766]) ).
fof(f28766,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(f28764,plain,
spl0_2322,
inference(avatar_split_clause,[],[f116,f28762]) ).
fof(f28762,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(f28738,plain,
spl0_2321,
inference(avatar_split_clause,[],[f13,f28736]) ).
fof(f28736,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(f28601,plain,
( spl0_2320
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2319 ),
inference(avatar_split_clause,[],[f28597,f28594,f11323,f10967,f7078,f6133,f28599]) ).
fof(f28599,plain,
( spl0_2320
<=> ! [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_2320])]) ).
fof(f28594,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_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_2319])]) ).
fof(f28597,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2319 ),
inference(forward_demodulation,[],[f28595,f12324]) ).
fof(f28595,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_2319 ),
inference(avatar_component_clause,[],[f28594]) ).
fof(f28596,plain,
spl0_2319,
inference(avatar_split_clause,[],[f3100,f28594]) ).
fof(f3100,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(f28592,plain,
spl0_2318,
inference(avatar_split_clause,[],[f2331,f28590]) ).
fof(f28590,plain,
( spl0_2318
<=> ! [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_2318])]) ).
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(f28588,plain,
spl0_2317,
inference(avatar_split_clause,[],[f2321,f28586]) ).
fof(f28586,plain,
( spl0_2317
<=> ! [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_2317])]) ).
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(f28584,plain,
( spl0_2316
| ~ spl0_816
| ~ spl0_2276
| ~ spl0_2296 ),
inference(avatar_split_clause,[],[f28358,f27955,f27289,f7630,f28581]) ).
fof(f27955,plain,
( spl0_2296
<=> ! [X0] : c_union(X0,c_Message_OsymKeys,tc_nat) = c_union(X0,c_insert(v_KAB,c_Message_OsymKeys,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2296])]) ).
fof(f28358,plain,
( c_Message_OsymKeys = c_insert(v_KAB,c_Message_OsymKeys,tc_nat)
| ~ spl0_816
| ~ spl0_2276
| ~ spl0_2296 ),
inference(forward_demodulation,[],[f28357,f7631]) ).
fof(f28357,plain,
( c_insert(v_KAB,c_Message_OsymKeys,tc_nat) = c_union(c_Message_OsymKeys,c_Message_OsymKeys,tc_nat)
| ~ spl0_816
| ~ spl0_2276
| ~ spl0_2296 ),
inference(forward_demodulation,[],[f28334,f27290]) ).
fof(f28334,plain,
( c_insert(v_KAB,c_Message_OsymKeys,tc_nat) = c_union(c_insert(v_KAB,c_Message_OsymKeys,tc_nat),c_Message_OsymKeys,tc_nat)
| ~ spl0_816
| ~ spl0_2296 ),
inference(superposition,[],[f27956,f7631]) ).
fof(f27956,plain,
( ! [X0] : c_union(X0,c_Message_OsymKeys,tc_nat) = c_union(X0,c_insert(v_KAB,c_Message_OsymKeys,tc_nat),tc_nat)
| ~ spl0_2296 ),
inference(avatar_component_clause,[],[f27955]) ).
fof(f28579,plain,
spl0_2315,
inference(avatar_split_clause,[],[f1469,f28577]) ).
fof(f28577,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(f28575,plain,
spl0_2314,
inference(avatar_split_clause,[],[f77,f28573]) ).
fof(f28573,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(f28189,plain,
spl0_2313,
inference(avatar_split_clause,[],[f3229,f28187]) ).
fof(f28187,plain,
( spl0_2313
<=> ! [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_2313])]) ).
fof(f3229,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(f28185,plain,
spl0_2312,
inference(avatar_split_clause,[],[f3228,f28183]) ).
fof(f28183,plain,
( spl0_2312
<=> ! [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_2312])]) ).
fof(f3228,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(f28181,plain,
spl0_2311,
inference(avatar_split_clause,[],[f3227,f28179]) ).
fof(f28179,plain,
( spl0_2311
<=> ! [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_2311])]) ).
fof(f3227,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(f28177,plain,
( spl0_2310
| ~ spl0_1092
| ~ spl0_2284 ),
inference(avatar_split_clause,[],[f27872,f27363,f8967,f28175]) ).
fof(f27872,plain,
( ! [X0] :
( c_emptyset != c_union(c_Message_OsymKeys,X0,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) )
| ~ spl0_1092
| ~ spl0_2284 ),
inference(superposition,[],[f8968,f27364]) ).
fof(f28173,plain,
spl0_2309,
inference(avatar_split_clause,[],[f3226,f28171]) ).
fof(f28171,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(f3226,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(f28169,plain,
spl0_2308,
inference(avatar_split_clause,[],[f3224,f28167]) ).
fof(f28167,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(f3224,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(f28165,plain,
spl0_2307,
inference(avatar_split_clause,[],[f2001,f28163]) ).
fof(f28163,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(f28161,plain,
spl0_2306,
inference(avatar_split_clause,[],[f1995,f28159]) ).
fof(f28159,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(f28157,plain,
spl0_2305,
inference(avatar_split_clause,[],[f1989,f28155]) ).
fof(f28155,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(f28153,plain,
spl0_2304,
inference(avatar_split_clause,[],[f1983,f28151]) ).
fof(f28151,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(f28149,plain,
spl0_2303,
inference(avatar_split_clause,[],[f1794,f28147]) ).
fof(f28147,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(f28145,plain,
spl0_2302,
inference(avatar_split_clause,[],[f1793,f28143]) ).
fof(f28143,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(f28141,plain,
spl0_2301,
inference(avatar_split_clause,[],[f1789,f28139]) ).
fof(f28139,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(f28137,plain,
spl0_2300,
inference(avatar_split_clause,[],[f1616,f28135]) ).
fof(f28135,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(f28133,plain,
( spl0_2299
| ~ spl0_1091
| ~ spl0_2276 ),
inference(avatar_split_clause,[],[f27564,f27289,f8963,f28131]) ).
fof(f28131,plain,
( spl0_2299
<=> ! [X0] :
( c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).
fof(f27564,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) )
| ~ spl0_1091
| ~ spl0_2276 ),
inference(superposition,[],[f8964,f27290]) ).
fof(f28129,plain,
spl0_2298,
inference(avatar_split_clause,[],[f1458,f28127]) ).
fof(f28127,plain,
( spl0_2298
<=> ! [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_2298])]) ).
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(f28125,plain,
spl0_2297,
inference(avatar_split_clause,[],[f118,f28123]) ).
fof(f28123,plain,
( spl0_2297
<=> ! [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_2297])]) ).
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(f27957,plain,
( spl0_2296
| ~ spl0_1762
| ~ spl0_2276 ),
inference(avatar_split_clause,[],[f27562,f27289,f16031,f27955]) ).
fof(f27562,plain,
( ! [X0] : c_union(X0,c_Message_OsymKeys,tc_nat) = c_union(X0,c_insert(v_KAB,c_Message_OsymKeys,tc_nat),tc_nat)
| ~ spl0_1762
| ~ spl0_2276 ),
inference(superposition,[],[f27290,f16032]) ).
fof(f27953,plain,
spl0_2295,
inference(avatar_split_clause,[],[f3223,f27951]) ).
fof(f27951,plain,
( spl0_2295
<=> ! [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_2295])]) ).
fof(f3223,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(f27949,plain,
spl0_2294,
inference(avatar_split_clause,[],[f3202,f27947]) ).
fof(f27947,plain,
( spl0_2294
<=> ! [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_2294])]) ).
fof(f3202,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,f2837]) ).
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(f27945,plain,
spl0_2293,
inference(avatar_split_clause,[],[f3193,f27943]) ).
fof(f27943,plain,
( spl0_2293
<=> ! [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_2293])]) ).
fof(f3193,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,[],[f2682,f2373,f2373]) ).
fof(f2682,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__2_2) ).
fof(f27941,plain,
spl0_2292,
inference(avatar_split_clause,[],[f3191,f27939]) ).
fof(f27939,plain,
( spl0_2292
<=> ! [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_2292])]) ).
fof(f3191,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(f27937,plain,
spl0_2291,
inference(avatar_split_clause,[],[f2942,f27935]) ).
fof(f27935,plain,
( spl0_2291
<=> ! [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_2291])]) ).
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(f27933,plain,
spl0_2290,
inference(avatar_split_clause,[],[f2848,f27931]) ).
fof(f27931,plain,
( spl0_2290
<=> ! [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_2290])]) ).
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(f27929,plain,
spl0_2289,
inference(avatar_split_clause,[],[f1792,f27927]) ).
fof(f27927,plain,
( spl0_2289
<=> ! [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_2289])]) ).
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(f27925,plain,
spl0_2288,
inference(avatar_split_clause,[],[f1698,f27923]) ).
fof(f27923,plain,
( spl0_2288
<=> ! [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_2288])]) ).
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(f27860,plain,
( spl0_2287
| ~ spl0_59
| ~ spl0_1590
| ~ spl0_2283 ),
inference(avatar_split_clause,[],[f27327,f27324,f12897,f3725,f27858]) ).
fof(f27858,plain,
( spl0_2287
<=> ! [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_2287])]) ).
fof(f12897,plain,
( spl0_1590
<=> ! [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_1590])]) ).
fof(f27324,plain,
( spl0_2283
<=> ! [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_2283])]) ).
fof(f27327,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_59
| ~ spl0_1590
| ~ spl0_2283 ),
inference(forward_demodulation,[],[f27325,f14224]) ).
fof(f14224,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_59
| ~ spl0_1590 ),
inference(resolution,[],[f12898,f3727]) ).
fof(f12898,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_1590 ),
inference(avatar_component_clause,[],[f12897]) ).
fof(f27325,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_2283 ),
inference(avatar_component_clause,[],[f27324]) ).
fof(f27410,plain,
( spl0_2286
| ~ spl0_1194
| ~ spl0_1543
| ~ spl0_2264 ),
inference(avatar_split_clause,[],[f27137,f27134,f12672,f9596,f27408]) ).
fof(f27408,plain,
( spl0_2286
<=> ! [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_2286])]) ).
fof(f27134,plain,
( spl0_2264
<=> ! [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_2264])]) ).
fof(f27137,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_1194
| ~ spl0_1543
| ~ spl0_2264 ),
inference(forward_demodulation,[],[f27135,f13772]) ).
fof(f27135,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_2264 ),
inference(avatar_component_clause,[],[f27134]) ).
fof(f27406,plain,
( spl0_2285
| ~ spl0_1193
| ~ spl0_1543
| ~ spl0_2263 ),
inference(avatar_split_clause,[],[f27132,f27129,f12672,f9592,f27404]) ).
fof(f27404,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(f27129,plain,
( spl0_2263
<=> ! [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_2263])]) ).
fof(f27132,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_1193
| ~ spl0_1543
| ~ spl0_2263 ),
inference(forward_demodulation,[],[f27130,f13773]) ).
fof(f27130,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_2263 ),
inference(avatar_component_clause,[],[f27129]) ).
fof(f27365,plain,
( spl0_2284
| ~ spl0_1556
| ~ spl0_2081 ),
inference(avatar_split_clause,[],[f27168,f23041,f12729,f27363]) ).
fof(f12729,plain,
( spl0_1556
<=> ! [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_1556])]) ).
fof(f23041,plain,
( spl0_2081
<=> ! [X0] : c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)) = c_minus(c_insert(v_KAB,X0,tc_nat),c_Message_OsymKeys,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f27168,plain,
( ! [X0] : c_union(c_Message_OsymKeys,c_insert(v_KAB,X0,tc_nat),tc_nat) = c_union(c_Message_OsymKeys,X0,tc_nat)
| ~ spl0_1556
| ~ spl0_2081 ),
inference(forward_demodulation,[],[f27153,f12730]) ).
fof(f12730,plain,
( ! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1)
| ~ spl0_1556 ),
inference(avatar_component_clause,[],[f12729]) ).
fof(f27153,plain,
( ! [X0] : c_union(c_Message_OsymKeys,c_insert(v_KAB,X0,tc_nat),tc_nat) = c_union(c_Message_OsymKeys,c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),tc_nat)
| ~ spl0_1556
| ~ spl0_2081 ),
inference(superposition,[],[f12730,f23042]) ).
fof(f23042,plain,
( ! [X0] : c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)) = c_minus(c_insert(v_KAB,X0,tc_nat),c_Message_OsymKeys,tc_set(tc_nat))
| ~ spl0_2081 ),
inference(avatar_component_clause,[],[f23041]) ).
fof(f27326,plain,
spl0_2283,
inference(avatar_split_clause,[],[f3200,f27324]) ).
fof(f3200,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(f27322,plain,
spl0_2282,
inference(avatar_split_clause,[],[f3109,f27320]) ).
fof(f27320,plain,
( spl0_2282
<=> ! [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_2282])]) ).
fof(f3109,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(f27312,plain,
( spl0_2281
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2280 ),
inference(avatar_split_clause,[],[f27308,f27305,f11323,f10967,f7078,f6133,f27310]) ).
fof(f27310,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_plus(c_1,X21,tc_nat),tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2281])]) ).
fof(f27305,plain,
( spl0_2280
<=> ! [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_2280])]) ).
fof(f27308,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2280 ),
inference(forward_demodulation,[],[f27306,f12324]) ).
fof(f27306,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_2280 ),
inference(avatar_component_clause,[],[f27305]) ).
fof(f27307,plain,
spl0_2280,
inference(avatar_split_clause,[],[f3095,f27305]) ).
fof(f3095,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(f27303,plain,
spl0_2279,
inference(avatar_split_clause,[],[f3090,f27301]) ).
fof(f27301,plain,
( spl0_2279
<=> ! [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_2279])]) ).
fof(f3090,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(f27299,plain,
spl0_2278,
inference(avatar_split_clause,[],[f3083,f27297]) ).
fof(f27297,plain,
( spl0_2278
<=> ! [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_2278])]) ).
fof(f3083,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(f27295,plain,
spl0_2277,
inference(avatar_split_clause,[],[f3082,f27293]) ).
fof(f27293,plain,
( spl0_2277
<=> ! [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_2277])]) ).
fof(f3082,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(f27291,plain,
( spl0_2276
| ~ spl0_1555
| ~ spl0_2081 ),
inference(avatar_split_clause,[],[f27167,f23041,f12725,f27289]) ).
fof(f12725,plain,
( spl0_1555
<=> ! [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_1555])]) ).
fof(f27167,plain,
( ! [X0] : c_union(c_insert(v_KAB,X0,tc_nat),c_Message_OsymKeys,tc_nat) = c_union(X0,c_Message_OsymKeys,tc_nat)
| ~ spl0_1555
| ~ spl0_2081 ),
inference(forward_demodulation,[],[f27152,f12726]) ).
fof(f12726,plain,
( ! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1)
| ~ spl0_1555 ),
inference(avatar_component_clause,[],[f12725]) ).
fof(f27152,plain,
( ! [X0] : c_union(c_insert(v_KAB,X0,tc_nat),c_Message_OsymKeys,tc_nat) = c_union(c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),c_Message_OsymKeys,tc_nat)
| ~ spl0_1555
| ~ spl0_2081 ),
inference(superposition,[],[f12726,f23042]) ).
fof(f27209,plain,
( spl0_2275
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2274 ),
inference(avatar_split_clause,[],[f27205,f27201,f11323,f10967,f7078,f6133,f27207]) ).
fof(f27207,plain,
( spl0_2275
<=> ! [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_2275])]) ).
fof(f27201,plain,
( spl0_2274
<=> ! [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_2274])]) ).
fof(f27205,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2274 ),
inference(forward_demodulation,[],[f27204,f12324]) ).
fof(f27204,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2274 ),
inference(forward_demodulation,[],[f27202,f12324]) ).
fof(f27202,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_2274 ),
inference(avatar_component_clause,[],[f27201]) ).
fof(f27203,plain,
spl0_2274,
inference(avatar_split_clause,[],[f3076,f27201]) ).
fof(f3076,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(f27197,plain,
spl0_2273,
inference(avatar_split_clause,[],[f3035,f27195]) ).
fof(f27195,plain,
( spl0_2273
<=> ! [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_2273])]) ).
fof(f3035,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(f27193,plain,
spl0_2272,
inference(avatar_split_clause,[],[f2949,f27191]) ).
fof(f27191,plain,
( spl0_2272
<=> ! [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_2272])]) ).
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(f27189,plain,
spl0_2271,
inference(avatar_split_clause,[],[f2934,f27187]) ).
fof(f27187,plain,
( spl0_2271
<=> ! [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_2271])]) ).
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(f27185,plain,
spl0_2270,
inference(avatar_split_clause,[],[f2316,f27183]) ).
fof(f27183,plain,
( spl0_2270
<=> ! [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_2270])]) ).
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(f27181,plain,
spl0_2269,
inference(avatar_split_clause,[],[f1826,f27179]) ).
fof(f27179,plain,
( spl0_2269
<=> ! [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_2269])]) ).
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(f27177,plain,
spl0_2268,
inference(avatar_split_clause,[],[f1695,f27175]) ).
fof(f27175,plain,
( spl0_2268
<=> ! [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_2268])]) ).
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(f27173,plain,
spl0_2267,
inference(avatar_split_clause,[],[f1573,f27171]) ).
fof(f27171,plain,
( spl0_2267
<=> ! [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_2267])]) ).
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(f27145,plain,
spl0_2266,
inference(avatar_split_clause,[],[f1571,f27143]) ).
fof(f27143,plain,
( spl0_2266
<=> ! [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_2266])]) ).
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(f27141,plain,
spl0_2265,
inference(avatar_split_clause,[],[f1526,f27139]) ).
fof(f27139,plain,
( spl0_2265
<=> ! [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_2265])]) ).
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(f27136,plain,
spl0_2264,
inference(avatar_split_clause,[],[f1447,f27134]) ).
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(f27131,plain,
spl0_2263,
inference(avatar_split_clause,[],[f1437,f27129]) ).
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(f27127,plain,
spl0_2262,
inference(avatar_split_clause,[],[f1381,f27125]) ).
fof(f27125,plain,
( spl0_2262
<=> ! [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_2262])]) ).
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(f27123,plain,
spl0_2261,
inference(avatar_split_clause,[],[f1269,f27121]) ).
fof(f27121,plain,
( spl0_2261
<=> ! [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_2261])]) ).
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(f27119,plain,
spl0_2260,
inference(avatar_split_clause,[],[f1266,f27117]) ).
fof(f27117,plain,
( spl0_2260
<=> ! [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_2260])]) ).
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(f27115,plain,
spl0_2259,
inference(avatar_split_clause,[],[f1262,f27113]) ).
fof(f27113,plain,
( spl0_2259
<=> ! [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_2259])]) ).
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(f27111,plain,
spl0_2258,
inference(avatar_split_clause,[],[f1259,f27109]) ).
fof(f27109,plain,
( spl0_2258
<=> ! [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_2258])]) ).
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(f27107,plain,
spl0_2257,
inference(avatar_split_clause,[],[f78,f27105]) ).
fof(f27105,plain,
( spl0_2257
<=> ! [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_2257])]) ).
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(f26767,plain,
( spl0_2256
| ~ spl0_1587
| ~ spl0_2225 ),
inference(avatar_split_clause,[],[f26453,f25997,f12875,f26765]) ).
fof(f26765,plain,
( spl0_2256
<=> ! [X0] : ~ c_in(v_Aa,c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).
fof(f25997,plain,
( spl0_2225
<=> ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent)
| ~ c_in(v_Aa,X0,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).
fof(f26453,plain,
( ! [X0] : ~ c_in(v_Aa,c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1587
| ~ spl0_2225 ),
inference(trivial_inequality_removal,[],[f26450]) ).
fof(f26450,plain,
( ! [X0] :
( c_emptyset != c_emptyset
| ~ c_in(v_Aa,c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) )
| ~ spl0_1587
| ~ spl0_2225 ),
inference(superposition,[],[f25998,f12876]) ).
fof(f25998,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent)
| ~ c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_2225 ),
inference(avatar_component_clause,[],[f25997]) ).
fof(f26317,plain,
( spl0_2255
| ~ spl0_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2254 ),
inference(avatar_split_clause,[],[f26313,f26310,f21069,f7557,f7521,f26315]) ).
fof(f26315,plain,
( spl0_2255
<=> ! [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_2255])]) ).
fof(f26310,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(f26313,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_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2254 ),
inference(forward_demodulation,[],[f26311,f21152]) ).
fof(f26311,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,[],[f26310]) ).
fof(f26312,plain,
spl0_2254,
inference(avatar_split_clause,[],[f3390,f26310]) ).
fof(f3390,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,[],[f3389,f2156]) ).
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_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ),
inference(forward_demodulation,[],[f3388,f2154]) ).
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_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(f26308,plain,
spl0_2253,
inference(avatar_split_clause,[],[f3323,f26306]) ).
fof(f26306,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(f3323,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,[],[f3322,f3055]) ).
fof(f3055,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(f3322,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,[],[f3130,f3055]) ).
fof(f3130,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(f26304,plain,
spl0_2252,
inference(avatar_split_clause,[],[f3321,f26302]) ).
fof(f26302,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(f3321,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,[],[f3320,f3054]) ).
fof(f3054,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(f3320,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,[],[f3129,f3054]) ).
fof(f3129,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(f26254,plain,
( spl0_2251
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2250 ),
inference(avatar_split_clause,[],[f26247,f26244,f11323,f10967,f7078,f6133,f26252]) ).
fof(f26252,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(f26244,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(f26247,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2250 ),
inference(forward_demodulation,[],[f26245,f12324]) ).
fof(f26245,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,[],[f26244]) ).
fof(f26246,plain,
spl0_2250,
inference(avatar_split_clause,[],[f3190,f26244]) ).
fof(f3190,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(f26221,plain,
( spl0_2249
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2248 ),
inference(avatar_split_clause,[],[f26217,f26214,f11323,f10967,f7078,f6133,f26219]) ).
fof(f26219,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(f26214,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(f26217,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2248 ),
inference(forward_demodulation,[],[f26215,f12324]) ).
fof(f26215,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,[],[f26214]) ).
fof(f26216,plain,
spl0_2248,
inference(avatar_split_clause,[],[f3085,f26214]) ).
fof(f3085,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(f26212,plain,
spl0_2247,
inference(avatar_split_clause,[],[f2952,f26210]) ).
fof(f26210,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(f26208,plain,
spl0_2246,
inference(avatar_split_clause,[],[f2829,f26206]) ).
fof(f26206,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(f26204,plain,
spl0_2245,
inference(avatar_split_clause,[],[f2385,f26202]) ).
fof(f26202,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(f26200,plain,
spl0_2244,
inference(avatar_split_clause,[],[f2384,f26198]) ).
fof(f26198,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(f26196,plain,
spl0_2243,
inference(avatar_split_clause,[],[f2332,f26194]) ).
fof(f26194,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(f26192,plain,
spl0_2242,
inference(avatar_split_clause,[],[f2322,f26190]) ).
fof(f26190,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(f26188,plain,
( ~ spl0_2241
| ~ spl0_1464
| ~ spl0_2224 ),
inference(avatar_split_clause,[],[f26143,f25707,f11319,f26185]) ).
fof(f26185,plain,
( spl0_2241
<=> c_in(v_Aa,c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f25707,plain,
( spl0_2224
<=> ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
| ~ c_in(v_Aa,X0,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).
fof(f26143,plain,
( ~ c_in(v_Aa,c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1464
| ~ spl0_2224 ),
inference(trivial_inequality_removal,[],[f26141]) ).
fof(f26141,plain,
( c_emptyset != c_emptyset
| ~ c_in(v_Aa,c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1464
| ~ spl0_2224 ),
inference(superposition,[],[f25708,f11320]) ).
fof(f25708,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
| ~ c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_2224 ),
inference(avatar_component_clause,[],[f25707]) ).
fof(f26183,plain,
spl0_2240,
inference(avatar_split_clause,[],[f1877,f26181]) ).
fof(f26181,plain,
( spl0_2240
<=> ! [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_2240])]) ).
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(f26179,plain,
spl0_2239,
inference(avatar_split_clause,[],[f1828,f26177]) ).
fof(f26177,plain,
( spl0_2239
<=> ! [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_2239])]) ).
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(f26175,plain,
spl0_2238,
inference(avatar_split_clause,[],[f1273,f26173]) ).
fof(f26173,plain,
( spl0_2238
<=> ! [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_2238])]) ).
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(f26171,plain,
spl0_2237,
inference(avatar_split_clause,[],[f1271,f26169]) ).
fof(f26169,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_less(X0,c_Main_OMin__gr__iff__1(X12,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).
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(f26167,plain,
spl0_2236,
inference(avatar_split_clause,[],[f1270,f26165]) ).
fof(f26165,plain,
( spl0_2236
<=> ! [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_2236])]) ).
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(f26163,plain,
spl0_2235,
inference(avatar_split_clause,[],[f1268,f26161]) ).
fof(f26161,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(f26159,plain,
spl0_2234,
inference(avatar_split_clause,[],[f1267,f26157]) ).
fof(f26157,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(f26155,plain,
spl0_2233,
inference(avatar_split_clause,[],[f1264,f26153]) ).
fof(f26153,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(f26151,plain,
spl0_2232,
inference(avatar_split_clause,[],[f1263,f26149]) ).
fof(f26149,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(f26147,plain,
spl0_2231,
inference(avatar_split_clause,[],[f1261,f26145]) ).
fof(f26145,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(f26138,plain,
spl0_2230,
inference(avatar_split_clause,[],[f1260,f26136]) ).
fof(f26136,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(f26134,plain,
spl0_2229,
inference(avatar_split_clause,[],[f1258,f26132]) ).
fof(f26132,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(f26130,plain,
spl0_2228,
inference(avatar_split_clause,[],[f73,f26128]) ).
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(f26126,plain,
spl0_2227,
inference(avatar_split_clause,[],[f15,f26124]) ).
fof(f26124,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(f26122,plain,
spl0_2226,
inference(avatar_split_clause,[],[f14,f26120]) ).
fof(f26120,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(f25999,plain,
( spl0_2225
| ~ spl0_1867
| ~ spl0_2175 ),
inference(avatar_split_clause,[],[f24206,f24091,f17805,f25997]) ).
fof(f24091,plain,
( spl0_2175
<=> c_Event_Obad = c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f24206,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_Event_Obad,tc_Message_Oagent),X0,tc_Message_Oagent,tc_Message_Oagent)
| ~ c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1867
| ~ spl0_2175 ),
inference(superposition,[],[f17806,f24093]) ).
fof(f24093,plain,
( c_Event_Obad = c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_2175 ),
inference(avatar_component_clause,[],[f24091]) ).
fof(f25709,plain,
( spl0_2224
| ~ spl0_1866
| ~ spl0_2175 ),
inference(avatar_split_clause,[],[f24205,f24091,f17801,f25707]) ).
fof(f24205,plain,
( ! [X0] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X0,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent,tc_Message_Oagent)
| ~ c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1866
| ~ spl0_2175 ),
inference(superposition,[],[f17802,f24093]) ).
fof(f25403,plain,
spl0_2223,
inference(avatar_split_clause,[],[f3199,f25401]) ).
fof(f25401,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(f3199,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(f25399,plain,
spl0_2222,
inference(avatar_split_clause,[],[f3198,f25397]) ).
fof(f25397,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(f3198,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(f25395,plain,
spl0_2221,
inference(avatar_split_clause,[],[f3171,f25393]) ).
fof(f25393,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(f3171,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(f25391,plain,
spl0_2220,
inference(avatar_split_clause,[],[f3050,f25389]) ).
fof(f25389,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(f3050,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(f25387,plain,
spl0_2219,
inference(avatar_split_clause,[],[f2849,f25385]) ).
fof(f25385,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(f25378,plain,
( ~ spl0_819
| ~ spl0_2207 ),
inference(avatar_contradiction_clause,[],[f25377]) ).
fof(f25377,plain,
( $false
| ~ spl0_819
| ~ spl0_2207 ),
inference(trivial_inequality_removal,[],[f25358]) ).
fof(f25358,plain,
( c_emptyset != c_emptyset
| ~ spl0_819
| ~ spl0_2207 ),
inference(superposition,[],[f7643,f25304]) ).
fof(f25304,plain,
( c_emptyset = c_insert(v_Aa,c_emptyset,tc_Message_Oagent)
| ~ spl0_2207 ),
inference(avatar_component_clause,[],[f25302]) ).
fof(f25302,plain,
( spl0_2207
<=> c_emptyset = c_insert(v_Aa,c_emptyset,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).
fof(f25348,plain,
spl0_2218,
inference(avatar_split_clause,[],[f2562,f25346]) ).
fof(f25346,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(f25344,plain,
spl0_2217,
inference(avatar_split_clause,[],[f2356,f25342]) ).
fof(f25342,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(f25340,plain,
spl0_2216,
inference(avatar_split_clause,[],[f2355,f25338]) ).
fof(f25338,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(f25336,plain,
spl0_2215,
inference(avatar_split_clause,[],[f2351,f25334]) ).
fof(f25334,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(f25332,plain,
spl0_2214,
inference(avatar_split_clause,[],[f2350,f25330]) ).
fof(f25330,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(f25328,plain,
spl0_2213,
inference(avatar_split_clause,[],[f2336,f25326]) ).
fof(f25326,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(f25324,plain,
spl0_2212,
inference(avatar_split_clause,[],[f2333,f25322]) ).
fof(f25322,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(f25320,plain,
spl0_2211,
inference(avatar_split_clause,[],[f2330,f25318]) ).
fof(f25318,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(f25316,plain,
spl0_2210,
inference(avatar_split_clause,[],[f2328,f25314]) ).
fof(f25314,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(f25312,plain,
spl0_2209,
inference(avatar_split_clause,[],[f2325,f25310]) ).
fof(f25310,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(f25308,plain,
( spl0_2207
| spl0_2208
| ~ spl0_1448
| ~ spl0_2156 ),
inference(avatar_split_clause,[],[f25260,f23932,f11255,f25306,f25302]) ).
fof(f25306,plain,
( spl0_2208
<=> ! [X0] : c_emptyset != c_union(X0,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f23932,plain,
( spl0_2156
<=> ! [X0] :
( c_emptyset != c_union(c_Event_Obad,X0,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f25260,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Event_Obad,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,c_emptyset,tc_Message_Oagent) )
| ~ spl0_1448
| ~ spl0_2156 ),
inference(inner_rewriting,[],[f25258]) ).
fof(f25258,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Event_Obad,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,c_union(X0,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent) )
| ~ spl0_1448
| ~ spl0_2156 ),
inference(superposition,[],[f23933,f11256]) ).
fof(f23933,plain,
( ! [X0] :
( c_emptyset != c_union(c_Event_Obad,X0,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_2156 ),
inference(avatar_component_clause,[],[f23932]) ).
fof(f25300,plain,
spl0_2206,
inference(avatar_split_clause,[],[f2319,f25298]) ).
fof(f25298,plain,
( spl0_2206
<=> ! [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_2206])]) ).
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(f25296,plain,
spl0_2205,
inference(avatar_split_clause,[],[f2168,f25294]) ).
fof(f25294,plain,
( spl0_2205
<=> ! [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_2205])]) ).
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(f25292,plain,
spl0_2204,
inference(avatar_split_clause,[],[f2108,f25290]) ).
fof(f25290,plain,
( spl0_2204
<=> ! [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_2204])]) ).
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(f25288,plain,
spl0_2203,
inference(avatar_split_clause,[],[f1861,f25286]) ).
fof(f25286,plain,
( spl0_2203
<=> ! [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_2203])]) ).
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(f25284,plain,
spl0_2202,
inference(avatar_split_clause,[],[f1834,f25282]) ).
fof(f25282,plain,
( spl0_2202
<=> ! [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_2202])]) ).
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(f25280,plain,
spl0_2201,
inference(avatar_split_clause,[],[f1825,f25278]) ).
fof(f25278,plain,
( spl0_2201
<=> ! [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_2201])]) ).
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(f25276,plain,
spl0_2200,
inference(avatar_split_clause,[],[f1635,f25274]) ).
fof(f25274,plain,
( spl0_2200
<=> ! [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_2200])]) ).
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(f25272,plain,
spl0_2199,
inference(avatar_split_clause,[],[f1634,f25270]) ).
fof(f25270,plain,
( spl0_2199
<=> ! [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_2199])]) ).
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(f25268,plain,
spl0_2198,
inference(avatar_split_clause,[],[f1355,f25266]) ).
fof(f25266,plain,
( spl0_2198
<=> ! [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_2198])]) ).
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(f25264,plain,
spl0_2197,
inference(avatar_split_clause,[],[f1294,f25262]) ).
fof(f25262,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_Omax(X3,c_Finite__Set_OMin(X12,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
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(f25252,plain,
spl0_2196,
inference(avatar_split_clause,[],[f1293,f25250]) ).
fof(f25250,plain,
( spl0_2196
<=> ! [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_2196])]) ).
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(f25248,plain,
spl0_2195,
inference(avatar_split_clause,[],[f1222,f25246]) ).
fof(f25246,plain,
( spl0_2195
<=> ! [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_2195])]) ).
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(f25244,plain,
spl0_2194,
inference(avatar_split_clause,[],[f1220,f25242]) ).
fof(f25242,plain,
( spl0_2194
<=> ! [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_2194])]) ).
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(f25240,plain,
spl0_2193,
inference(avatar_split_clause,[],[f121,f25238]) ).
fof(f25238,plain,
( spl0_2193
<=> ! [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_2193])]) ).
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(f25236,plain,
spl0_2192,
inference(avatar_split_clause,[],[f74,f25234]) ).
fof(f25234,plain,
( spl0_2192
<=> ! [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_2192])]) ).
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(f24634,plain,
( spl0_2191
| ~ spl0_1441
| ~ spl0_2175 ),
inference(avatar_split_clause,[],[f24199,f24091,f11226,f24632]) ).
fof(f24632,plain,
( spl0_2191
<=> ! [X0] :
( c_Event_Obad != c_insert(X0,c_emptyset,tc_Message_Oagent)
| v_Aa = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f24199,plain,
( ! [X0] :
( c_Event_Obad != c_insert(X0,c_emptyset,tc_Message_Oagent)
| v_Aa = X0 )
| ~ spl0_1441
| ~ spl0_2175 ),
inference(superposition,[],[f11227,f24093]) ).
fof(f24630,plain,
( spl0_2190
| ~ spl0_1440
| ~ spl0_2175 ),
inference(avatar_split_clause,[],[f24198,f24091,f11222,f24628]) ).
fof(f24198,plain,
( ! [X0] :
( ~ c_lessequals(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1440
| ~ spl0_2175 ),
inference(superposition,[],[f11223,f24093]) ).
fof(f24324,plain,
( ~ spl0_2189
| ~ spl0_819
| ~ spl0_2175 ),
inference(avatar_split_clause,[],[f24194,f24091,f7642,f24321]) ).
fof(f24321,plain,
( spl0_2189
<=> c_emptyset = c_Event_Obad ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f24194,plain,
( c_emptyset != c_Event_Obad
| ~ spl0_819
| ~ spl0_2175 ),
inference(superposition,[],[f7643,f24093]) ).
fof(f24251,plain,
( spl0_2188
| ~ spl0_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2187 ),
inference(avatar_split_clause,[],[f24247,f24243,f21069,f7557,f7521,f24249]) ).
fof(f24249,plain,
( spl0_2188
<=> ! [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_2188])]) ).
fof(f24243,plain,
( spl0_2187
<=> ! [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_2187])]) ).
fof(f24247,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_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2187 ),
inference(forward_demodulation,[],[f24246,f21152]) ).
fof(f24246,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_789
| ~ spl0_798
| ~ spl0_2033
| ~ spl0_2187 ),
inference(forward_demodulation,[],[f24244,f21152]) ).
fof(f24244,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_2187 ),
inference(avatar_component_clause,[],[f24243]) ).
fof(f24245,plain,
spl0_2187,
inference(avatar_split_clause,[],[f3376,f24243]) ).
fof(f3376,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,[],[f3375,f2156]) ).
fof(f3375,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,[],[f3374,f2154]) ).
fof(f3374,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,[],[f3373,f2156]) ).
fof(f3373,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,[],[f3372,f2156]) ).
fof(f3372,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,[],[f3371,f2154]) ).
fof(f3371,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(f24218,plain,
( spl0_2186
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2185 ),
inference(avatar_split_clause,[],[f24214,f24211,f11323,f10967,f7078,f6133,f24216]) ).
fof(f24216,plain,
( spl0_2186
<=> ! [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_2186])]) ).
fof(f24211,plain,
( spl0_2185
<=> ! [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_2185])]) ).
fof(f24214,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2185 ),
inference(forward_demodulation,[],[f24212,f12324]) ).
fof(f24212,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_2185 ),
inference(avatar_component_clause,[],[f24211]) ).
fof(f24213,plain,
spl0_2185,
inference(avatar_split_clause,[],[f3277,f24211]) ).
fof(f3277,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,[],[f3276,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(f3276,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,[],[f3086,f3055]) ).
fof(f3086,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(f24193,plain,
spl0_2184,
inference(avatar_split_clause,[],[f3222,f24191]) ).
fof(f24191,plain,
( spl0_2184
<=> ! [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_2184])]) ).
fof(f3222,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(f24189,plain,
spl0_2183,
inference(avatar_split_clause,[],[f3221,f24187]) ).
fof(f24187,plain,
( spl0_2183
<=> ! [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_2183])]) ).
fof(f3221,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(f24185,plain,
spl0_2182,
inference(avatar_split_clause,[],[f3220,f24183]) ).
fof(f24183,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(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_2182])]) ).
fof(f3220,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(f24181,plain,
spl0_2181,
inference(avatar_split_clause,[],[f3219,f24179]) ).
fof(f24179,plain,
( spl0_2181
<=> ! [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_2181])]) ).
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,[],[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(f24177,plain,
spl0_2180,
inference(avatar_split_clause,[],[f3197,f24175]) ).
fof(f24175,plain,
( spl0_2180
<=> ! [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_2180])]) ).
fof(f3197,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(f24173,plain,
spl0_2179,
inference(avatar_split_clause,[],[f3166,f24171]) ).
fof(f24171,plain,
( spl0_2179
<=> ! [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_2179])]) ).
fof(f3166,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(f24169,plain,
spl0_2178,
inference(avatar_split_clause,[],[f3164,f24167]) ).
fof(f24167,plain,
( spl0_2178
<=> ! [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_2178])]) ).
fof(f3164,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(f24104,plain,
( spl0_2177
| ~ spl0_648
| ~ spl0_689
| ~ spl0_784
| ~ spl0_789
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1853
| ~ spl0_2176 ),
inference(avatar_split_clause,[],[f24100,f24096,f17687,f11323,f10967,f7521,f7501,f7078,f6133,f24102]) ).
fof(f24102,plain,
( spl0_2177
<=> ! [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_2177])]) ).
fof(f7501,plain,
( spl0_784
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f17687,plain,
( spl0_1853
<=> ! [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_1853])]) ).
fof(f24096,plain,
( spl0_2176
<=> ! [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_2176])]) ).
fof(f24100,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_648
| ~ spl0_689
| ~ spl0_784
| ~ spl0_789
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1853
| ~ spl0_2176 ),
inference(forward_demodulation,[],[f24099,f17720]) ).
fof(f17720,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_784
| ~ spl0_789
| ~ spl0_1853 ),
inference(forward_demodulation,[],[f17690,f7522]) ).
fof(f17690,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_784
| ~ spl0_1853 ),
inference(superposition,[],[f17688,f7502]) ).
fof(f7502,plain,
( ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41)
| ~ spl0_784 ),
inference(avatar_component_clause,[],[f7501]) ).
fof(f17688,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_1853 ),
inference(avatar_component_clause,[],[f17687]) ).
fof(f24099,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2176 ),
inference(forward_demodulation,[],[f24097,f12324]) ).
fof(f24097,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_2176 ),
inference(avatar_component_clause,[],[f24096]) ).
fof(f24098,plain,
spl0_2176,
inference(avatar_split_clause,[],[f3128,f24096]) ).
fof(f3128,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(f24094,plain,
( spl0_2175
| ~ spl0_816
| ~ spl0_2102
| ~ spl0_2134 ),
inference(avatar_split_clause,[],[f23999,f23844,f23542,f7630,f24091]) ).
fof(f23844,plain,
( spl0_2134
<=> ! [X0] : c_union(X0,c_Event_Obad,tc_Message_Oagent) = c_union(X0,c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f23999,plain,
( c_Event_Obad = c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_816
| ~ spl0_2102
| ~ spl0_2134 ),
inference(forward_demodulation,[],[f23998,f7631]) ).
fof(f23998,plain,
( c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent) = c_union(c_Event_Obad,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_816
| ~ spl0_2102
| ~ spl0_2134 ),
inference(forward_demodulation,[],[f23975,f23543]) ).
fof(f23975,plain,
( c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent) = c_union(c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent)
| ~ spl0_816
| ~ spl0_2134 ),
inference(superposition,[],[f23845,f7631]) ).
fof(f23845,plain,
( ! [X0] : c_union(X0,c_Event_Obad,tc_Message_Oagent) = c_union(X0,c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2134 ),
inference(avatar_component_clause,[],[f23844]) ).
fof(f24089,plain,
spl0_2174,
inference(avatar_split_clause,[],[f3089,f24087]) ).
fof(f24087,plain,
( spl0_2174
<=> ! [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_2174])]) ).
fof(f3089,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(f24085,plain,
spl0_2173,
inference(avatar_split_clause,[],[f3088,f24083]) ).
fof(f24083,plain,
( spl0_2173
<=> ! [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_2173])]) ).
fof(f3088,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(f24081,plain,
spl0_2172,
inference(avatar_split_clause,[],[f3081,f24079]) ).
fof(f24079,plain,
( spl0_2172
<=> ! [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_2172])]) ).
fof(f3081,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(f24058,plain,
( spl0_2171
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2170 ),
inference(avatar_split_clause,[],[f24054,f24049,f11323,f10967,f7078,f6133,f24056]) ).
fof(f24056,plain,
( spl0_2171
<=> ! [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_2171])]) ).
fof(f24049,plain,
( spl0_2170
<=> ! [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_2170])]) ).
fof(f24054,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2170 ),
inference(forward_demodulation,[],[f24053,f12324]) ).
fof(f24053,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2170 ),
inference(forward_demodulation,[],[f24052,f12324]) ).
fof(f24052,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2170 ),
inference(forward_demodulation,[],[f24050,f12324]) ).
fof(f24050,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_2170 ),
inference(avatar_component_clause,[],[f24049]) ).
fof(f24051,plain,
spl0_2170,
inference(avatar_split_clause,[],[f3057,f24049]) ).
fof(f3057,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(f24031,plain,
( spl0_2169
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2168 ),
inference(avatar_split_clause,[],[f24027,f24022,f11323,f10967,f7078,f6133,f24029]) ).
fof(f24029,plain,
( spl0_2169
<=> ! [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_2169])]) ).
fof(f24022,plain,
( spl0_2168
<=> ! [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_2168])]) ).
fof(f24027,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2168 ),
inference(forward_demodulation,[],[f24026,f12324]) ).
fof(f24026,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2168 ),
inference(forward_demodulation,[],[f24025,f12324]) ).
fof(f24025,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2168 ),
inference(forward_demodulation,[],[f24023,f12324]) ).
fof(f24023,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_2168 ),
inference(avatar_component_clause,[],[f24022]) ).
fof(f24024,plain,
spl0_2168,
inference(avatar_split_clause,[],[f3056,f24022]) ).
fof(f3056,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(f24020,plain,
spl0_2167,
inference(avatar_split_clause,[],[f2877,f24018]) ).
fof(f24018,plain,
( spl0_2167
<=> ! [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_2167])]) ).
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(f23974,plain,
spl0_2166,
inference(avatar_split_clause,[],[f2859,f23972]) ).
fof(f23972,plain,
( spl0_2166
<=> ! [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_2166])]) ).
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(f23970,plain,
spl0_2165,
inference(avatar_split_clause,[],[f2566,f23968]) ).
fof(f23968,plain,
( spl0_2165
<=> ! [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_2165])]) ).
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(f23966,plain,
spl0_2164,
inference(avatar_split_clause,[],[f2564,f23964]) ).
fof(f23964,plain,
( spl0_2164
<=> ! [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_2164])]) ).
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(f23962,plain,
spl0_2163,
inference(avatar_split_clause,[],[f2563,f23960]) ).
fof(f23960,plain,
( spl0_2163
<=> ! [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_2163])]) ).
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(f23958,plain,
spl0_2162,
inference(avatar_split_clause,[],[f2376,f23956]) ).
fof(f23956,plain,
( spl0_2162
<=> ! [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_2162])]) ).
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(f23954,plain,
spl0_2161,
inference(avatar_split_clause,[],[f2375,f23952]) ).
fof(f23952,plain,
( spl0_2161
<=> ! [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_2161])]) ).
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(f23950,plain,
spl0_2160,
inference(avatar_split_clause,[],[f2335,f23948]) ).
fof(f23948,plain,
( spl0_2160
<=> ! [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_2160])]) ).
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(f23946,plain,
spl0_2159,
inference(avatar_split_clause,[],[f2318,f23944]) ).
fof(f23944,plain,
( spl0_2159
<=> ! [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_2159])]) ).
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(f23942,plain,
spl0_2158,
inference(avatar_split_clause,[],[f2174,f23940]) ).
fof(f23940,plain,
( spl0_2158
<=> ! [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_2158])]) ).
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(f23938,plain,
spl0_2157,
inference(avatar_split_clause,[],[f2121,f23936]) ).
fof(f23936,plain,
( spl0_2157
<=> ! [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_2157])]) ).
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(f23934,plain,
( spl0_2156
| ~ spl0_1092
| ~ spl0_2105 ),
inference(avatar_split_clause,[],[f23789,f23663,f8967,f23932]) ).
fof(f23789,plain,
( ! [X0] :
( c_emptyset != c_union(c_Event_Obad,X0,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1092
| ~ spl0_2105 ),
inference(superposition,[],[f8968,f23664]) ).
fof(f23930,plain,
spl0_2155,
inference(avatar_split_clause,[],[f1810,f23928]) ).
fof(f23928,plain,
( spl0_2155
<=> ! [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_2155])]) ).
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(f23926,plain,
spl0_2154,
inference(avatar_split_clause,[],[f1672,f23924]) ).
fof(f23924,plain,
( spl0_2154
<=> ! [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_2154])]) ).
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(f23922,plain,
spl0_2153,
inference(avatar_split_clause,[],[f1671,f23920]) ).
fof(f23920,plain,
( spl0_2153
<=> ! [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_2153])]) ).
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(f23918,plain,
spl0_2152,
inference(avatar_split_clause,[],[f1670,f23916]) ).
fof(f23916,plain,
( spl0_2152
<=> ! [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_2152])]) ).
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(f23914,plain,
spl0_2151,
inference(avatar_split_clause,[],[f1669,f23912]) ).
fof(f23912,plain,
( spl0_2151
<=> ! [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_2151])]) ).
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(f23910,plain,
spl0_2150,
inference(avatar_split_clause,[],[f1668,f23908]) ).
fof(f23908,plain,
( spl0_2150
<=> ! [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_2150])]) ).
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(f23906,plain,
spl0_2149,
inference(avatar_split_clause,[],[f1667,f23904]) ).
fof(f23904,plain,
( spl0_2149
<=> ! [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_2149])]) ).
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(f23902,plain,
spl0_2148,
inference(avatar_split_clause,[],[f1666,f23900]) ).
fof(f23900,plain,
( spl0_2148
<=> ! [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_2148])]) ).
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(f23898,plain,
spl0_2147,
inference(avatar_split_clause,[],[f1665,f23896]) ).
fof(f23896,plain,
( spl0_2147
<=> ! [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_2147])]) ).
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(f23894,plain,
spl0_2146,
inference(avatar_split_clause,[],[f1664,f23892]) ).
fof(f23892,plain,
( spl0_2146
<=> ! [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_2146])]) ).
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(f23890,plain,
( spl0_2145
| ~ spl0_1091
| ~ spl0_2102 ),
inference(avatar_split_clause,[],[f23730,f23542,f8963,f23888]) ).
fof(f23888,plain,
( spl0_2145
<=> ! [X0] :
( c_emptyset != c_union(X0,c_Event_Obad,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f23730,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Event_Obad,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1091
| ~ spl0_2102 ),
inference(superposition,[],[f8964,f23543]) ).
fof(f23886,plain,
spl0_2144,
inference(avatar_split_clause,[],[f1663,f23884]) ).
fof(f23884,plain,
( spl0_2144
<=> ! [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_2144])]) ).
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(f23882,plain,
spl0_2143,
inference(avatar_split_clause,[],[f1662,f23880]) ).
fof(f23880,plain,
( spl0_2143
<=> ! [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_2143])]) ).
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(f23878,plain,
spl0_2142,
inference(avatar_split_clause,[],[f1661,f23876]) ).
fof(f23876,plain,
( spl0_2142
<=> ! [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_2142])]) ).
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(f23874,plain,
spl0_2141,
inference(avatar_split_clause,[],[f1660,f23872]) ).
fof(f23872,plain,
( spl0_2141
<=> ! [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_2141])]) ).
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(f23870,plain,
spl0_2140,
inference(avatar_split_clause,[],[f1659,f23868]) ).
fof(f23868,plain,
( spl0_2140
<=> ! [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_2140])]) ).
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(f23866,plain,
spl0_2139,
inference(avatar_split_clause,[],[f1658,f23864]) ).
fof(f23864,plain,
( spl0_2139
<=> ! [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_2139])]) ).
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(f23862,plain,
spl0_2138,
inference(avatar_split_clause,[],[f1657,f23860]) ).
fof(f23860,plain,
( spl0_2138
<=> ! [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_2138])]) ).
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(f23858,plain,
spl0_2137,
inference(avatar_split_clause,[],[f1656,f23856]) ).
fof(f23856,plain,
( spl0_2137
<=> ! [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_2137])]) ).
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(f23854,plain,
spl0_2136,
inference(avatar_split_clause,[],[f1655,f23852]) ).
fof(f23852,plain,
( spl0_2136
<=> ! [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_2136])]) ).
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(f23850,plain,
spl0_2135,
inference(avatar_split_clause,[],[f1654,f23848]) ).
fof(f23848,plain,
( spl0_2135
<=> ! [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_2135])]) ).
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(f23846,plain,
( spl0_2134
| ~ spl0_1762
| ~ spl0_2102 ),
inference(avatar_split_clause,[],[f23728,f23542,f16031,f23844]) ).
fof(f23728,plain,
( ! [X0] : c_union(X0,c_Event_Obad,tc_Message_Oagent) = c_union(X0,c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_1762
| ~ spl0_2102 ),
inference(superposition,[],[f23543,f16032]) ).
fof(f23842,plain,
spl0_2133,
inference(avatar_split_clause,[],[f1653,f23840]) ).
fof(f23840,plain,
( spl0_2133
<=> ! [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_2133])]) ).
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(f23838,plain,
spl0_2132,
inference(avatar_split_clause,[],[f1652,f23836]) ).
fof(f23836,plain,
( spl0_2132
<=> ! [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_2132])]) ).
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(f23834,plain,
spl0_2131,
inference(avatar_split_clause,[],[f1651,f23832]) ).
fof(f23832,plain,
( spl0_2131
<=> ! [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_2131])]) ).
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(f23830,plain,
spl0_2130,
inference(avatar_split_clause,[],[f1650,f23828]) ).
fof(f23828,plain,
( spl0_2130
<=> ! [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_2130])]) ).
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(f23826,plain,
spl0_2129,
inference(avatar_split_clause,[],[f1649,f23824]) ).
fof(f23824,plain,
( spl0_2129
<=> ! [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_2129])]) ).
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(f23822,plain,
spl0_2128,
inference(avatar_split_clause,[],[f1648,f23820]) ).
fof(f23820,plain,
( spl0_2128
<=> ! [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_2128])]) ).
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(f23818,plain,
spl0_2127,
inference(avatar_split_clause,[],[f1647,f23816]) ).
fof(f23816,plain,
( spl0_2127
<=> ! [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_2127])]) ).
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(f23814,plain,
spl0_2126,
inference(avatar_split_clause,[],[f1646,f23812]) ).
fof(f23812,plain,
( spl0_2126
<=> ! [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_2126])]) ).
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(f23810,plain,
spl0_2125,
inference(avatar_split_clause,[],[f1645,f23808]) ).
fof(f23808,plain,
( spl0_2125
<=> ! [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_2125])]) ).
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(f23806,plain,
spl0_2124,
inference(avatar_split_clause,[],[f1644,f23804]) ).
fof(f23804,plain,
( spl0_2124
<=> ! [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_2124])]) ).
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(f23784,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1643,f23782]) ).
fof(f23782,plain,
( spl0_2123
<=> ! [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_2123])]) ).
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(f23780,plain,
spl0_2122,
inference(avatar_split_clause,[],[f1642,f23778]) ).
fof(f23778,plain,
( spl0_2122
<=> ! [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_2122])]) ).
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(f23776,plain,
spl0_2121,
inference(avatar_split_clause,[],[f1641,f23774]) ).
fof(f23774,plain,
( spl0_2121
<=> ! [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_2121])]) ).
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(f23772,plain,
spl0_2120,
inference(avatar_split_clause,[],[f1629,f23770]) ).
fof(f23770,plain,
( spl0_2120
<=> ! [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_2120])]) ).
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(f23768,plain,
spl0_2119,
inference(avatar_split_clause,[],[f1614,f23766]) ).
fof(f23766,plain,
( spl0_2119
<=> ! [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_2119])]) ).
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(f23764,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1523,f23762]) ).
fof(f23762,plain,
( spl0_2118
<=> ! [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_2118])]) ).
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(f23760,plain,
spl0_2117,
inference(avatar_split_clause,[],[f1522,f23758]) ).
fof(f23758,plain,
( spl0_2117
<=> ! [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_2117])]) ).
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(f23756,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1521,f23754]) ).
fof(f23754,plain,
( spl0_2116
<=> ! [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_2116])]) ).
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(f23752,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1520,f23750]) ).
fof(f23750,plain,
( spl0_2115
<=> ! [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_2115])]) ).
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(f23748,plain,
spl0_2114,
inference(avatar_split_clause,[],[f1468,f23746]) ).
fof(f23746,plain,
( spl0_2114
<=> ! [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_2114])]) ).
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(f23724,plain,
spl0_2113,
inference(avatar_split_clause,[],[f1283,f23722]) ).
fof(f23722,plain,
( spl0_2113
<=> ! [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_2113])]) ).
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(f23720,plain,
spl0_2112,
inference(avatar_split_clause,[],[f1282,f23718]) ).
fof(f23718,plain,
( spl0_2112
<=> ! [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_2112])]) ).
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(f23716,plain,
spl0_2111,
inference(avatar_split_clause,[],[f79,f23714]) ).
fof(f23714,plain,
( spl0_2111
<=> ! [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_2111])]) ).
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(f23712,plain,
spl0_2110,
inference(avatar_split_clause,[],[f75,f23710]) ).
fof(f23710,plain,
( spl0_2110
<=> ! [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_2110])]) ).
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(f23708,plain,
spl0_2109,
inference(avatar_split_clause,[],[f69,f23706]) ).
fof(f23706,plain,
( spl0_2109
<=> ! [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_2109])]) ).
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(f23704,plain,
spl0_2108,
inference(avatar_split_clause,[],[f60,f23702]) ).
fof(f23702,plain,
( spl0_2108
<=> ! [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_2108])]) ).
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(f23700,plain,
spl0_2107,
inference(avatar_split_clause,[],[f22,f23698]) ).
fof(f23698,plain,
( spl0_2107
<=> ! [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_2107])]) ).
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(f23696,plain,
spl0_2106,
inference(avatar_split_clause,[],[f21,f23694]) ).
fof(f23694,plain,
( spl0_2106
<=> ! [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_2106])]) ).
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(f23665,plain,
( spl0_2105
| ~ spl0_1556
| ~ spl0_2070 ),
inference(avatar_split_clause,[],[f23395,f22997,f12729,f23663]) ).
fof(f22997,plain,
( spl0_2070
<=> ! [X0] : c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)) = c_minus(c_insert(v_Aa,X0,tc_Message_Oagent),c_Event_Obad,tc_set(tc_Message_Oagent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f23395,plain,
( ! [X0] : c_union(c_Event_Obad,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) = c_union(c_Event_Obad,X0,tc_Message_Oagent)
| ~ spl0_1556
| ~ spl0_2070 ),
inference(forward_demodulation,[],[f23381,f12730]) ).
fof(f23381,plain,
( ! [X0] : c_union(c_Event_Obad,c_insert(v_Aa,X0,tc_Message_Oagent),tc_Message_Oagent) = c_union(c_Event_Obad,c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1556
| ~ spl0_2070 ),
inference(superposition,[],[f12730,f22998]) ).
fof(f22998,plain,
( ! [X0] : c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)) = c_minus(c_insert(v_Aa,X0,tc_Message_Oagent),c_Event_Obad,tc_set(tc_Message_Oagent))
| ~ spl0_2070 ),
inference(avatar_component_clause,[],[f22997]) ).
fof(f23591,plain,
( spl0_2104
| ~ spl0_59
| ~ spl0_1590
| ~ spl0_2087 ),
inference(avatar_split_clause,[],[f23069,f23066,f12897,f3725,f23589]) ).
fof(f23589,plain,
( spl0_2104
<=> ! [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_2104])]) ).
fof(f23066,plain,
( spl0_2087
<=> ! [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_2087])]) ).
fof(f23069,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_59
| ~ spl0_1590
| ~ spl0_2087 ),
inference(forward_demodulation,[],[f23067,f14224]) ).
fof(f23067,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_2087 ),
inference(avatar_component_clause,[],[f23066]) ).
fof(f23587,plain,
( spl0_2103
| ~ spl0_59
| ~ spl0_1590
| ~ spl0_2086 ),
inference(avatar_split_clause,[],[f23064,f23061,f12897,f3725,f23585]) ).
fof(f23585,plain,
( spl0_2103
<=> ! [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_2103])]) ).
fof(f23061,plain,
( spl0_2086
<=> ! [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_2086])]) ).
fof(f23064,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_59
| ~ spl0_1590
| ~ spl0_2086 ),
inference(forward_demodulation,[],[f23062,f14224]) ).
fof(f23062,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_2086 ),
inference(avatar_component_clause,[],[f23061]) ).
fof(f23544,plain,
( spl0_2102
| ~ spl0_1555
| ~ spl0_2070 ),
inference(avatar_split_clause,[],[f23394,f22997,f12725,f23542]) ).
fof(f23394,plain,
( ! [X0] : c_union(c_insert(v_Aa,X0,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) = c_union(X0,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_1555
| ~ spl0_2070 ),
inference(forward_demodulation,[],[f23380,f12726]) ).
fof(f23380,plain,
( ! [X0] : c_union(c_insert(v_Aa,X0,tc_Message_Oagent),c_Event_Obad,tc_Message_Oagent) = c_union(c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)),c_Event_Obad,tc_Message_Oagent)
| ~ spl0_1555
| ~ spl0_2070 ),
inference(superposition,[],[f12726,f22998]) ).
fof(f23237,plain,
( spl0_2101
| ~ spl0_1672
| ~ spl0_2100 ),
inference(avatar_split_clause,[],[f23233,f23230,f14555,f23235]) ).
fof(f23235,plain,
( spl0_2101
<=> ! [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_2101])]) ).
fof(f14555,plain,
( spl0_1672
<=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f23230,plain,
( spl0_2100
<=> ! [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_2100])]) ).
fof(f23233,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_1672
| ~ spl0_2100 ),
inference(forward_demodulation,[],[f23231,f14557]) ).
fof(f14557,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1672 ),
inference(avatar_component_clause,[],[f14555]) ).
fof(f23231,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_2100 ),
inference(avatar_component_clause,[],[f23230]) ).
fof(f23232,plain,
spl0_2100,
inference(avatar_split_clause,[],[f3429,f23230]) ).
fof(f3429,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,[],[f3217,f2156]) ).
fof(f3217,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(f23228,plain,
spl0_2099,
inference(avatar_split_clause,[],[f3427,f23226]) ).
fof(f23226,plain,
( spl0_2099
<=> ! [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_2099])]) ).
fof(f3427,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,[],[f3215,f2156]) ).
fof(f3215,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(f23224,plain,
spl0_2098,
inference(avatar_split_clause,[],[f3425,f23222]) ).
fof(f23222,plain,
( spl0_2098
<=> ! [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_2098])]) ).
fof(f3425,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,[],[f3213,f2156]) ).
fof(f3213,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(f23180,plain,
( spl0_2097
| ~ spl0_1672
| ~ spl0_2096 ),
inference(avatar_split_clause,[],[f23176,f23173,f14555,f23178]) ).
fof(f23178,plain,
( spl0_2097
<=> ! [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_2097])]) ).
fof(f23173,plain,
( spl0_2096
<=> ! [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_2096])]) ).
fof(f23176,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_1672
| ~ spl0_2096 ),
inference(forward_demodulation,[],[f23174,f14557]) ).
fof(f23174,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_2096 ),
inference(avatar_component_clause,[],[f23173]) ).
fof(f23175,plain,
spl0_2096,
inference(avatar_split_clause,[],[f3422,f23173]) ).
fof(f3422,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,[],[f3211,f2156]) ).
fof(f3211,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(f23154,plain,
( spl0_2095
| ~ spl0_1672
| ~ spl0_2094 ),
inference(avatar_split_clause,[],[f23150,f23147,f14555,f23152]) ).
fof(f23152,plain,
( spl0_2095
<=> ! [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_2095])]) ).
fof(f23147,plain,
( spl0_2094
<=> ! [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_2094])]) ).
fof(f23150,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_1672
| ~ spl0_2094 ),
inference(forward_demodulation,[],[f23148,f14557]) ).
fof(f23148,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_2094 ),
inference(avatar_component_clause,[],[f23147]) ).
fof(f23149,plain,
spl0_2094,
inference(avatar_split_clause,[],[f3419,f23147]) ).
fof(f3419,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,[],[f3209,f2156]) ).
fof(f3209,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(f23145,plain,
spl0_2093,
inference(avatar_split_clause,[],[f3417,f23143]) ).
fof(f23143,plain,
( spl0_2093
<=> ! [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_2093])]) ).
fof(f3417,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,[],[f3207,f2156]) ).
fof(f3207,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(f23141,plain,
spl0_2092,
inference(avatar_split_clause,[],[f3415,f23139]) ).
fof(f23139,plain,
( spl0_2092
<=> ! [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_2092])]) ).
fof(f3415,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,[],[f3205,f2156]) ).
fof(f3205,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(f23128,plain,
( spl0_2091
| ~ spl0_1672
| ~ spl0_2090 ),
inference(avatar_split_clause,[],[f23101,f23098,f14555,f23126]) ).
fof(f23126,plain,
( spl0_2091
<=> ! [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_2091])]) ).
fof(f23098,plain,
( spl0_2090
<=> ! [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_2090])]) ).
fof(f23101,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_1672
| ~ spl0_2090 ),
inference(forward_demodulation,[],[f23099,f14557]) ).
fof(f23099,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_2090 ),
inference(avatar_component_clause,[],[f23098]) ).
fof(f23100,plain,
spl0_2090,
inference(avatar_split_clause,[],[f3412,f23098]) ).
fof(f3412,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,[],[f3203,f2156]) ).
fof(f3203,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(f23079,plain,
( spl0_2089
| ~ spl0_59
| ~ spl0_1470
| ~ spl0_2088 ),
inference(avatar_split_clause,[],[f23075,f23071,f11343,f3725,f23077]) ).
fof(f23077,plain,
( spl0_2089
<=> ! [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_2089])]) ).
fof(f11343,plain,
( spl0_1470
<=> ! [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_1470])]) ).
fof(f23071,plain,
( spl0_2088
<=> ! [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_2088])]) ).
fof(f23075,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_59
| ~ spl0_1470
| ~ spl0_2088 ),
inference(forward_demodulation,[],[f23074,f12391]) ).
fof(f12391,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_59
| ~ spl0_1470 ),
inference(resolution,[],[f11344,f3727]) ).
fof(f11344,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_1470 ),
inference(avatar_component_clause,[],[f11343]) ).
fof(f23074,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_59
| ~ spl0_1470
| ~ spl0_2088 ),
inference(forward_demodulation,[],[f23072,f12391]) ).
fof(f23072,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_2088 ),
inference(avatar_component_clause,[],[f23071]) ).
fof(f23073,plain,
spl0_2088,
inference(avatar_split_clause,[],[f3370,f23071]) ).
fof(f3370,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,[],[f3369,f2156]) ).
fof(f3369,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,[],[f3368,f2154]) ).
fof(f3368,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,[],[f3367,f2156]) ).
fof(f3367,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,[],[f3366,f2156]) ).
fof(f3366,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,[],[f3365,f2154]) ).
fof(f3365,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(f23068,plain,
spl0_2087,
inference(avatar_split_clause,[],[f3196,f23066]) ).
fof(f3196,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(f23063,plain,
spl0_2086,
inference(avatar_split_clause,[],[f3195,f23061]) ).
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__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(f23059,plain,
spl0_2085,
inference(avatar_split_clause,[],[f2954,f23057]) ).
fof(f23057,plain,
( spl0_2085
<=> ! [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_2085])]) ).
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(f23055,plain,
spl0_2084,
inference(avatar_split_clause,[],[f2936,f23053]) ).
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(f23051,plain,
spl0_2083,
inference(avatar_split_clause,[],[f2352,f23049]) ).
fof(f23049,plain,
( spl0_2083
<=> ! [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_2083])]) ).
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(f23047,plain,
spl0_2082,
inference(avatar_split_clause,[],[f2327,f23045]) ).
fof(f23045,plain,
( spl0_2082
<=> ! [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_2082])]) ).
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(f23043,plain,
( spl0_2081
| ~ spl0_3
| ~ spl0_2013 ),
inference(avatar_split_clause,[],[f22057,f20976,f3445,f23041]) ).
fof(f3445,plain,
( spl0_3
<=> c_in(v_KAB,c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f22057,plain,
( ! [X0] : c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)) = c_minus(c_insert(v_KAB,X0,tc_nat),c_Message_OsymKeys,tc_set(tc_nat))
| ~ spl0_3
| ~ spl0_2013 ),
inference(resolution,[],[f20977,f3447]) ).
fof(f3447,plain,
( c_in(v_KAB,c_Message_OsymKeys,tc_nat)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f3445]) ).
fof(f23039,plain,
spl0_2080,
inference(avatar_split_clause,[],[f2320,f23037]) ).
fof(f23037,plain,
( spl0_2080
<=> ! [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_2080])]) ).
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(f23035,plain,
spl0_2079,
inference(avatar_split_clause,[],[f1973,f23033]) ).
fof(f23033,plain,
( spl0_2079
<=> ! [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_2079])]) ).
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(f23031,plain,
spl0_2078,
inference(avatar_split_clause,[],[f1972,f23029]) ).
fof(f23029,plain,
( spl0_2078
<=> ! [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_2078])]) ).
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(f23027,plain,
spl0_2077,
inference(avatar_split_clause,[],[f1969,f23025]) ).
fof(f23025,plain,
( spl0_2077
<=> ! [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_2077])]) ).
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(f23023,plain,
spl0_2076,
inference(avatar_split_clause,[],[f1968,f23021]) ).
fof(f23021,plain,
( spl0_2076
<=> ! [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_2076])]) ).
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(f23019,plain,
spl0_2075,
inference(avatar_split_clause,[],[f1962,f23017]) ).
fof(f23017,plain,
( spl0_2075
<=> ! [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_2075])]) ).
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(f23015,plain,
spl0_2074,
inference(avatar_split_clause,[],[f1961,f23013]) ).
fof(f23013,plain,
( spl0_2074
<=> ! [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_2074])]) ).
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(f23011,plain,
spl0_2073,
inference(avatar_split_clause,[],[f1946,f23009]) ).
fof(f23009,plain,
( spl0_2073
<=> ! [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_2073])]) ).
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(f23007,plain,
spl0_2072,
inference(avatar_split_clause,[],[f1945,f23005]) ).
fof(f23005,plain,
( spl0_2072
<=> ! [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_2072])]) ).
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(f23003,plain,
spl0_2071,
inference(avatar_split_clause,[],[f1876,f23001]) ).
fof(f23001,plain,
( spl0_2071
<=> ! [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_2071])]) ).
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(f22999,plain,
( spl0_2070
| ~ spl0_4
| ~ spl0_2013 ),
inference(avatar_split_clause,[],[f22055,f20976,f3450,f22997]) ).
fof(f22055,plain,
( ! [X0] : c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)) = c_minus(c_insert(v_Aa,X0,tc_Message_Oagent),c_Event_Obad,tc_set(tc_Message_Oagent))
| ~ spl0_4
| ~ spl0_2013 ),
inference(resolution,[],[f20977,f3452]) ).
fof(f22995,plain,
spl0_2069,
inference(avatar_split_clause,[],[f1755,f22993]) ).
fof(f22993,plain,
( spl0_2069
<=> ! [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_2069])]) ).
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(f22991,plain,
spl0_2068,
inference(avatar_split_clause,[],[f1274,f22989]) ).
fof(f22989,plain,
( spl0_2068
<=> ! [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_2068])]) ).
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(f22987,plain,
spl0_2067,
inference(avatar_split_clause,[],[f1256,f22985]) ).
fof(f22985,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(X0,c_Finite__Set_OMax(X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
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(f22983,plain,
spl0_2066,
inference(avatar_split_clause,[],[f33,f22981]) ).
fof(f22981,plain,
( spl0_2066
<=> ! [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_2066])]) ).
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(f22979,plain,
spl0_2065,
inference(avatar_split_clause,[],[f32,f22977]) ).
fof(f22977,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),X12,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(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(f22892,plain,
( spl0_2064
| spl0_2
| ~ spl0_2011 ),
inference(avatar_split_clause,[],[f21878,f20968,f3440,f22890]) ).
fof(f22890,plain,
( spl0_2064
<=> ! [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_2064])]) ).
fof(f3440,plain,
( spl0_2
<=> c_in(v_B,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f21878,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_2
| ~ spl0_2011 ),
inference(resolution,[],[f20969,f3442]) ).
fof(f3442,plain,
( ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent)
| spl0_2 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f22571,plain,
( spl0_2063
| spl0_1
| ~ spl0_2011 ),
inference(avatar_split_clause,[],[f21877,f20968,f3435,f22569]) ).
fof(f22569,plain,
( spl0_2063
<=> ! [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_2063])]) ).
fof(f21877,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_1
| ~ spl0_2011 ),
inference(resolution,[],[f20969,f3437]) ).
fof(f3437,plain,
( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| spl0_1 ),
inference(avatar_component_clause,[],[f3435]) ).
fof(f22567,plain,
( spl0_2062
| ~ spl0_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_2046 ),
inference(avatar_split_clause,[],[f22411,f22408,f17687,f7521,f7501,f22565]) ).
fof(f22565,plain,
( spl0_2062
<=> ! [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_2062])]) ).
fof(f22408,plain,
( spl0_2046
<=> ! [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_2046])]) ).
fof(f22411,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_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_2046 ),
inference(forward_demodulation,[],[f22409,f17720]) ).
fof(f22409,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_2046 ),
inference(avatar_component_clause,[],[f22408]) ).
fof(f22531,plain,
( spl0_2061
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_2043 ),
inference(avatar_split_clause,[],[f22398,f22395,f8897,f3725,f22529]) ).
fof(f22529,plain,
( spl0_2061
<=> ! [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_2061])]) ).
fof(f22395,plain,
( spl0_2043
<=> ! [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_2043])]) ).
fof(f22398,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_59
| ~ spl0_1075
| ~ spl0_2043 ),
inference(forward_demodulation,[],[f22396,f9261]) ).
fof(f22396,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_2043 ),
inference(avatar_component_clause,[],[f22395]) ).
fof(f22473,plain,
spl0_2060,
inference(avatar_split_clause,[],[f3343,f22471]) ).
fof(f22471,plain,
( spl0_2060
<=> ! [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_2060])]) ).
fof(f3343,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,[],[f3157,f2982]) ).
fof(f2982,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(f3157,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(f22469,plain,
spl0_2059,
inference(avatar_split_clause,[],[f3163,f22467]) ).
fof(f22467,plain,
( spl0_2059
<=> ! [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_2059])]) ).
fof(f3163,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(f22459,plain,
spl0_2058,
inference(avatar_split_clause,[],[f3161,f22457]) ).
fof(f22457,plain,
( spl0_2058
<=> ! [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_2058])]) ).
fof(f3161,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(f22455,plain,
spl0_2057,
inference(avatar_split_clause,[],[f3108,f22453]) ).
fof(f22453,plain,
( spl0_2057
<=> ! [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_2057])]) ).
fof(f3108,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(f22451,plain,
spl0_2056,
inference(avatar_split_clause,[],[f3079,f22449]) ).
fof(f22449,plain,
( spl0_2056
<=> ! [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_2056])]) ).
fof(f3079,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(f22447,plain,
spl0_2055,
inference(avatar_split_clause,[],[f2858,f22445]) ).
fof(f22445,plain,
( spl0_2055
<=> ! [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_2055])]) ).
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(f22443,plain,
spl0_2054,
inference(avatar_split_clause,[],[f2846,f22441]) ).
fof(f22441,plain,
( spl0_2054
<=> ! [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_2054])]) ).
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(f22439,plain,
spl0_2053,
inference(avatar_split_clause,[],[f2797,f22437]) ).
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(f22435,plain,
spl0_2052,
inference(avatar_split_clause,[],[f2122,f22433]) ).
fof(f22433,plain,
( spl0_2052
<=> ! [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_2052])]) ).
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(f22431,plain,
spl0_2051,
inference(avatar_split_clause,[],[f1864,f22429]) ).
fof(f22429,plain,
( spl0_2051
<=> ! [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_2051])]) ).
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(f22427,plain,
spl0_2050,
inference(avatar_split_clause,[],[f1800,f22425]) ).
fof(f22425,plain,
( spl0_2050
<=> ! [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_2050])]) ).
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(f22423,plain,
spl0_2049,
inference(avatar_split_clause,[],[f1796,f22421]) ).
fof(f22421,plain,
( spl0_2049
<=> ! [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_2049])]) ).
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(f22419,plain,
( spl0_2048
| ~ spl0_1004
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f21650,f21381,f8474,f22417]) ).
fof(f22417,plain,
( spl0_2048
<=> ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f21381,plain,
( spl0_2034
<=> v_KAB = c_Message_OinvKey(v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f21650,plain,
( ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB) = X0 )
| ~ spl0_1004
| ~ spl0_2034 ),
inference(superposition,[],[f8475,f21383]) ).
fof(f21383,plain,
( v_KAB = c_Message_OinvKey(v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB))
| ~ spl0_2034 ),
inference(avatar_component_clause,[],[f21381]) ).
fof(f22415,plain,
spl0_2047,
inference(avatar_split_clause,[],[f1795,f22413]) ).
fof(f22413,plain,
( spl0_2047
<=> ! [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_2047])]) ).
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(f22410,plain,
spl0_2046,
inference(avatar_split_clause,[],[f1726,f22408]) ).
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(f22406,plain,
spl0_2045,
inference(avatar_split_clause,[],[f1714,f22404]) ).
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(f22402,plain,
spl0_2044,
inference(avatar_split_clause,[],[f1617,f22400]) ).
fof(f22400,plain,
( spl0_2044
<=> ! [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_2044])]) ).
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(f22397,plain,
spl0_2043,
inference(avatar_split_clause,[],[f1453,f22395]) ).
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(f22393,plain,
spl0_2042,
inference(avatar_split_clause,[],[f1219,f22391]) ).
fof(f22391,plain,
( spl0_2042
<=> ! [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_2042])]) ).
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(f22389,plain,
spl0_2041,
inference(avatar_split_clause,[],[f1218,f22387]) ).
fof(f22387,plain,
( spl0_2041
<=> ! [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_2041])]) ).
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(f22385,plain,
spl0_2040,
inference(avatar_split_clause,[],[f57,f22383]) ).
fof(f22383,plain,
( spl0_2040
<=> ! [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_2040])]) ).
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(f22381,plain,
spl0_2039,
inference(avatar_split_clause,[],[f56,f22379]) ).
fof(f22379,plain,
( spl0_2039
<=> ! [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_2039])]) ).
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(f22233,plain,
( ~ spl0_657
| ~ spl0_2035 ),
inference(avatar_contradiction_clause,[],[f22231]) ).
fof(f22231,plain,
( $false
| ~ spl0_657
| ~ spl0_2035 ),
inference(resolution,[],[f21387,f6175]) ).
fof(f21387,plain,
( c_in(v_KAB,c_emptyset,tc_nat)
| ~ spl0_2035 ),
inference(avatar_component_clause,[],[f21385]) ).
fof(f21385,plain,
( spl0_2035
<=> c_in(v_KAB,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f21907,plain,
( spl0_2038
| ~ spl0_741
| ~ spl0_1026
| ~ spl0_2034 ),
inference(avatar_split_clause,[],[f21657,f21381,f8693,f7311,f21904]) ).
fof(f21904,plain,
( spl0_2038
<=> v_KAB = v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f8693,plain,
( spl0_1026
<=> v_KAB = c_Message_OinvKey(v_KAB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f21657,plain,
( v_KAB = v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB)
| ~ spl0_741
| ~ spl0_1026
| ~ spl0_2034 ),
inference(forward_demodulation,[],[f21649,f8695]) ).
fof(f8695,plain,
( v_KAB = c_Message_OinvKey(v_KAB)
| ~ spl0_1026 ),
inference(avatar_component_clause,[],[f8693]) ).
fof(f21649,plain,
( c_Message_OinvKey(v_KAB) = v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB)
| ~ spl0_741
| ~ spl0_2034 ),
inference(superposition,[],[f7312,f21383]) ).
fof(f21407,plain,
( spl0_2037
| ~ spl0_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_1994 ),
inference(avatar_split_clause,[],[f20902,f20898,f17687,f7521,f7501,f21405]) ).
fof(f21405,plain,
( spl0_2037
<=> ! [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_2037])]) ).
fof(f20898,plain,
( spl0_1994
<=> ! [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_1994])]) ).
fof(f20902,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_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_1994 ),
inference(forward_demodulation,[],[f20901,f17720]) ).
fof(f20901,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_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_1994 ),
inference(forward_demodulation,[],[f20899,f17720]) ).
fof(f20899,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_1994 ),
inference(avatar_component_clause,[],[f20898]) ).
fof(f21403,plain,
( spl0_2036
| ~ spl0_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_1993 ),
inference(avatar_split_clause,[],[f20896,f20892,f17687,f7521,f7501,f21401]) ).
fof(f21401,plain,
( spl0_2036
<=> ! [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_2036])]) ).
fof(f20892,plain,
( spl0_1993
<=> ! [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_1993])]) ).
fof(f20896,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_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_1993 ),
inference(forward_demodulation,[],[f20895,f17720]) ).
fof(f20895,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_784
| ~ spl0_789
| ~ spl0_1853
| ~ spl0_1993 ),
inference(forward_demodulation,[],[f20893,f17720]) ).
fof(f20893,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_1993 ),
inference(avatar_component_clause,[],[f20892]) ).
fof(f21388,plain,
( spl0_2034
| spl0_2035
| ~ spl0_660
| ~ spl0_2019 ),
inference(avatar_split_clause,[],[f21044,f21000,f6186,f21385,f21381]) ).
fof(f6186,plain,
( spl0_660
<=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f21000,plain,
( spl0_2019
<=> ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(X0),tc_nat)
| v_KAB = c_Message_OinvKey(v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg),v_KAB)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f21044,plain,
( c_in(v_KAB,c_emptyset,tc_nat)
| v_KAB = c_Message_OinvKey(v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB))
| ~ spl0_660
| ~ spl0_2019 ),
inference(superposition,[],[f21001,f6188]) ).
fof(f6188,plain,
( c_emptyset = c_Message_OkeysFor(c_emptyset)
| ~ spl0_660 ),
inference(avatar_component_clause,[],[f6186]) ).
fof(f21001,plain,
( ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(X0),tc_nat)
| v_KAB = c_Message_OinvKey(v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg),v_KAB)) )
| ~ spl0_2019 ),
inference(avatar_component_clause,[],[f21000]) ).
fof(f21071,plain,
( spl0_2033
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2032 ),
inference(avatar_split_clause,[],[f21067,f21063,f11323,f10967,f7078,f6133,f21069]) ).
fof(f21063,plain,
( spl0_2032
<=> ! [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_2032])]) ).
fof(f21067,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2032 ),
inference(forward_demodulation,[],[f21066,f12324]) ).
fof(f21066,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_2032 ),
inference(forward_demodulation,[],[f21064,f12324]) ).
fof(f21064,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_2032 ),
inference(avatar_component_clause,[],[f21063]) ).
fof(f21065,plain,
spl0_2032,
inference(avatar_split_clause,[],[f3265,f21063]) ).
fof(f21061,plain,
spl0_2031,
inference(avatar_split_clause,[],[f3189,f21059]) ).
fof(f21059,plain,
( spl0_2031
<=> ! [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_2031])]) ).
fof(f3189,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(f21057,plain,
spl0_2030,
inference(avatar_split_clause,[],[f3184,f21055]) ).
fof(f21055,plain,
( spl0_2030
<=> ! [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_2030])]) ).
fof(f3184,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(f21042,plain,
spl0_2029,
inference(avatar_split_clause,[],[f3183,f21040]) ).
fof(f21040,plain,
( spl0_2029
<=> ! [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_2029])]) ).
fof(f3183,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(f21038,plain,
spl0_2028,
inference(avatar_split_clause,[],[f3133,f21036]) ).
fof(f21036,plain,
( spl0_2028
<=> ! [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_2028])]) ).
fof(f3133,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(f21034,plain,
spl0_2027,
inference(avatar_split_clause,[],[f3105,f21032]) ).
fof(f21032,plain,
( spl0_2027
<=> ! [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_2027])]) ).
fof(f3105,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(f21030,plain,
spl0_2026,
inference(avatar_split_clause,[],[f2940,f21028]) ).
fof(f21028,plain,
( spl0_2026
<=> ! [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_2026])]) ).
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(f21026,plain,
spl0_2025,
inference(avatar_split_clause,[],[f2939,f21024]) ).
fof(f21024,plain,
( spl0_2025
<=> ! [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_2025])]) ).
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(f21022,plain,
spl0_2024,
inference(avatar_split_clause,[],[f2938,f21020]) ).
fof(f21020,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_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
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(f21018,plain,
spl0_2023,
inference(avatar_split_clause,[],[f2937,f21016]) ).
fof(f21016,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_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
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(f21014,plain,
spl0_2022,
inference(avatar_split_clause,[],[f2873,f21012]) ).
fof(f21012,plain,
( spl0_2022
<=> ! [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_2022])]) ).
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(f21010,plain,
spl0_2021,
inference(avatar_split_clause,[],[f2867,f21008]) ).
fof(f21008,plain,
( spl0_2021
<=> ! [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_2021])]) ).
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(f21006,plain,
spl0_2020,
inference(avatar_split_clause,[],[f2839,f21004]) ).
fof(f21004,plain,
( spl0_2020
<=> ! [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_2020])]) ).
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(f21002,plain,
( spl0_2019
| ~ spl0_897
| ~ spl0_1100
| ~ spl0_1984 ),
inference(avatar_split_clause,[],[f20706,f20440,f8999,f7967,f21000]) ).
fof(f8999,plain,
( spl0_1100
<=> ! [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_1100])]) ).
fof(f20440,plain,
( spl0_1984
<=> ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(X0),tc_nat)
| v_KAB = c_Message_OinvKey(v_sko__uhi(X0,v_KAB))
| ~ c_in(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f20706,plain,
( ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(X0),tc_nat)
| v_KAB = c_Message_OinvKey(v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg),v_KAB)) )
| ~ spl0_897
| ~ spl0_1100
| ~ spl0_1984 ),
inference(forward_demodulation,[],[f20683,f9000]) ).
fof(f9000,plain,
( ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg))
| ~ spl0_1100 ),
inference(avatar_component_clause,[],[f8999]) ).
fof(f20683,plain,
( ! [X0] :
( v_KAB = c_Message_OinvKey(v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg),v_KAB))
| c_in(v_KAB,c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg)),tc_nat) )
| ~ spl0_897
| ~ spl0_1984 ),
inference(resolution,[],[f20441,f7968]) ).
fof(f20441,plain,
( ! [X0] :
( ~ c_in(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg)
| v_KAB = c_Message_OinvKey(v_sko__uhi(X0,v_KAB))
| c_in(v_KAB,c_Message_OkeysFor(X0),tc_nat) )
| ~ spl0_1984 ),
inference(avatar_component_clause,[],[f20440]) ).
fof(f20998,plain,
spl0_2018,
inference(avatar_split_clause,[],[f2838,f20996]) ).
fof(f20996,plain,
( spl0_2018
<=> ! [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_2018])]) ).
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(f20994,plain,
spl0_2017,
inference(avatar_split_clause,[],[f2805,f20992]) ).
fof(f20992,plain,
( spl0_2017
<=> ! [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_2017])]) ).
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(f20990,plain,
spl0_2016,
inference(avatar_split_clause,[],[f2804,f20988]) ).
fof(f20988,plain,
( spl0_2016
<=> ! [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_2016])]) ).
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(f20986,plain,
spl0_2015,
inference(avatar_split_clause,[],[f2802,f20984]) ).
fof(f20984,plain,
( spl0_2015
<=> ! [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_2015])]) ).
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(f20982,plain,
spl0_2014,
inference(avatar_split_clause,[],[f2791,f20980]) ).
fof(f20980,plain,
( spl0_2014
<=> ! [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_2014])]) ).
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(f20978,plain,
spl0_2013,
inference(avatar_split_clause,[],[f2674,f20976]) ).
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(f20974,plain,
spl0_2012,
inference(avatar_split_clause,[],[f2647,f20972]) ).
fof(f20972,plain,
( spl0_2012
<=> ! [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_2012])]) ).
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(f20970,plain,
spl0_2011,
inference(avatar_split_clause,[],[f2597,f20968]) ).
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(f20966,plain,
spl0_2010,
inference(avatar_split_clause,[],[f2337,f20964]) ).
fof(f20964,plain,
( spl0_2010
<=> ! [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_2010])]) ).
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(f20962,plain,
spl0_2009,
inference(avatar_split_clause,[],[f2329,f20960]) ).
fof(f20960,plain,
( spl0_2009
<=> ! [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_2009])]) ).
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(f20958,plain,
spl0_2008,
inference(avatar_split_clause,[],[f2326,f20956]) ).
fof(f20956,plain,
( spl0_2008
<=> ! [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_2008])]) ).
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(f20954,plain,
spl0_2007,
inference(avatar_split_clause,[],[f2323,f20952]) ).
fof(f20952,plain,
( spl0_2007
<=> ! [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_2007])]) ).
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(f20950,plain,
spl0_2006,
inference(avatar_split_clause,[],[f2077,f20948]) ).
fof(f20948,plain,
( spl0_2006
<=> ! [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_2006])]) ).
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(f20946,plain,
spl0_2005,
inference(avatar_split_clause,[],[f2074,f20944]) ).
fof(f20944,plain,
( spl0_2005
<=> ! [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_2005])]) ).
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(f20942,plain,
spl0_2004,
inference(avatar_split_clause,[],[f2069,f20940]) ).
fof(f20940,plain,
( spl0_2004
<=> ! [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_2004])]) ).
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(f20938,plain,
spl0_2003,
inference(avatar_split_clause,[],[f2066,f20936]) ).
fof(f20936,plain,
( spl0_2003
<=> ! [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_2003])]) ).
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(f20934,plain,
spl0_2002,
inference(avatar_split_clause,[],[f1929,f20932]) ).
fof(f20932,plain,
( spl0_2002
<=> ! [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_2002])]) ).
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(f20930,plain,
spl0_2001,
inference(avatar_split_clause,[],[f1830,f20928]) ).
fof(f20928,plain,
( spl0_2001
<=> ! [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_2001])]) ).
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(f20926,plain,
spl0_2000,
inference(avatar_split_clause,[],[f1829,f20924]) ).
fof(f20924,plain,
( spl0_2000
<=> ! [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_2000])]) ).
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(f20922,plain,
spl0_1999,
inference(avatar_split_clause,[],[f1721,f20920]) ).
fof(f20920,plain,
( spl0_1999
<=> ! [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_1999])]) ).
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(f20918,plain,
spl0_1998,
inference(avatar_split_clause,[],[f1704,f20916]) ).
fof(f20916,plain,
( spl0_1998
<=> ! [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_1998])]) ).
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(f20914,plain,
spl0_1997,
inference(avatar_split_clause,[],[f1697,f20912]) ).
fof(f20912,plain,
( spl0_1997
<=> ! [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_1997])]) ).
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(f20910,plain,
spl0_1996,
inference(avatar_split_clause,[],[f1630,f20908]) ).
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(f20906,plain,
spl0_1995,
inference(avatar_split_clause,[],[f1599,f20904]) ).
fof(f20904,plain,
( spl0_1995
<=> ! [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_1995])]) ).
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(f20900,plain,
spl0_1994,
inference(avatar_split_clause,[],[f1517,f20898]) ).
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(f20894,plain,
spl0_1993,
inference(avatar_split_clause,[],[f1516,f20892]) ).
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(f20890,plain,
spl0_1992,
inference(avatar_split_clause,[],[f1481,f20888]) ).
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(f20886,plain,
spl0_1991,
inference(avatar_split_clause,[],[f1480,f20884]) ).
fof(f20884,plain,
( spl0_1991
<=> ! [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_1991])]) ).
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(f20882,plain,
spl0_1990,
inference(avatar_split_clause,[],[f1473,f20880]) ).
fof(f20880,plain,
( spl0_1990
<=> ! [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_1990])]) ).
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(f20878,plain,
spl0_1989,
inference(avatar_split_clause,[],[f1472,f20876]) ).
fof(f20876,plain,
( spl0_1989
<=> ! [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_1989])]) ).
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(f20874,plain,
( spl0_1987
| spl0_1988
| ~ spl0_122
| ~ spl0_1984 ),
inference(avatar_split_clause,[],[f20693,f20440,f4029,f20871,f20867]) ).
fof(f20867,plain,
( spl0_1987
<=> c_in(v_KAB,c_Message_OkeysFor(c_UNIV),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f20871,plain,
( spl0_1988
<=> v_KAB = c_Message_OinvKey(v_sko__uhi(c_UNIV,v_KAB)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f20693,plain,
( v_KAB = c_Message_OinvKey(v_sko__uhi(c_UNIV,v_KAB))
| c_in(v_KAB,c_Message_OkeysFor(c_UNIV),tc_nat)
| ~ spl0_122
| ~ spl0_1984 ),
inference(resolution,[],[f20441,f4030]) ).
fof(f20865,plain,
spl0_1986,
inference(avatar_split_clause,[],[f1292,f20863]) ).
fof(f20863,plain,
( spl0_1986
<=> ! [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_1986])]) ).
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(f20861,plain,
spl0_1985,
inference(avatar_split_clause,[],[f1288,f20859]) ).
fof(f20859,plain,
( spl0_1985
<=> ! [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_1985])]) ).
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(f20442,plain,
( spl0_1984
| ~ spl0_1477
| ~ spl0_1935 ),
inference(avatar_split_clause,[],[f20437,f19417,f12268,f20440]) ).
fof(f12268,plain,
( spl0_1477
<=> ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(c_Message_Osynth(X0)),tc_nat)
| ~ c_in(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f19417,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(f20437,plain,
( ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(X0),tc_nat)
| v_KAB = c_Message_OinvKey(v_sko__uhi(X0,v_KAB))
| ~ c_in(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg) )
| ~ spl0_1477
| ~ spl0_1935 ),
inference(resolution,[],[f19418,f12269]) ).
fof(f12269,plain,
( ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(c_Message_Osynth(X0)),tc_nat)
| ~ c_in(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg) )
| ~ spl0_1477 ),
inference(avatar_component_clause,[],[f12268]) ).
fof(f19418,plain,
( ! [X91,X88] :
( ~ c_in(X91,c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
| c_in(X91,c_Message_OkeysFor(X88),tc_nat)
| c_Message_OinvKey(v_sko__uhi(X88,X91)) = X91 )
| ~ spl0_1935 ),
inference(avatar_component_clause,[],[f19417]) ).
fof(f20306,plain,
( spl0_1983
| ~ spl0_1758
| ~ spl0_1981 ),
inference(avatar_split_clause,[],[f20135,f19903,f15984,f20303]) ).
fof(f20303,plain,
( spl0_1983
<=> c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f19903,plain,
( spl0_1981
<=> c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f20135,plain,
( c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1758
| ~ spl0_1981 ),
inference(superposition,[],[f19905,f15985]) ).
fof(f19905,plain,
( c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1981 ),
inference(avatar_component_clause,[],[f19903]) ).
fof(f20012,plain,
( spl0_1982
| ~ spl0_1625
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f18875,f18600,f14367,f20010]) ).
fof(f20010,plain,
( spl0_1982
<=> ! [X0] : c_List_Oremdups(v_evs3,tc_Event_Oevent) = c_List_Olist__update(c_List_Oremdups(v_evs3,tc_Event_Oevent),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),X0,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f14367,plain,
( spl0_1625
<=> ! [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_1625])]) ).
fof(f18600,plain,
( spl0_1882
<=> c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f18875,plain,
( ! [X0] : c_List_Oremdups(v_evs3,tc_Event_Oevent) = c_List_Olist__update(c_List_Oremdups(v_evs3,tc_Event_Oevent),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),X0,tc_Event_Oevent)
| ~ spl0_1625
| ~ spl0_1882 ),
inference(resolution,[],[f18602,f14368]) ).
fof(f14368,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_1625 ),
inference(avatar_component_clause,[],[f14367]) ).
fof(f18602,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1882 ),
inference(avatar_component_clause,[],[f18600]) ).
fof(f19906,plain,
( spl0_1981
| ~ spl0_1180
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f18870,f18600,f9540,f19903]) ).
fof(f18870,plain,
( c_0 = c_minus(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1180
| ~ spl0_1882 ),
inference(resolution,[],[f18602,f9541]) ).
fof(f19793,plain,
spl0_1980,
inference(avatar_split_clause,[],[f3428,f19791]) ).
fof(f19791,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(f3428,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,[],[f3216,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(f3216,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(f19789,plain,
spl0_1979,
inference(avatar_split_clause,[],[f3426,f19787]) ).
fof(f19787,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(f3426,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,[],[f3214,f2114]) ).
fof(f3214,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(f19785,plain,
spl0_1978,
inference(avatar_split_clause,[],[f3418,f19783]) ).
fof(f19783,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(f3418,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,[],[f3208,f2114]) ).
fof(f3208,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(f19781,plain,
spl0_1977,
inference(avatar_split_clause,[],[f3416,f19779]) ).
fof(f19779,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(f3416,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,[],[f3206,f2114]) ).
fof(f3206,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(f19777,plain,
spl0_1976,
inference(avatar_split_clause,[],[f3384,f19775]) ).
fof(f19775,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(f3384,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,[],[f3180,f2156]) ).
fof(f3180,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(f19768,plain,
( spl0_1975
| ~ spl0_1672
| ~ spl0_1974 ),
inference(avatar_split_clause,[],[f19764,f19761,f14555,f19766]) ).
fof(f19766,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(f19761,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(f19764,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_1672
| ~ spl0_1974 ),
inference(forward_demodulation,[],[f19762,f14557]) ).
fof(f19762,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,[],[f19761]) ).
fof(f19763,plain,
spl0_1974,
inference(avatar_split_clause,[],[f3383,f19761]) ).
fof(f3383,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,[],[f3179,f2156]) ).
fof(f3179,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(f19759,plain,
spl0_1973,
inference(avatar_split_clause,[],[f3378,f19757]) ).
fof(f19757,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(f3378,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,[],[f3176,f2156]) ).
fof(f3176,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(f19739,plain,
( spl0_1972
| ~ spl0_1672
| ~ spl0_1971 ),
inference(avatar_split_clause,[],[f19735,f19732,f14555,f19737]) ).
fof(f19737,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(f19732,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(f19735,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_1672
| ~ spl0_1971 ),
inference(forward_demodulation,[],[f19733,f14557]) ).
fof(f19733,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,[],[f19732]) ).
fof(f19734,plain,
spl0_1971,
inference(avatar_split_clause,[],[f3377,f19732]) ).
fof(f3377,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,[],[f3175,f2156]) ).
fof(f3175,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(f19728,plain,
( spl0_1970
| ~ spl0_59
| ~ spl0_1470
| ~ spl0_1969 ),
inference(avatar_split_clause,[],[f19724,f19721,f11343,f3725,f19726]) ).
fof(f19726,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(f19721,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(f19724,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_59
| ~ spl0_1470
| ~ spl0_1969 ),
inference(forward_demodulation,[],[f19722,f12391]) ).
fof(f19722,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,[],[f19721]) ).
fof(f19723,plain,
spl0_1969,
inference(avatar_split_clause,[],[f3346,f19721]) ).
fof(f3346,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,[],[f3345,f2156]) ).
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_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,[],[f3344,f2154]) ).
fof(f3344,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(f19717,plain,
( spl0_1968
| ~ spl0_59
| ~ spl0_1470
| ~ spl0_1967 ),
inference(avatar_split_clause,[],[f19713,f19710,f11343,f3725,f19715]) ).
fof(f19715,plain,
( spl0_1968
<=> ! [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_1968])]) ).
fof(f19710,plain,
( spl0_1967
<=> ! [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_1967])]) ).
fof(f19713,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_59
| ~ spl0_1470
| ~ spl0_1967 ),
inference(forward_demodulation,[],[f19711,f12391]) ).
fof(f19711,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_1967 ),
inference(avatar_component_clause,[],[f19710]) ).
fof(f19712,plain,
spl0_1967,
inference(avatar_split_clause,[],[f3342,f19710]) ).
fof(f3342,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,[],[f3341,f2156]) ).
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_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,[],[f3340,f2154]) ).
fof(f3340,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(f19707,plain,
( spl0_1966
| ~ spl0_1672
| ~ spl0_1964 ),
inference(avatar_split_clause,[],[f19699,f19696,f14555,f19705]) ).
fof(f19705,plain,
( spl0_1966
<=> ! [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_1966])]) ).
fof(f19696,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(f19699,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_1672
| ~ spl0_1964 ),
inference(forward_demodulation,[],[f19697,f14557]) ).
fof(f19697,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,[],[f19696]) ).
fof(f19703,plain,
( spl0_1965
| ~ spl0_1449
| ~ spl0_1888 ),
inference(avatar_split_clause,[],[f19296,f19199,f11259,f19701]) ).
fof(f19701,plain,
( spl0_1965
<=> ! [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_1965])]) ).
fof(f19199,plain,
( spl0_1888
<=> ! [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_1888])]) ).
fof(f19296,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_1449
| ~ spl0_1888 ),
inference(superposition,[],[f11260,f19200]) ).
fof(f19200,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_1888 ),
inference(avatar_component_clause,[],[f19199]) ).
fof(f19698,plain,
spl0_1964,
inference(avatar_split_clause,[],[f3311,f19696]) ).
fof(f3311,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,[],[f3107,f2156]) ).
fof(f3107,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(f19694,plain,
spl0_1963,
inference(avatar_split_clause,[],[f3310,f19692]) ).
fof(f19692,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(f3310,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,[],[f3106,f2156]) ).
fof(f3106,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(f19690,plain,
spl0_1962,
inference(avatar_split_clause,[],[f3278,f19688]) ).
fof(f3278,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,[],[f3087,f2982]) ).
fof(f3087,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(f19686,plain,
spl0_1961,
inference(avatar_split_clause,[],[f3269,f19684]) ).
fof(f19684,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(f3269,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,[],[f3268,f2156]) ).
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_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3267,f2154]) ).
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_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3266,f2156]) ).
fof(f3266,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,[],[f3075,f3265]) ).
fof(f3075,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(f19664,plain,
( spl0_1960
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1959 ),
inference(avatar_split_clause,[],[f19660,f19657,f11323,f10967,f7078,f6133,f19662]) ).
fof(f19662,plain,
( spl0_1960
<=> ! [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_1960])]) ).
fof(f19657,plain,
( spl0_1959
<=> ! [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_1959])]) ).
fof(f19660,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1959 ),
inference(forward_demodulation,[],[f19658,f12324]) ).
fof(f19658,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_1959 ),
inference(avatar_component_clause,[],[f19657]) ).
fof(f19659,plain,
spl0_1959,
inference(avatar_split_clause,[],[f3156,f19657]) ).
fof(f3156,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(f19655,plain,
spl0_1958,
inference(avatar_split_clause,[],[f3080,f19653]) ).
fof(f19653,plain,
( spl0_1958
<=> ! [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_1958])]) ).
fof(f3080,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(f19651,plain,
spl0_1957,
inference(avatar_split_clause,[],[f3078,f19649]) ).
fof(f19649,plain,
( spl0_1957
<=> ! [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_1957])]) ).
fof(f3078,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(f19647,plain,
spl0_1956,
inference(avatar_split_clause,[],[f3074,f19645]) ).
fof(f19645,plain,
( spl0_1956
<=> ! [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_1956])]) ).
fof(f3074,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(f19643,plain,
( spl0_1955
| ~ spl0_1449
| ~ spl0_1883 ),
inference(avatar_split_clause,[],[f19247,f19078,f11259,f19641]) ).
fof(f19641,plain,
( spl0_1955
<=> ! [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_1955])]) ).
fof(f19078,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(f19247,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_1449
| ~ spl0_1883 ),
inference(superposition,[],[f11260,f19079]) ).
fof(f19079,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,[],[f19078]) ).
fof(f19638,plain,
( spl0_1954
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1953 ),
inference(avatar_split_clause,[],[f19634,f19631,f11323,f10967,f7078,f6133,f19636]) ).
fof(f19636,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(f19631,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(f19634,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1953 ),
inference(forward_demodulation,[],[f19632,f12324]) ).
fof(f19632,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,[],[f19631]) ).
fof(f19633,plain,
spl0_1953,
inference(avatar_split_clause,[],[f3073,f19631]) ).
fof(f3073,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(f19628,plain,
( spl0_1952
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1951 ),
inference(avatar_split_clause,[],[f19624,f19621,f11323,f10967,f7078,f6133,f19626]) ).
fof(f19626,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(f19621,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(f19624,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1951 ),
inference(forward_demodulation,[],[f19622,f12324]) ).
fof(f19622,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,[],[f19621]) ).
fof(f19623,plain,
spl0_1951,
inference(avatar_split_clause,[],[f3072,f19621]) ).
fof(f3072,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(f19618,plain,
( spl0_1950
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1949 ),
inference(avatar_split_clause,[],[f19614,f19611,f11323,f10967,f7078,f6133,f19616]) ).
fof(f19616,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(f19611,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(f19614,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1949 ),
inference(forward_demodulation,[],[f19612,f12324]) ).
fof(f19612,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,[],[f19611]) ).
fof(f19613,plain,
spl0_1949,
inference(avatar_split_clause,[],[f3071,f19611]) ).
fof(f3071,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(f19609,plain,
spl0_1948,
inference(avatar_split_clause,[],[f3059,f19607]) ).
fof(f19607,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(f3059,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(f19597,plain,
spl0_1947,
inference(avatar_split_clause,[],[f3051,f19595]) ).
fof(f19595,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(f3051,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(f19572,plain,
( spl0_1946
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1945 ),
inference(avatar_split_clause,[],[f19568,f19565,f11323,f10967,f7078,f6133,f19570]) ).
fof(f19570,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(f19565,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(f19568,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1945 ),
inference(forward_demodulation,[],[f19566,f12324]) ).
fof(f19566,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,[],[f19565]) ).
fof(f19567,plain,
spl0_1945,
inference(avatar_split_clause,[],[f3049,f19565]) ).
fof(f3049,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(f19482,plain,
( spl0_1944
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1943 ),
inference(avatar_split_clause,[],[f19478,f19474,f11323,f10967,f7078,f6133,f19480]) ).
fof(f19480,plain,
( spl0_1944
<=> ! [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_1944])]) ).
fof(f19474,plain,
( spl0_1943
<=> ! [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_1943])]) ).
fof(f19478,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1943 ),
inference(forward_demodulation,[],[f19477,f12324]) ).
fof(f19477,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1943 ),
inference(forward_demodulation,[],[f19475,f12324]) ).
fof(f19475,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_1943 ),
inference(avatar_component_clause,[],[f19474]) ).
fof(f19476,plain,
spl0_1943,
inference(avatar_split_clause,[],[f3048,f19474]) ).
fof(f19450,plain,
( spl0_1942
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1941 ),
inference(avatar_split_clause,[],[f19446,f19442,f11323,f10967,f7078,f6133,f19448]) ).
fof(f19448,plain,
( spl0_1942
<=> ! [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_1942])]) ).
fof(f19442,plain,
( spl0_1941
<=> ! [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_1941])]) ).
fof(f19446,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1941 ),
inference(forward_demodulation,[],[f19445,f12324]) ).
fof(f19445,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1941 ),
inference(forward_demodulation,[],[f19443,f12324]) ).
fof(f19443,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_1941 ),
inference(avatar_component_clause,[],[f19442]) ).
fof(f19444,plain,
spl0_1941,
inference(avatar_split_clause,[],[f3047,f19442]) ).
fof(f3047,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(f19440,plain,
( spl0_1940
| ~ spl0_1072
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f18871,f18600,f8885,f19437]) ).
fof(f19437,plain,
( spl0_1940
<=> c_List_Olist_ONil = c_List_Oupt(c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f18871,plain,
( c_List_Olist_ONil = c_List_Oupt(c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)))
| ~ spl0_1072
| ~ spl0_1882 ),
inference(resolution,[],[f18602,f8886]) ).
fof(f19435,plain,
spl0_1939,
inference(avatar_split_clause,[],[f2947,f19433]) ).
fof(f19433,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(f19431,plain,
spl0_1938,
inference(avatar_split_clause,[],[f2887,f19429]) ).
fof(f19429,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(f19427,plain,
spl0_1937,
inference(avatar_split_clause,[],[f2884,f19425]) ).
fof(f19425,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(f19423,plain,
spl0_1936,
inference(avatar_split_clause,[],[f2801,f19421]) ).
fof(f19421,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(f19419,plain,
spl0_1935,
inference(avatar_split_clause,[],[f2792,f19417]) ).
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(f19415,plain,
spl0_1934,
inference(avatar_split_clause,[],[f2697,f19413]) ).
fof(f19413,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(f19411,plain,
spl0_1933,
inference(avatar_split_clause,[],[f2696,f19409]) ).
fof(f19409,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(f19407,plain,
spl0_1932,
inference(avatar_split_clause,[],[f2690,f19405]) ).
fof(f19405,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(f19403,plain,
spl0_1931,
inference(avatar_split_clause,[],[f2573,f19401]) ).
fof(f19401,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(f19399,plain,
spl0_1930,
inference(avatar_split_clause,[],[f2565,f19397]) ).
fof(f19397,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(f19384,plain,
spl0_1929,
inference(avatar_split_clause,[],[f2556,f19382]) ).
fof(f19382,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(f19380,plain,
spl0_1928,
inference(avatar_split_clause,[],[f2553,f19378]) ).
fof(f19378,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(f19376,plain,
spl0_1927,
inference(avatar_split_clause,[],[f2526,f19374]) ).
fof(f19374,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(f19372,plain,
spl0_1926,
inference(avatar_split_clause,[],[f2521,f19370]) ).
fof(f19370,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(f19368,plain,
spl0_1925,
inference(avatar_split_clause,[],[f2324,f19366]) ).
fof(f19366,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(f19364,plain,
spl0_1924,
inference(avatar_split_clause,[],[f2307,f19362]) ).
fof(f19362,plain,
( spl0_1924
<=> ! [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_1924])]) ).
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(f19360,plain,
spl0_1923,
inference(avatar_split_clause,[],[f2305,f19358]) ).
fof(f19358,plain,
( spl0_1923
<=> ! [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_1923])]) ).
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(f19356,plain,
spl0_1922,
inference(avatar_split_clause,[],[f2266,f19354]) ).
fof(f19354,plain,
( spl0_1922
<=> ! [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_1922])]) ).
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(f19352,plain,
spl0_1921,
inference(avatar_split_clause,[],[f2261,f19350]) ).
fof(f19350,plain,
( spl0_1921
<=> ! [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_1921])]) ).
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(f19348,plain,
spl0_1920,
inference(avatar_split_clause,[],[f2258,f19346]) ).
fof(f19346,plain,
( spl0_1920
<=> ! [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_1920])]) ).
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(f19344,plain,
( spl0_1919
| ~ spl0_1497
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f18876,f18600,f12476,f19341]) ).
fof(f19341,plain,
( spl0_1919
<=> c_List_Olist_ONil = c_List_Odrop(c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f12476,plain,
( spl0_1497
<=> ! [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_1497])]) ).
fof(f18876,plain,
( c_List_Olist_ONil = c_List_Odrop(c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_1497
| ~ spl0_1882 ),
inference(resolution,[],[f18602,f12477]) ).
fof(f12477,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_1497 ),
inference(avatar_component_clause,[],[f12476]) ).
fof(f19339,plain,
spl0_1918,
inference(avatar_split_clause,[],[f2255,f19337]) ).
fof(f19337,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(f19335,plain,
spl0_1917,
inference(avatar_split_clause,[],[f2237,f19333]) ).
fof(f19333,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(f19331,plain,
spl0_1916,
inference(avatar_split_clause,[],[f2228,f19329]) ).
fof(f19329,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(f19327,plain,
spl0_1915,
inference(avatar_split_clause,[],[f2214,f19325]) ).
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(f19323,plain,
spl0_1914,
inference(avatar_split_clause,[],[f1843,f19321]) ).
fof(f19321,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(f19319,plain,
spl0_1913,
inference(avatar_split_clause,[],[f1836,f19317]) ).
fof(f19317,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(f19315,plain,
spl0_1912,
inference(avatar_split_clause,[],[f1824,f19313]) ).
fof(f19313,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(f19311,plain,
spl0_1911,
inference(avatar_split_clause,[],[f1821,f19309]) ).
fof(f19309,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(f19307,plain,
spl0_1910,
inference(avatar_split_clause,[],[f1809,f19305]) ).
fof(f19305,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(f19303,plain,
spl0_1909,
inference(avatar_split_clause,[],[f1781,f19301]) ).
fof(f19301,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(f19290,plain,
spl0_1908,
inference(avatar_split_clause,[],[f1699,f19288]) ).
fof(f19288,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(f19286,plain,
spl0_1907,
inference(avatar_split_clause,[],[f1633,f19284]) ).
fof(f19284,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(f19282,plain,
spl0_1906,
inference(avatar_split_clause,[],[f1592,f19280]) ).
fof(f19280,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(f19278,plain,
spl0_1905,
inference(avatar_split_clause,[],[f1525,f19276]) ).
fof(f19276,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(f19274,plain,
spl0_1904,
inference(avatar_split_clause,[],[f1524,f19272]) ).
fof(f19272,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(f19270,plain,
spl0_1903,
inference(avatar_split_clause,[],[f1417,f19268]) ).
fof(f19268,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(f19266,plain,
spl0_1902,
inference(avatar_split_clause,[],[f1403,f19264]) ).
fof(f19264,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(f19262,plain,
spl0_1901,
inference(avatar_split_clause,[],[f1402,f19260]) ).
fof(f19260,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(f19258,plain,
spl0_1900,
inference(avatar_split_clause,[],[f1366,f19256]) ).
fof(f19256,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(f19254,plain,
spl0_1899,
inference(avatar_split_clause,[],[f1365,f19252]) ).
fof(f19252,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(f19241,plain,
spl0_1898,
inference(avatar_split_clause,[],[f1362,f19239]) ).
fof(f19239,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(f19237,plain,
spl0_1897,
inference(avatar_split_clause,[],[f1360,f19235]) ).
fof(f19235,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(f19233,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1359,f19231]) ).
fof(f19231,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(f19229,plain,
spl0_1895,
inference(avatar_split_clause,[],[f1306,f19227]) ).
fof(f19227,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(f19225,plain,
spl0_1894,
inference(avatar_split_clause,[],[f1290,f19223]) ).
fof(f19223,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(f19221,plain,
spl0_1893,
inference(avatar_split_clause,[],[f1289,f19219]) ).
fof(f19219,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(f19217,plain,
spl0_1892,
inference(avatar_split_clause,[],[f114,f19215]) ).
fof(f19215,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(f19213,plain,
spl0_1891,
inference(avatar_split_clause,[],[f113,f19211]) ).
fof(f19211,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(f19209,plain,
spl0_1890,
inference(avatar_split_clause,[],[f76,f19207]) ).
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(f19205,plain,
spl0_1889,
inference(avatar_split_clause,[],[f72,f19203]) ).
fof(f19203,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(f19201,plain,
( spl0_1888
| spl0_2
| ~ spl0_1835 ),
inference(avatar_split_clause,[],[f18943,f17346,f3440,f19199]) ).
fof(f17346,plain,
( spl0_1835
<=> ! [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_1835])]) ).
fof(f18943,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_2
| ~ spl0_1835 ),
inference(resolution,[],[f17347,f3442]) ).
fof(f17347,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_1835 ),
inference(avatar_component_clause,[],[f17346]) ).
fof(f19197,plain,
spl0_1887,
inference(avatar_split_clause,[],[f71,f19195]) ).
fof(f19195,plain,
( spl0_1887
<=> ! [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_1887])]) ).
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(f19193,plain,
spl0_1886,
inference(avatar_split_clause,[],[f70,f19191]) ).
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(f19189,plain,
spl0_1885,
inference(avatar_split_clause,[],[f58,f19187]) ).
fof(f19187,plain,
( spl0_1885
<=> ! [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_1885])]) ).
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(f19185,plain,
spl0_1884,
inference(avatar_split_clause,[],[f46,f19183]) ).
fof(f19183,plain,
( spl0_1884
<=> ! [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_1884])]) ).
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(f19080,plain,
( spl0_1883
| spl0_1
| ~ spl0_1835 ),
inference(avatar_split_clause,[],[f18942,f17346,f3435,f19078]) ).
fof(f18942,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_1
| ~ spl0_1835 ),
inference(resolution,[],[f17347,f3437]) ).
fof(f18603,plain,
( spl0_1882
| ~ spl0_1061
| ~ spl0_1332
| ~ spl0_1763
| ~ spl0_1853
| ~ spl0_1881 ),
inference(avatar_split_clause,[],[f18407,f18299,f17687,f16035,f10780,f8841,f18600]) ).
fof(f10780,plain,
( spl0_1332
<=> ! [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_1332])]) ).
fof(f16035,plain,
( spl0_1763
<=> ! [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_1763])]) ).
fof(f18299,plain,
( spl0_1881
<=> c_List_Oremdups(v_evs3,tc_Event_Oevent) = c_List_Oremdups(c_List_Olist_OCons(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)))))),v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f18407,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_1,c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),tc_nat),tc_nat)
| ~ spl0_1061
| ~ spl0_1332
| ~ spl0_1763
| ~ spl0_1853
| ~ spl0_1881 ),
inference(forward_demodulation,[],[f18406,f17722]) ).
fof(f17722,plain,
( ! [X1] : c_plus(X1,c_1,tc_nat) = c_plus(c_1,X1,tc_nat)
| ~ spl0_1061
| ~ spl0_1763
| ~ spl0_1853 ),
inference(forward_demodulation,[],[f17721,f8842]) ).
fof(f17721,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_1061
| ~ spl0_1763
| ~ spl0_1853 ),
inference(forward_demodulation,[],[f17710,f8842]) ).
fof(f17710,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_1763
| ~ spl0_1853 ),
inference(superposition,[],[f16036,f17688]) ).
fof(f16036,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_1763 ),
inference(avatar_component_clause,[],[f16035]) ).
fof(f18406,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_plus(c_Nat_Osize(v_evs3,tc_List_Olist(tc_Event_Oevent)),c_1,tc_nat),tc_nat)
| ~ spl0_1332
| ~ spl0_1763
| ~ spl0_1881 ),
inference(forward_demodulation,[],[f18402,f16036]) ).
fof(f18402,plain,
( c_lessequals(c_Nat_Osize(c_List_Oremdups(v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),c_Nat_Osize(c_List_Olist_OCons(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)))))),v_evs3,tc_Event_Oevent),tc_List_Olist(tc_Event_Oevent)),tc_nat)
| ~ spl0_1332
| ~ spl0_1881 ),
inference(superposition,[],[f10781,f18301]) ).
fof(f18301,plain,
( c_List_Oremdups(v_evs3,tc_Event_Oevent) = c_List_Oremdups(c_List_Olist_OCons(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)))))),v_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_1881 ),
inference(avatar_component_clause,[],[f18299]) ).
fof(f10781,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_1332 ),
inference(avatar_component_clause,[],[f10780]) ).
fof(f18302,plain,
( spl0_1881
| ~ spl0_751
| ~ spl0_1798 ),
inference(avatar_split_clause,[],[f18212,f17129,f7366,f18299]) ).
fof(f18212,plain,
( c_List_Oremdups(v_evs3,tc_Event_Oevent) = c_List_Oremdups(c_List_Olist_OCons(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)))))),v_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ spl0_751
| ~ spl0_1798 ),
inference(resolution,[],[f17130,f7368]) ).
fof(f18107,plain,
( spl0_1880
| ~ spl0_897
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9225,f8845,f7967,f18105]) ).
fof(f18105,plain,
( spl0_1880
<=> ! [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_1880])]) ).
fof(f9225,plain,
( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_897
| ~ spl0_1062 ),
inference(superposition,[],[f7968,f8846]) ).
fof(f17932,plain,
( spl0_1879
| ~ spl0_1000
| ~ spl0_1001 ),
inference(avatar_split_clause,[],[f8667,f8462,f8457,f17929]) ).
fof(f17929,plain,
( spl0_1879
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f8667,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_1000
| ~ spl0_1001 ),
inference(superposition,[],[f8463,f8459]) ).
fof(f17896,plain,
( spl0_1876
| spl0_1878 ),
inference(avatar_split_clause,[],[f3433,f17894,f17873]) ).
fof(f17873,plain,
( spl0_1876
<=> ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f17894,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(f3433,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(f17882,plain,
( ~ spl0_717
| ~ spl0_1876 ),
inference(avatar_contradiction_clause,[],[f17881]) ).
fof(f17881,plain,
( $false
| ~ spl0_717
| ~ spl0_1876 ),
inference(trivial_inequality_removal,[],[f17879]) ).
fof(f17879,plain,
( c_0 != c_0
| ~ spl0_717
| ~ spl0_1876 ),
inference(superposition,[],[f17874,f7208]) ).
fof(f7208,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_717 ),
inference(avatar_component_clause,[],[f7206]) ).
fof(f7206,plain,
( spl0_717
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f17874,plain,
( ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ spl0_1876 ),
inference(avatar_component_clause,[],[f17873]) ).
fof(f17878,plain,
( spl0_1876
| spl0_1877 ),
inference(avatar_split_clause,[],[f3432,f17876,f17873]) ).
fof(f17876,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(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_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(f17845,plain,
( spl0_1875
| ~ spl0_648
| ~ spl0_689
| ~ spl0_789
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1758
| ~ spl0_1874 ),
inference(avatar_split_clause,[],[f17841,f17837,f15984,f11323,f10967,f7521,f7078,f6133,f17843]) ).
fof(f17843,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(f17837,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(f17841,plain,
( ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_648
| ~ spl0_689
| ~ spl0_789
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1758
| ~ spl0_1874 ),
inference(forward_demodulation,[],[f17840,f15987]) ).
fof(f15987,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_789
| ~ spl0_1758 ),
inference(superposition,[],[f15985,f7522]) ).
fof(f17840,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1874 ),
inference(forward_demodulation,[],[f17838,f12324]) ).
fof(f17838,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,[],[f17837]) ).
fof(f17839,plain,
spl0_1874,
inference(avatar_split_clause,[],[f3326,f17837]) ).
fof(f3326,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,[],[f3135,f3054]) ).
fof(f3135,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(f17835,plain,
spl0_1873,
inference(avatar_split_clause,[],[f3159,f17833]) ).
fof(f17833,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(f3159,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(f17831,plain,
spl0_1872,
inference(avatar_split_clause,[],[f3158,f17829]) ).
fof(f17829,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(f3158,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(f17827,plain,
spl0_1871,
inference(avatar_split_clause,[],[f3154,f17825]) ).
fof(f17825,plain,
( spl0_1871
<=> ! [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_1871])]) ).
fof(f3154,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(f17823,plain,
spl0_1870,
inference(avatar_split_clause,[],[f3153,f17821]) ).
fof(f17821,plain,
( spl0_1870
<=> ! [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_1870])]) ).
fof(f3153,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(f17817,plain,
spl0_1869,
inference(avatar_split_clause,[],[f3146,f17815]) ).
fof(f17815,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(f3146,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(f17811,plain,
spl0_1868,
inference(avatar_split_clause,[],[f3142,f17809]) ).
fof(f17809,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(f17807,plain,
spl0_1867,
inference(avatar_split_clause,[],[f3139,f17805]) ).
fof(f3139,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,[],[f2680,f2373]) ).
fof(f2680,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__2_0) ).
fof(f17803,plain,
spl0_1866,
inference(avatar_split_clause,[],[f3137,f17801]) ).
fof(f3137,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(f17797,plain,
spl0_1865,
inference(avatar_split_clause,[],[f3132,f17795]) ).
fof(f17795,plain,
( spl0_1865
<=> ! [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_1865])]) ).
fof(f3132,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(f17791,plain,
spl0_1864,
inference(avatar_split_clause,[],[f3127,f17789]) ).
fof(f17789,plain,
( spl0_1864
<=> ! [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_1864])]) ).
fof(f3127,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(f17787,plain,
( spl0_1862
| ~ spl0_1863
| ~ spl0_872
| ~ spl0_978 ),
inference(avatar_split_clause,[],[f8636,f8367,f7867,f17784,f17781]) ).
fof(f17781,plain,
( spl0_1862
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f17784,plain,
( spl0_1863
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f8636,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_872
| ~ spl0_978 ),
inference(resolution,[],[f8368,f7868]) ).
fof(f17779,plain,
spl0_1861,
inference(avatar_split_clause,[],[f3115,f17777]) ).
fof(f17777,plain,
( spl0_1861
<=> ! [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_1861])]) ).
fof(f3115,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,f2837,f2837]) ).
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(f17771,plain,
( spl0_1860
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1859 ),
inference(avatar_split_clause,[],[f17767,f17764,f11323,f10967,f7078,f6133,f17769]) ).
fof(f17769,plain,
( spl0_1860
<=> ! [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_1860])]) ).
fof(f17764,plain,
( spl0_1859
<=> ! [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_1859])]) ).
fof(f17767,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1859 ),
inference(forward_demodulation,[],[f17765,f12324]) ).
fof(f17765,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_1859 ),
inference(avatar_component_clause,[],[f17764]) ).
fof(f17766,plain,
spl0_1859,
inference(avatar_split_clause,[],[f3111,f17764]) ).
fof(f3111,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(f17758,plain,
( spl0_1858
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1857 ),
inference(avatar_split_clause,[],[f17754,f17751,f11323,f10967,f7078,f6133,f17756]) ).
fof(f17756,plain,
( spl0_1858
<=> ! [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_1858])]) ).
fof(f17751,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(f17754,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1857 ),
inference(forward_demodulation,[],[f17752,f12324]) ).
fof(f17752,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,[],[f17751]) ).
fof(f17753,plain,
spl0_1857,
inference(avatar_split_clause,[],[f3068,f17751]) ).
fof(f3068,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(f17735,plain,
( spl0_1856
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1855 ),
inference(avatar_split_clause,[],[f17731,f17728,f11323,f10967,f7078,f6133,f17733]) ).
fof(f17733,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(f17728,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(f17731,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1855 ),
inference(forward_demodulation,[],[f17729,f12324]) ).
fof(f17729,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,[],[f17728]) ).
fof(f17730,plain,
spl0_1855,
inference(avatar_split_clause,[],[f3067,f17728]) ).
fof(f3067,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(f17726,plain,
( spl0_1854
| ~ spl0_648
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f8576,f8234,f6133,f17724]) ).
fof(f17724,plain,
( spl0_1854
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f8234,plain,
( spl0_945
<=> ! [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_945])]) ).
fof(f8576,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_945 ),
inference(superposition,[],[f8235,f6135]) ).
fof(f8235,plain,
( ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_945 ),
inference(avatar_component_clause,[],[f8234]) ).
fof(f17689,plain,
( spl0_1853
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1852 ),
inference(avatar_split_clause,[],[f17685,f17682,f11323,f10967,f7078,f6133,f17687]) ).
fof(f17682,plain,
( spl0_1852
<=> ! [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_1852])]) ).
fof(f17685,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1852 ),
inference(forward_demodulation,[],[f17683,f12324]) ).
fof(f17683,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_1852 ),
inference(avatar_component_clause,[],[f17682]) ).
fof(f17684,plain,
spl0_1852,
inference(avatar_split_clause,[],[f3065,f17682]) ).
fof(f3065,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(f17585,plain,
( spl0_1851
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1850 ),
inference(avatar_split_clause,[],[f17581,f17578,f11323,f10967,f7078,f6133,f17583]) ).
fof(f17583,plain,
( spl0_1851
<=> ! [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_1851])]) ).
fof(f17578,plain,
( spl0_1850
<=> ! [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_1850])]) ).
fof(f17581,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1850 ),
inference(forward_demodulation,[],[f17579,f12324]) ).
fof(f17579,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_1850 ),
inference(avatar_component_clause,[],[f17578]) ).
fof(f17580,plain,
spl0_1850,
inference(avatar_split_clause,[],[f3064,f17578]) ).
fof(f3064,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(f17485,plain,
( spl0_1849
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1848 ),
inference(avatar_split_clause,[],[f17481,f17478,f11323,f10967,f7078,f6133,f17483]) ).
fof(f17483,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(f17478,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(f17481,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1848 ),
inference(forward_demodulation,[],[f17479,f12324]) ).
fof(f17479,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,[],[f17478]) ).
fof(f17480,plain,
spl0_1848,
inference(avatar_split_clause,[],[f3063,f17478]) ).
fof(f3063,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(f17422,plain,
( spl0_1847
| ~ spl0_649
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f8575,f8234,f6138,f17420]) ).
fof(f17420,plain,
( spl0_1847
<=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f8575,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_945 ),
inference(superposition,[],[f8235,f6140]) ).
fof(f17418,plain,
( spl0_1846
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1845 ),
inference(avatar_split_clause,[],[f17414,f17411,f11323,f10967,f7078,f6133,f17416]) ).
fof(f17416,plain,
( spl0_1846
<=> ! [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_1846])]) ).
fof(f17411,plain,
( spl0_1845
<=> ! [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_1845])]) ).
fof(f17414,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1845 ),
inference(forward_demodulation,[],[f17412,f12324]) ).
fof(f17412,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_1845 ),
inference(avatar_component_clause,[],[f17411]) ).
fof(f17413,plain,
spl0_1845,
inference(avatar_split_clause,[],[f3062,f17411]) ).
fof(f3062,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(f17385,plain,
( spl0_1844
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1843 ),
inference(avatar_split_clause,[],[f17381,f17378,f11323,f10967,f7078,f6133,f17383]) ).
fof(f17383,plain,
( spl0_1844
<=> ! [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_1844])]) ).
fof(f17378,plain,
( spl0_1843
<=> ! [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_1843])]) ).
fof(f17381,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1843 ),
inference(forward_demodulation,[],[f17379,f12324]) ).
fof(f17379,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_1843 ),
inference(avatar_component_clause,[],[f17378]) ).
fof(f17380,plain,
spl0_1843,
inference(avatar_split_clause,[],[f3061,f17378]) ).
fof(f3061,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(f17376,plain,
spl0_1842,
inference(avatar_split_clause,[],[f3060,f17374]) ).
fof(f17374,plain,
( spl0_1842
<=> ! [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_1842])]) ).
fof(f3060,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(f17372,plain,
spl0_1841,
inference(avatar_split_clause,[],[f2933,f17370]) ).
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(f17368,plain,
spl0_1840,
inference(avatar_split_clause,[],[f2866,f17366]) ).
fof(f17366,plain,
( spl0_1840
<=> ! [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_1840])]) ).
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(f17364,plain,
spl0_1839,
inference(avatar_split_clause,[],[f2828,f17362]) ).
fof(f17362,plain,
( spl0_1839
<=> ! [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_1839])]) ).
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(f17360,plain,
spl0_1838,
inference(avatar_split_clause,[],[f2807,f17358]) ).
fof(f17358,plain,
( spl0_1838
<=> ! [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_1838])]) ).
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(f17356,plain,
( spl0_1837
| ~ spl0_648
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f8574,f8234,f6133,f17354]) ).
fof(f17354,plain,
( spl0_1837
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f8574,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_945 ),
inference(superposition,[],[f8235,f6135]) ).
fof(f17352,plain,
spl0_1836,
inference(avatar_split_clause,[],[f2799,f17350]) ).
fof(f17350,plain,
( spl0_1836
<=> ! [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_1836])]) ).
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(f17348,plain,
spl0_1835,
inference(avatar_split_clause,[],[f2798,f17346]) ).
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(f17344,plain,
spl0_1834,
inference(avatar_split_clause,[],[f2675,f17342]) ).
fof(f17342,plain,
( spl0_1834
<=> ! [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_1834])]) ).
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(f17340,plain,
spl0_1833,
inference(avatar_split_clause,[],[f2650,f17338]) ).
fof(f17338,plain,
( spl0_1833
<=> ! [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_1833])]) ).
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(f17336,plain,
spl0_1832,
inference(avatar_split_clause,[],[f2596,f17334]) ).
fof(f17334,plain,
( spl0_1832
<=> ! [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_1832])]) ).
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(f17332,plain,
spl0_1831,
inference(avatar_split_clause,[],[f2585,f17330]) ).
fof(f17330,plain,
( spl0_1831
<=> ! [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_1831])]) ).
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(f17328,plain,
spl0_1830,
inference(avatar_split_clause,[],[f2584,f17326]) ).
fof(f17326,plain,
( spl0_1830
<=> ! [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_1830])]) ).
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(f17324,plain,
spl0_1829,
inference(avatar_split_clause,[],[f2574,f17322]) ).
fof(f17322,plain,
( spl0_1829
<=> ! [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_1829])]) ).
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(f17320,plain,
spl0_1828,
inference(avatar_split_clause,[],[f2360,f17318]) ).
fof(f17318,plain,
( spl0_1828
<=> ! [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_1828])]) ).
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(f17316,plain,
spl0_1827,
inference(avatar_split_clause,[],[f2359,f17314]) ).
fof(f17314,plain,
( spl0_1827
<=> ! [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_1827])]) ).
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(f17312,plain,
( spl0_1826
| ~ spl0_648
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8565,f8222,f6133,f17310]) ).
fof(f17310,plain,
( spl0_1826
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f8222,plain,
( spl0_942
<=> ! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f8565,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_648
| ~ spl0_942 ),
inference(superposition,[],[f8223,f6135]) ).
fof(f8223,plain,
( ! [X21,X15] :
( c_IntDef_Oint(X21) != c_IntDef_Oint(X15)
| X15 = X21 )
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f8222]) ).
fof(f17308,plain,
spl0_1825,
inference(avatar_split_clause,[],[f2194,f17306]) ).
fof(f17306,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(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
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(f17304,plain,
spl0_1824,
inference(avatar_split_clause,[],[f2193,f17302]) ).
fof(f17302,plain,
( spl0_1824
<=> ! [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_1824])]) ).
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(f17300,plain,
spl0_1823,
inference(avatar_split_clause,[],[f2192,f17298]) ).
fof(f17298,plain,
( spl0_1823
<=> ! [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_1823])]) ).
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(f17296,plain,
spl0_1822,
inference(avatar_split_clause,[],[f2191,f17294]) ).
fof(f17294,plain,
( spl0_1822
<=> ! [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_1822])]) ).
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(f17292,plain,
spl0_1821,
inference(avatar_split_clause,[],[f2189,f17290]) ).
fof(f17290,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(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
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(f17288,plain,
spl0_1820,
inference(avatar_split_clause,[],[f2188,f17286]) ).
fof(f17286,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(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
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(f17284,plain,
spl0_1819,
inference(avatar_split_clause,[],[f2187,f17282]) ).
fof(f17282,plain,
( spl0_1819
<=> ! [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_1819])]) ).
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(f17280,plain,
spl0_1818,
inference(avatar_split_clause,[],[f2186,f17278]) ).
fof(f17278,plain,
( spl0_1818
<=> ! [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_1818])]) ).
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(f17276,plain,
spl0_1817,
inference(avatar_split_clause,[],[f2146,f17274]) ).
fof(f17274,plain,
( spl0_1817
<=> ! [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_1817])]) ).
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(f17272,plain,
spl0_1816,
inference(avatar_split_clause,[],[f2145,f17270]) ).
fof(f17270,plain,
( spl0_1816
<=> ! [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_1816])]) ).
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(f17253,plain,
spl0_1815,
inference(avatar_split_clause,[],[f2138,f17251]) ).
fof(f17251,plain,
( spl0_1815
<=> ! [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_1815])]) ).
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(f17249,plain,
spl0_1814,
inference(avatar_split_clause,[],[f2137,f17247]) ).
fof(f17247,plain,
( spl0_1814
<=> ! [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_1814])]) ).
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(f17245,plain,
spl0_1813,
inference(avatar_split_clause,[],[f2119,f17243]) ).
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(f17241,plain,
spl0_1812,
inference(avatar_split_clause,[],[f2116,f17239]) ).
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(f17237,plain,
spl0_1811,
inference(avatar_split_clause,[],[f1971,f17235]) ).
fof(f17235,plain,
( spl0_1811
<=> ! [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_1811])]) ).
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(f17233,plain,
spl0_1810,
inference(avatar_split_clause,[],[f1970,f17231]) ).
fof(f17231,plain,
( spl0_1810
<=> ! [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_1810])]) ).
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(f17229,plain,
spl0_1809,
inference(avatar_split_clause,[],[f1967,f17227]) ).
fof(f17227,plain,
( spl0_1809
<=> ! [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_1809])]) ).
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(f17225,plain,
spl0_1808,
inference(avatar_split_clause,[],[f1966,f17223]) ).
fof(f17223,plain,
( spl0_1808
<=> ! [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_1808])]) ).
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(f17221,plain,
spl0_1807,
inference(avatar_split_clause,[],[f1960,f17219]) ).
fof(f17219,plain,
( spl0_1807
<=> ! [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_1807])]) ).
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(f17217,plain,
spl0_1806,
inference(avatar_split_clause,[],[f1959,f17215]) ).
fof(f17215,plain,
( spl0_1806
<=> ! [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_1806])]) ).
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(f17160,plain,
spl0_1805,
inference(avatar_split_clause,[],[f1944,f17158]) ).
fof(f17158,plain,
( spl0_1805
<=> ! [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_1805])]) ).
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(f17156,plain,
spl0_1804,
inference(avatar_split_clause,[],[f1943,f17154]) ).
fof(f17154,plain,
( spl0_1804
<=> ! [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_1804])]) ).
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(f17152,plain,
spl0_1803,
inference(avatar_split_clause,[],[f1869,f17150]) ).
fof(f17150,plain,
( spl0_1803
<=> ! [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_1803])]) ).
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(f17148,plain,
spl0_1802,
inference(avatar_split_clause,[],[f1780,f17146]) ).
fof(f17146,plain,
( spl0_1802
<=> ! [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_1802])]) ).
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(f17144,plain,
spl0_1801,
inference(avatar_split_clause,[],[f1764,f17142]) ).
fof(f17142,plain,
( spl0_1801
<=> ! [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_1801])]) ).
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(f17139,plain,
spl0_1800,
inference(avatar_split_clause,[],[f1727,f17137]) ).
fof(f17137,plain,
( spl0_1800
<=> ! [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_1800])]) ).
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(f17135,plain,
spl0_1799,
inference(avatar_split_clause,[],[f1724,f17133]) ).
fof(f17133,plain,
( spl0_1799
<=> ! [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_1799])]) ).
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(f17131,plain,
spl0_1798,
inference(avatar_split_clause,[],[f1713,f17129]) ).
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(f17127,plain,
spl0_1797,
inference(avatar_split_clause,[],[f1701,f17125]) ).
fof(f17125,plain,
( spl0_1797
<=> ! [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_1797])]) ).
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(f17123,plain,
spl0_1796,
inference(avatar_split_clause,[],[f1700,f17121]) ).
fof(f17121,plain,
( spl0_1796
<=> ! [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_1796])]) ).
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(f17119,plain,
( spl0_1795
| ~ spl0_814
| ~ spl0_1749 ),
inference(avatar_split_clause,[],[f16775,f15926,f7622,f17117]) ).
fof(f17117,plain,
( spl0_1795
<=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f15926,plain,
( spl0_1749
<=> ! [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_1749])]) ).
fof(f16775,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_814
| ~ spl0_1749 ),
inference(forward_demodulation,[],[f16745,f7623]) ).
fof(f16745,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_814
| ~ spl0_1749 ),
inference(superposition,[],[f15927,f7623]) ).
fof(f15927,plain,
( ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1)
| ~ spl0_1749 ),
inference(avatar_component_clause,[],[f15926]) ).
fof(f17115,plain,
spl0_1794,
inference(avatar_split_clause,[],[f1618,f17113]) ).
fof(f17113,plain,
( spl0_1794
<=> ! [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_1794])]) ).
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(f17111,plain,
spl0_1793,
inference(avatar_split_clause,[],[f1605,f17109]) ).
fof(f17109,plain,
( spl0_1793
<=> ! [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_1793])]) ).
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(f17107,plain,
spl0_1792,
inference(avatar_split_clause,[],[f1546,f17105]) ).
fof(f17105,plain,
( spl0_1792
<=> ! [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_1792])]) ).
fof(f1546,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_Oconcat__eq__Nil__conv_0) ).
fof(f17103,plain,
spl0_1791,
inference(avatar_split_clause,[],[f1545,f17101]) ).
fof(f17101,plain,
( spl0_1791
<=> ! [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_1791])]) ).
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(f17099,plain,
spl0_1790,
inference(avatar_split_clause,[],[f1538,f17097]) ).
fof(f17097,plain,
( spl0_1790
<=> ! [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_1790])]) ).
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(f17095,plain,
spl0_1789,
inference(avatar_split_clause,[],[f1519,f17093]) ).
fof(f17093,plain,
( spl0_1789
<=> ! [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_1789])]) ).
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(f17091,plain,
spl0_1788,
inference(avatar_split_clause,[],[f1515,f17089]) ).
fof(f17089,plain,
( spl0_1788
<=> ! [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_1788])]) ).
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(f17087,plain,
spl0_1787,
inference(avatar_split_clause,[],[f1506,f17085]) ).
fof(f17085,plain,
( spl0_1787
<=> ! [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_1787])]) ).
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(f17083,plain,
spl0_1786,
inference(avatar_split_clause,[],[f1311,f17081]) ).
fof(f17081,plain,
( spl0_1786
<=> ! [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_1786])]) ).
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(f17079,plain,
spl0_1785,
inference(avatar_split_clause,[],[f1303,f17077]) ).
fof(f17077,plain,
( spl0_1785
<=> ! [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_1785])]) ).
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(f17075,plain,
spl0_1784,
inference(avatar_split_clause,[],[f1302,f17073]) ).
fof(f17073,plain,
( spl0_1784
<=> ! [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_1784])]) ).
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(f17071,plain,
spl0_1783,
inference(avatar_split_clause,[],[f1301,f17069]) ).
fof(f17069,plain,
( spl0_1783
<=> ! [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_1783])]) ).
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(f17067,plain,
spl0_1782,
inference(avatar_split_clause,[],[f1272,f17065]) ).
fof(f17065,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_OMin(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
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(f17063,plain,
spl0_1781,
inference(avatar_split_clause,[],[f1257,f17061]) ).
fof(f17061,plain,
( spl0_1781
<=> ! [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_1781])]) ).
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(f17059,plain,
spl0_1780,
inference(avatar_split_clause,[],[f81,f17057]) ).
fof(f17057,plain,
( spl0_1780
<=> ! [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_1780])]) ).
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(f17055,plain,
spl0_1779,
inference(avatar_split_clause,[],[f47,f17053]) ).
fof(f17053,plain,
( spl0_1779
<=> ! [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_1779])]) ).
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(f17002,plain,
( spl0_1778
| ~ spl0_752
| ~ spl0_1753 ),
inference(avatar_split_clause,[],[f16847,f15942,f7371,f16999]) ).
fof(f16999,plain,
( spl0_1778
<=> 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_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f15942,plain,
( spl0_1753
<=> ! [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_1753])]) ).
fof(f16847,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_evs3),tc_Message_Omsg)
| ~ spl0_752
| ~ spl0_1753 ),
inference(resolution,[],[f15943,f7373]) ).
fof(f15943,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_1753 ),
inference(avatar_component_clause,[],[f15942]) ).
fof(f16834,plain,
( spl0_1777
| ~ spl0_674
| ~ spl0_1742 ),
inference(avatar_split_clause,[],[f16657,f15898,f7014,f16832]) ).
fof(f16832,plain,
( spl0_1777
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f15898,plain,
( spl0_1742
<=> ! [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_1742])]) ).
fof(f16657,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_674
| ~ spl0_1742 ),
inference(resolution,[],[f15899,f7015]) ).
fof(f15899,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_1742 ),
inference(avatar_component_clause,[],[f15898]) ).
fof(f16593,plain,
( spl0_1776
| ~ spl0_760
| ~ spl0_1715 ),
inference(avatar_split_clause,[],[f16410,f15780,f7404,f16591]) ).
fof(f16591,plain,
( spl0_1776
<=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f15780,plain,
( spl0_1715
<=> ! [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_1715])]) ).
fof(f16410,plain,
( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
| ~ spl0_760
| ~ spl0_1715 ),
inference(trivial_inequality_removal,[],[f16400]) ).
fof(f16400,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_0,X0,X1) = X0 )
| ~ spl0_760
| ~ spl0_1715 ),
inference(superposition,[],[f15781,f7405]) ).
fof(f15781,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_1715 ),
inference(avatar_component_clause,[],[f15780]) ).
fof(f16276,plain,
( ~ spl0_1774
| spl0_1775
| ~ spl0_116
| ~ spl0_1705 ),
inference(avatar_split_clause,[],[f16194,f15739,f4005,f16274,f16270]) ).
fof(f16270,plain,
( spl0_1774
<=> c_List_Odistinct(v_evs3,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f16274,plain,
( spl0_1775
<=> ! [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_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f15739,plain,
( spl0_1705
<=> ! [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_1705])]) ).
fof(f16194,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_evs3,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_List_Odistinct(v_evs3,tc_Event_Oevent) )
| ~ spl0_116
| ~ spl0_1705 ),
inference(resolution,[],[f15740,f4006]) ).
fof(f15740,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_1705 ),
inference(avatar_component_clause,[],[f15739]) ).
fof(f16095,plain,
( spl0_1773
| ~ spl0_649
| ~ spl0_923 ),
inference(avatar_split_clause,[],[f8562,f8144,f6138,f16093]) ).
fof(f16093,plain,
( spl0_1773
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f8144,plain,
( spl0_923
<=> ! [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_923])]) ).
fof(f8562,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_923 ),
inference(superposition,[],[f8145,f6140]) ).
fof(f8145,plain,
( ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_923 ),
inference(avatar_component_clause,[],[f8144]) ).
fof(f16073,plain,
spl0_1772,
inference(avatar_split_clause,[],[f3431,f16071]) ).
fof(f16071,plain,
( spl0_1772
<=> ! [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_1772])]) ).
fof(f3431,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,[],[f3430,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(f3430,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,[],[f3218,f2981]) ).
fof(f2981,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(f3218,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(f16069,plain,
spl0_1771,
inference(avatar_split_clause,[],[f3424,f16067]) ).
fof(f16067,plain,
( spl0_1771
<=> ! [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_1771])]) ).
fof(f3424,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,[],[f3423,f2115]) ).
fof(f3423,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,[],[f3212,f2981]) ).
fof(f3212,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(f16065,plain,
spl0_1770,
inference(avatar_split_clause,[],[f3421,f16063]) ).
fof(f16063,plain,
( spl0_1770
<=> ! [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_1770])]) ).
fof(f3421,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,[],[f3420,f2115]) ).
fof(f3420,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,[],[f3210,f2981]) ).
fof(f3210,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(f16061,plain,
spl0_1769,
inference(avatar_split_clause,[],[f3414,f16059]) ).
fof(f16059,plain,
( spl0_1769
<=> ! [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_1769])]) ).
fof(f3414,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,[],[f3413,f2115]) ).
fof(f3413,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,[],[f3204,f2981]) ).
fof(f3204,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(f16057,plain,
spl0_1768,
inference(avatar_split_clause,[],[f3395,f16055]) ).
fof(f16055,plain,
( spl0_1768
<=> ! [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_1768])]) ).
fof(f3395,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,[],[f3188,f2982]) ).
fof(f3188,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(f16053,plain,
spl0_1767,
inference(avatar_split_clause,[],[f3309,f16051]) ).
fof(f16051,plain,
( spl0_1767
<=> ! [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_1767])]) ).
fof(f3309,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(f16049,plain,
( spl0_1766
| ~ spl0_648
| ~ spl0_923 ),
inference(avatar_split_clause,[],[f8561,f8144,f6133,f16047]) ).
fof(f16047,plain,
( spl0_1766
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f8561,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_923 ),
inference(superposition,[],[f8145,f6135]) ).
fof(f16045,plain,
spl0_1765,
inference(avatar_split_clause,[],[f3308,f16043]) ).
fof(f16043,plain,
( spl0_1765
<=> ! [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_1765])]) ).
fof(f3308,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(f16041,plain,
spl0_1764,
inference(avatar_split_clause,[],[f3279,f16039]) ).
fof(f16039,plain,
( spl0_1764
<=> ! [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_1764])]) ).
fof(f3279,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(f16037,plain,
spl0_1763,
inference(avatar_split_clause,[],[f3275,f16035]) ).
fof(f3275,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,[],[f3084,f2982]) ).
fof(f3084,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(f16033,plain,
spl0_1762,
inference(avatar_split_clause,[],[f3271,f16031]) ).
fof(f3271,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(f16029,plain,
spl0_1761,
inference(avatar_split_clause,[],[f3170,f16027]) ).
fof(f16027,plain,
( spl0_1761
<=> ! [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_1761])]) ).
fof(f3170,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(f16009,plain,
( spl0_1760
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1759 ),
inference(avatar_split_clause,[],[f16005,f16002,f11323,f10967,f7078,f6133,f16007]) ).
fof(f16007,plain,
( spl0_1760
<=> ! [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_1760])]) ).
fof(f16002,plain,
( spl0_1759
<=> ! [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_1759])]) ).
fof(f16005,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1759 ),
inference(forward_demodulation,[],[f16003,f12324]) ).
fof(f16003,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_1759 ),
inference(avatar_component_clause,[],[f16002]) ).
fof(f16004,plain,
spl0_1759,
inference(avatar_split_clause,[],[f3055,f16002]) ).
fof(f15986,plain,
( spl0_1758
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1756 ),
inference(avatar_split_clause,[],[f15978,f15975,f11323,f10967,f7078,f6133,f15984]) ).
fof(f15975,plain,
( spl0_1756
<=> ! [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_1756])]) ).
fof(f15978,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1756 ),
inference(forward_demodulation,[],[f15976,f12324]) ).
fof(f15976,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_1756 ),
inference(avatar_component_clause,[],[f15975]) ).
fof(f15982,plain,
( spl0_1757
| ~ spl0_648
| ~ spl0_923 ),
inference(avatar_split_clause,[],[f8559,f8144,f6133,f15980]) ).
fof(f15980,plain,
( spl0_1757
<=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f8559,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_923 ),
inference(superposition,[],[f8145,f6135]) ).
fof(f15977,plain,
spl0_1756,
inference(avatar_split_clause,[],[f3054,f15975]) ).
fof(f15953,plain,
( spl0_1755
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1754 ),
inference(avatar_split_clause,[],[f15949,f15946,f11323,f10967,f7078,f6133,f15951]) ).
fof(f15951,plain,
( spl0_1755
<=> ! [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_1755])]) ).
fof(f15946,plain,
( spl0_1754
<=> ! [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_1754])]) ).
fof(f15949,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1754 ),
inference(forward_demodulation,[],[f15947,f12324]) ).
fof(f15947,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_1754 ),
inference(avatar_component_clause,[],[f15946]) ).
fof(f15948,plain,
spl0_1754,
inference(avatar_split_clause,[],[f3053,f15946]) ).
fof(f3053,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(f15944,plain,
spl0_1753,
inference(avatar_split_clause,[],[f2953,f15942]) ).
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(f15940,plain,
spl0_1752,
inference(avatar_split_clause,[],[f2722,f15938]) ).
fof(f15938,plain,
( spl0_1752
<=> ! [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_1752])]) ).
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(f15936,plain,
spl0_1751,
inference(avatar_split_clause,[],[f2719,f15934]) ).
fof(f15934,plain,
( spl0_1751
<=> ! [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_1751])]) ).
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(f15932,plain,
spl0_1750,
inference(avatar_split_clause,[],[f2657,f15930]) ).
fof(f15930,plain,
( spl0_1750
<=> ! [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_1750])]) ).
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(f15928,plain,
spl0_1749,
inference(avatar_split_clause,[],[f2644,f15926]) ).
fof(f15924,plain,
spl0_1748,
inference(avatar_split_clause,[],[f2640,f15922]) ).
fof(f15922,plain,
( spl0_1748
<=> ! [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_1748])]) ).
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(f15920,plain,
spl0_1747,
inference(avatar_split_clause,[],[f2620,f15918]) ).
fof(f15918,plain,
( spl0_1747
<=> ! [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_1747])]) ).
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(f15916,plain,
spl0_1746,
inference(avatar_split_clause,[],[f2593,f15914]) ).
fof(f15914,plain,
( spl0_1746
<=> ! [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_1746])]) ).
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(f15912,plain,
spl0_1745,
inference(avatar_split_clause,[],[f2572,f15910]) ).
fof(f15910,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(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(f15908,plain,
spl0_1744,
inference(avatar_split_clause,[],[f2571,f15906]) ).
fof(f15906,plain,
( spl0_1744
<=> ! [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_1744])]) ).
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(f15904,plain,
spl0_1743,
inference(avatar_split_clause,[],[f2561,f15902]) ).
fof(f15902,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(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(f15900,plain,
spl0_1742,
inference(avatar_split_clause,[],[f2560,f15898]) ).
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(f15896,plain,
spl0_1741,
inference(avatar_split_clause,[],[f2548,f15894]) ).
fof(f15894,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(f15892,plain,
spl0_1740,
inference(avatar_split_clause,[],[f2541,f15890]) ).
fof(f15890,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(f15888,plain,
spl0_1739,
inference(avatar_split_clause,[],[f2539,f15886]) ).
fof(f15886,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(f15884,plain,
spl0_1738,
inference(avatar_split_clause,[],[f2538,f15882]) ).
fof(f15882,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(f15871,plain,
spl0_1737,
inference(avatar_split_clause,[],[f2533,f15869]) ).
fof(f15869,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(f15867,plain,
spl0_1736,
inference(avatar_split_clause,[],[f2532,f15865]) ).
fof(f15865,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(f15863,plain,
spl0_1735,
inference(avatar_split_clause,[],[f2490,f15861]) ).
fof(f15861,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(f15859,plain,
spl0_1734,
inference(avatar_split_clause,[],[f2489,f15857]) ).
fof(f15857,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(f15855,plain,
spl0_1733,
inference(avatar_split_clause,[],[f2467,f15853]) ).
fof(f15853,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(f15851,plain,
spl0_1732,
inference(avatar_split_clause,[],[f2312,f15849]) ).
fof(f15849,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(f15847,plain,
spl0_1731,
inference(avatar_split_clause,[],[f2306,f15845]) ).
fof(f15845,plain,
( spl0_1731
<=> ! [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_1731])]) ).
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(f15843,plain,
spl0_1730,
inference(avatar_split_clause,[],[f2304,f15841]) ).
fof(f15841,plain,
( spl0_1730
<=> ! [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_1730])]) ).
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(f15839,plain,
spl0_1729,
inference(avatar_split_clause,[],[f2209,f15837]) ).
fof(f15837,plain,
( spl0_1729
<=> ! [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_1729])]) ).
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(f15835,plain,
spl0_1728,
inference(avatar_split_clause,[],[f2208,f15833]) ).
fof(f15833,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(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(f15831,plain,
spl0_1727,
inference(avatar_split_clause,[],[f2080,f15829]) ).
fof(f15829,plain,
( spl0_1727
<=> ! [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_1727])]) ).
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(f15827,plain,
spl0_1726,
inference(avatar_split_clause,[],[f2060,f15825]) ).
fof(f15825,plain,
( spl0_1726
<=> ! [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_1726])]) ).
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(f15823,plain,
spl0_1725,
inference(avatar_split_clause,[],[f2058,f15821]) ).
fof(f15821,plain,
( spl0_1725
<=> ! [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_1725])]) ).
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(f15819,plain,
spl0_1724,
inference(avatar_split_clause,[],[f2037,f15817]) ).
fof(f15817,plain,
( spl0_1724
<=> ! [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_1724])]) ).
fof(f15815,plain,
spl0_1723,
inference(avatar_split_clause,[],[f2028,f15813]) ).
fof(f15813,plain,
( spl0_1723
<=> ! [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_1723])]) ).
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(f15811,plain,
spl0_1722,
inference(avatar_split_clause,[],[f1863,f15809]) ).
fof(f15809,plain,
( spl0_1722
<=> ! [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_1722])]) ).
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(f15807,plain,
spl0_1721,
inference(avatar_split_clause,[],[f1860,f15805]) ).
fof(f15805,plain,
( spl0_1721
<=> ! [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_1721])]) ).
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(f15803,plain,
spl0_1720,
inference(avatar_split_clause,[],[f1831,f15801]) ).
fof(f15801,plain,
( spl0_1720
<=> ! [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_1720])]) ).
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(f15799,plain,
spl0_1719,
inference(avatar_split_clause,[],[f1827,f15797]) ).
fof(f15797,plain,
( spl0_1719
<=> ! [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_1719])]) ).
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(f15795,plain,
spl0_1718,
inference(avatar_split_clause,[],[f1801,f15793]) ).
fof(f15793,plain,
( spl0_1718
<=> ! [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_1718])]) ).
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(f15791,plain,
( ~ spl0_46
| ~ spl0_1717
| ~ spl0_1385
| spl0_1539 ),
inference(avatar_split_clause,[],[f14335,f12655,f10995,f15788,f3660]) ).
fof(f3660,plain,
( spl0_46
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f15788,plain,
( spl0_1717
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f10995,plain,
( spl0_1385
<=> ! [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_1385])]) ).
fof(f12655,plain,
( spl0_1539
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f14335,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| ~ spl0_1385
| spl0_1539 ),
inference(resolution,[],[f12657,f10996]) ).
fof(f10996,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_1385 ),
inference(avatar_component_clause,[],[f10995]) ).
fof(f12657,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_1539 ),
inference(avatar_component_clause,[],[f12655]) ).
fof(f15786,plain,
spl0_1716,
inference(avatar_split_clause,[],[f1749,f15784]) ).
fof(f15784,plain,
( spl0_1716
<=> ! [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_1716])]) ).
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(f15782,plain,
spl0_1715,
inference(avatar_split_clause,[],[f1739,f15780]) ).
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(f15778,plain,
spl0_1714,
inference(avatar_split_clause,[],[f1725,f15776]) ).
fof(f15776,plain,
( spl0_1714
<=> ! [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_1714])]) ).
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(f15774,plain,
spl0_1713,
inference(avatar_split_clause,[],[f1708,f15772]) ).
fof(f15772,plain,
( spl0_1713
<=> ! [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_1713])]) ).
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(f15770,plain,
spl0_1712,
inference(avatar_split_clause,[],[f1696,f15768]) ).
fof(f15768,plain,
( spl0_1712
<=> ! [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_1712])]) ).
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(f15766,plain,
spl0_1711,
inference(avatar_split_clause,[],[f1691,f15764]) ).
fof(f15764,plain,
( spl0_1711
<=> ! [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_1711])]) ).
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(f15762,plain,
spl0_1710,
inference(avatar_split_clause,[],[f1690,f15760]) ).
fof(f15760,plain,
( spl0_1710
<=> ! [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_1710])]) ).
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(f15758,plain,
spl0_1709,
inference(avatar_split_clause,[],[f1601,f15756]) ).
fof(f15756,plain,
( spl0_1709
<=> ! [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_1709])]) ).
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(f15754,plain,
spl0_1708,
inference(avatar_split_clause,[],[f1577,f15752]) ).
fof(f15752,plain,
( spl0_1708
<=> ! [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_1708])]) ).
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(f15750,plain,
spl0_1707,
inference(avatar_split_clause,[],[f1574,f15748]) ).
fof(f15748,plain,
( spl0_1707
<=> ! [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_1707])]) ).
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(f15746,plain,
( spl0_1706
| ~ spl0_914
| ~ spl0_1376 ),
inference(avatar_split_clause,[],[f12883,f10958,f8037,f15743]) ).
fof(f15743,plain,
( spl0_1706
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f10958,plain,
( spl0_1376
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f12883,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_914
| ~ spl0_1376 ),
inference(superposition,[],[f10960,f8038]) ).
fof(f10960,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_1376 ),
inference(avatar_component_clause,[],[f10958]) ).
fof(f15741,plain,
spl0_1705,
inference(avatar_split_clause,[],[f1554,f15739]) ).
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(f15737,plain,
spl0_1704,
inference(avatar_split_clause,[],[f1547,f15735]) ).
fof(f15735,plain,
( spl0_1704
<=> ! [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_1704])]) ).
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(f15733,plain,
spl0_1703,
inference(avatar_split_clause,[],[f1518,f15731]) ).
fof(f15731,plain,
( spl0_1703
<=> ! [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_1703])]) ).
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(f15729,plain,
spl0_1702,
inference(avatar_split_clause,[],[f1508,f15727]) ).
fof(f15727,plain,
( spl0_1702
<=> ! [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_1702])]) ).
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(f15725,plain,
spl0_1701,
inference(avatar_split_clause,[],[f1495,f15723]) ).
fof(f15723,plain,
( spl0_1701
<=> ! [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_1701])]) ).
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(f15721,plain,
spl0_1700,
inference(avatar_split_clause,[],[f1239,f15719]) ).
fof(f15719,plain,
( spl0_1700
<=> ! [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_1700])]) ).
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(f15717,plain,
spl0_1699,
inference(avatar_split_clause,[],[f1237,f15715]) ).
fof(f15715,plain,
( spl0_1699
<=> ! [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_1699])]) ).
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(f15713,plain,
spl0_1698,
inference(avatar_split_clause,[],[f1217,f15711]) ).
fof(f15711,plain,
( spl0_1698
<=> ! [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_1698])]) ).
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(f15709,plain,
spl0_1697,
inference(avatar_split_clause,[],[f127,f15707]) ).
fof(f15707,plain,
( spl0_1697
<=> ! [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_1697])]) ).
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(f15705,plain,
spl0_1696,
inference(avatar_split_clause,[],[f125,f15703]) ).
fof(f15703,plain,
( spl0_1696
<=> ! [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_1696])]) ).
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(f15701,plain,
spl0_1695,
inference(avatar_split_clause,[],[f80,f15699]) ).
fof(f15699,plain,
( spl0_1695
<=> ! [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_1695])]) ).
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(f15602,plain,
( ~ spl0_1694
| spl0_106
| ~ spl0_837
| ~ spl0_1178
| ~ spl0_1327 ),
inference(avatar_split_clause,[],[f12794,f10444,f9532,f7715,f3957,f15599]) ).
fof(f15599,plain,
( spl0_1694
<=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f7715,plain,
( spl0_837
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f9532,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(f10444,plain,
( spl0_1327
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f12794,plain,
( c_0 = c_1
| ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| ~ spl0_837
| ~ spl0_1178
| ~ spl0_1327 ),
inference(forward_demodulation,[],[f12788,f7717]) ).
fof(f7717,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_837 ),
inference(avatar_component_clause,[],[f7715]) ).
fof(f12788,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_1327 ),
inference(superposition,[],[f9533,f10446]) ).
fof(f10446,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_1327 ),
inference(avatar_component_clause,[],[f10444]) ).
fof(f9533,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,[],[f9532]) ).
fof(f15484,plain,
( spl0_1693
| ~ spl0_1047
| ~ spl0_1313 ),
inference(avatar_split_clause,[],[f12613,f10305,f8782,f15482]) ).
fof(f15482,plain,
( spl0_1693
<=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f10305,plain,
( spl0_1313
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f12613,plain,
( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1047
| ~ spl0_1313 ),
inference(superposition,[],[f8783,f10306]) ).
fof(f10306,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_1313 ),
inference(avatar_component_clause,[],[f10305]) ).
fof(f14644,plain,
spl0_1692,
inference(avatar_split_clause,[],[f3387,f14642]) ).
fof(f14642,plain,
( spl0_1692
<=> ! [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_1692])]) ).
fof(f3387,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,[],[f3182,f2114]) ).
fof(f3182,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(f14640,plain,
spl0_1691,
inference(avatar_split_clause,[],[f3382,f14638]) ).
fof(f14638,plain,
( spl0_1691
<=> ! [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_1691])]) ).
fof(f3382,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,[],[f3178,f2114]) ).
fof(f3178,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(f14636,plain,
spl0_1690,
inference(avatar_split_clause,[],[f3270,f14634]) ).
fof(f14634,plain,
( spl0_1690
<=> ! [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_1690])]) ).
fof(f3270,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,[],[f3077,f2982]) ).
fof(f3077,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(f14632,plain,
spl0_1689,
inference(avatar_split_clause,[],[f3187,f14630]) ).
fof(f14630,plain,
( spl0_1689
<=> ! [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_1689])]) ).
fof(f3187,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(f14623,plain,
( spl0_1688
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1687 ),
inference(avatar_split_clause,[],[f14619,f14616,f11323,f10967,f7078,f6133,f14621]) ).
fof(f14621,plain,
( spl0_1688
<=> ! [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_1688])]) ).
fof(f14616,plain,
( spl0_1687
<=> ! [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_1687])]) ).
fof(f14619,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1687 ),
inference(forward_demodulation,[],[f14617,f12324]) ).
fof(f14617,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_1687 ),
inference(avatar_component_clause,[],[f14616]) ).
fof(f14618,plain,
spl0_1687,
inference(avatar_split_clause,[],[f3151,f14616]) ).
fof(f3151,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(f14614,plain,
spl0_1686,
inference(avatar_split_clause,[],[f3149,f14612]) ).
fof(f14612,plain,
( spl0_1686
<=> ! [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_1686])]) ).
fof(f3149,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(f14610,plain,
spl0_1685,
inference(avatar_split_clause,[],[f3148,f14608]) ).
fof(f14608,plain,
( spl0_1685
<=> ! [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_1685])]) ).
fof(f3148,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(f14606,plain,
spl0_1684,
inference(avatar_split_clause,[],[f3114,f14604]) ).
fof(f14604,plain,
( spl0_1684
<=> ! [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_1684])]) ).
fof(f3114,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(f14602,plain,
( spl0_1683
| ~ spl0_719
| ~ spl0_720
| ~ spl0_722
| ~ spl0_800
| ~ spl0_1596 ),
inference(avatar_split_clause,[],[f14267,f12950,f7565,f7229,f7221,f7216,f14600]) ).
fof(f7221,plain,
( spl0_720
<=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f7229,plain,
( spl0_722
<=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f12950,plain,
( spl0_1596
<=> ! [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_1596])]) ).
fof(f14267,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_719
| ~ spl0_720
| ~ spl0_722
| ~ spl0_800
| ~ spl0_1596 ),
inference(forward_demodulation,[],[f14266,f7222]) ).
fof(f7222,plain,
( ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3
| ~ spl0_720 ),
inference(avatar_component_clause,[],[f7221]) ).
fof(f14266,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ spl0_719
| ~ spl0_722
| ~ spl0_800
| ~ spl0_1596 ),
inference(forward_demodulation,[],[f14265,f7567]) ).
fof(f14265,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_719
| ~ spl0_722
| ~ spl0_1596 ),
inference(forward_demodulation,[],[f14254,f7230]) ).
fof(f7230,plain,
( ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11)
| ~ spl0_722 ),
inference(avatar_component_clause,[],[f7229]) ).
fof(f14254,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_719
| ~ spl0_1596 ),
inference(superposition,[],[f12951,f7218]) ).
fof(f12951,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_1596 ),
inference(avatar_component_clause,[],[f12950]) ).
fof(f14598,plain,
spl0_1682,
inference(avatar_split_clause,[],[f3058,f14596]) ).
fof(f14596,plain,
( spl0_1682
<=> ! [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_1682])]) ).
fof(f3058,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(f14594,plain,
spl0_1681,
inference(avatar_split_clause,[],[f2950,f14592]) ).
fof(f14592,plain,
( spl0_1681
<=> ! [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_1681])]) ).
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(f14590,plain,
spl0_1680,
inference(avatar_split_clause,[],[f2896,f14588]) ).
fof(f14588,plain,
( spl0_1680
<=> ! [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_1680])]) ).
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(f14586,plain,
spl0_1679,
inference(avatar_split_clause,[],[f2841,f14584]) ).
fof(f14584,plain,
( spl0_1679
<=> ! [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_1679])]) ).
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(f14582,plain,
spl0_1678,
inference(avatar_split_clause,[],[f2840,f14580]) ).
fof(f14580,plain,
( spl0_1678
<=> ! [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_1678])]) ).
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(f14578,plain,
spl0_1677,
inference(avatar_split_clause,[],[f2745,f14576]) ).
fof(f14576,plain,
( spl0_1677
<=> ! [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_1677])]) ).
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(f14574,plain,
spl0_1676,
inference(avatar_split_clause,[],[f2727,f14572]) ).
fof(f14572,plain,
( spl0_1676
<=> ! [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_1676])]) ).
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(f14570,plain,
spl0_1675,
inference(avatar_split_clause,[],[f2726,f14568]) ).
fof(f14568,plain,
( spl0_1675
<=> ! [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_1675])]) ).
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(f14566,plain,
spl0_1674,
inference(avatar_split_clause,[],[f2683,f14564]) ).
fof(f14564,plain,
( spl0_1674
<=> ! [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_1674])]) ).
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(f14562,plain,
spl0_1673,
inference(avatar_split_clause,[],[f2658,f14560]) ).
fof(f14560,plain,
( spl0_1673
<=> ! [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_1673])]) ).
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(f14558,plain,
( spl0_1672
| ~ spl0_718
| ~ spl0_720
| ~ spl0_745
| ~ spl0_800
| ~ spl0_914
| ~ spl0_1595 ),
inference(avatar_split_clause,[],[f14248,f12946,f8037,f7565,f7329,f7221,f7211,f14555]) ).
fof(f7211,plain,
( spl0_718
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f12946,plain,
( spl0_1595
<=> ! [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_1595])]) ).
fof(f14248,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_718
| ~ spl0_720
| ~ spl0_745
| ~ spl0_800
| ~ spl0_914
| ~ spl0_1595 ),
inference(forward_demodulation,[],[f14247,f7213]) ).
fof(f7213,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_718 ),
inference(avatar_component_clause,[],[f7211]) ).
fof(f14247,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_720
| ~ spl0_745
| ~ spl0_800
| ~ spl0_914
| ~ spl0_1595 ),
inference(forward_demodulation,[],[f14246,f7567]) ).
fof(f14246,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_720
| ~ spl0_745
| ~ spl0_914
| ~ spl0_1595 ),
inference(forward_demodulation,[],[f14245,f7222]) ).
fof(f14245,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_745
| ~ spl0_914
| ~ spl0_1595 ),
inference(forward_demodulation,[],[f14239,f8038]) ).
fof(f14239,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_745
| ~ spl0_1595 ),
inference(superposition,[],[f12947,f7331]) ).
fof(f12947,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_1595 ),
inference(avatar_component_clause,[],[f12946]) ).
fof(f14553,plain,
spl0_1671,
inference(avatar_split_clause,[],[f2655,f14551]) ).
fof(f14551,plain,
( spl0_1671
<=> ! [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_1671])]) ).
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(f14549,plain,
spl0_1670,
inference(avatar_split_clause,[],[f2621,f14547]) ).
fof(f14547,plain,
( spl0_1670
<=> ! [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_1670])]) ).
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(f14545,plain,
spl0_1669,
inference(avatar_split_clause,[],[f2488,f14543]) ).
fof(f14543,plain,
( spl0_1669
<=> ! [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_1669])]) ).
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(f14541,plain,
spl0_1668,
inference(avatar_split_clause,[],[f2472,f14539]) ).
fof(f14539,plain,
( spl0_1668
<=> ! [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_1668])]) ).
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(f14537,plain,
spl0_1667,
inference(avatar_split_clause,[],[f2468,f14535]) ).
fof(f14535,plain,
( spl0_1667
<=> ! [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_1667])]) ).
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(f14533,plain,
spl0_1666,
inference(avatar_split_clause,[],[f2363,f14531]) ).
fof(f14531,plain,
( spl0_1666
<=> ! [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_1666])]) ).
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(f14529,plain,
spl0_1665,
inference(avatar_split_clause,[],[f2362,f14527]) ).
fof(f14527,plain,
( spl0_1665
<=> ! [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_1665])]) ).
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(f14525,plain,
spl0_1664,
inference(avatar_split_clause,[],[f2349,f14523]) ).
fof(f14523,plain,
( spl0_1664
<=> ! [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_1664])]) ).
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(f14521,plain,
spl0_1663,
inference(avatar_split_clause,[],[f2348,f14519]) ).
fof(f14519,plain,
( spl0_1663
<=> ! [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_1663])]) ).
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(f14517,plain,
spl0_1662,
inference(avatar_split_clause,[],[f2268,f14515]) ).
fof(f14515,plain,
( spl0_1662
<=> ! [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_1662])]) ).
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(f14513,plain,
( spl0_1661
| ~ spl0_674
| ~ spl0_1577 ),
inference(avatar_split_clause,[],[f14187,f12825,f7014,f14511]) ).
fof(f14511,plain,
( spl0_1661
<=> ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f12825,plain,
( spl0_1577
<=> ! [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_1577])]) ).
fof(f14187,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg))
| ~ spl0_674
| ~ spl0_1577 ),
inference(resolution,[],[f12826,f7015]) ).
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_1577 ),
inference(avatar_component_clause,[],[f12825]) ).
fof(f14509,plain,
spl0_1660,
inference(avatar_split_clause,[],[f2263,f14507]) ).
fof(f14507,plain,
( spl0_1660
<=> ! [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_1660])]) ).
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(f14505,plain,
spl0_1659,
inference(avatar_split_clause,[],[f2246,f14503]) ).
fof(f14503,plain,
( spl0_1659
<=> ! [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_1659])]) ).
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(f14501,plain,
spl0_1658,
inference(avatar_split_clause,[],[f2242,f14499]) ).
fof(f14499,plain,
( spl0_1658
<=> ! [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_1658])]) ).
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(f14497,plain,
spl0_1657,
inference(avatar_split_clause,[],[f2236,f14495]) ).
fof(f14495,plain,
( spl0_1657
<=> ! [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_1657])]) ).
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(f14493,plain,
spl0_1656,
inference(avatar_split_clause,[],[f2235,f14491]) ).
fof(f14491,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(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(f14489,plain,
spl0_1655,
inference(avatar_split_clause,[],[f2232,f14487]) ).
fof(f14487,plain,
( spl0_1655
<=> ! [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_1655])]) ).
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(f14485,plain,
spl0_1654,
inference(avatar_split_clause,[],[f2231,f14483]) ).
fof(f14483,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(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(f14481,plain,
spl0_1653,
inference(avatar_split_clause,[],[f2195,f14479]) ).
fof(f14479,plain,
( spl0_1653
<=> ! [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_1653])]) ).
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(f14477,plain,
spl0_1652,
inference(avatar_split_clause,[],[f2190,f14475]) ).
fof(f14475,plain,
( spl0_1652
<=> ! [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_1652])]) ).
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(f14473,plain,
spl0_1651,
inference(avatar_split_clause,[],[f2111,f14471]) ).
fof(f14471,plain,
( spl0_1651
<=> ! [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_1651])]) ).
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(f14469,plain,
( spl0_1650
| ~ spl0_674
| ~ spl0_1575 ),
inference(avatar_split_clause,[],[f14158,f12817,f7014,f14467]) ).
fof(f14467,plain,
( spl0_1650
<=> ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f12817,plain,
( spl0_1575
<=> ! [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_1575])]) ).
fof(f14158,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_674
| ~ spl0_1575 ),
inference(resolution,[],[f12818,f7015]) ).
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_1575 ),
inference(avatar_component_clause,[],[f12817]) ).
fof(f14465,plain,
spl0_1649,
inference(avatar_split_clause,[],[f2085,f14463]) ).
fof(f14463,plain,
( spl0_1649
<=> ! [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_1649])]) ).
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(f14461,plain,
spl0_1648,
inference(avatar_split_clause,[],[f2084,f14459]) ).
fof(f14459,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(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(f14457,plain,
spl0_1647,
inference(avatar_split_clause,[],[f2083,f14455]) ).
fof(f14455,plain,
( spl0_1647
<=> ! [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_1647])]) ).
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(f14453,plain,
spl0_1646,
inference(avatar_split_clause,[],[f2082,f14451]) ).
fof(f14451,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(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(f14449,plain,
spl0_1645,
inference(avatar_split_clause,[],[f2076,f14447]) ).
fof(f14447,plain,
( spl0_1645
<=> ! [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_1645])]) ).
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(f14445,plain,
spl0_1644,
inference(avatar_split_clause,[],[f2075,f14443]) ).
fof(f14443,plain,
( spl0_1644
<=> ! [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_1644])]) ).
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(f14441,plain,
spl0_1643,
inference(avatar_split_clause,[],[f2073,f14439]) ).
fof(f14439,plain,
( spl0_1643
<=> ! [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_1643])]) ).
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(f14437,plain,
spl0_1642,
inference(avatar_split_clause,[],[f2072,f14435]) ).
fof(f14435,plain,
( spl0_1642
<=> ! [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_1642])]) ).
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(f14433,plain,
spl0_1641,
inference(avatar_split_clause,[],[f2071,f14431]) ).
fof(f14431,plain,
( spl0_1641
<=> ! [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_1641])]) ).
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(f14429,plain,
spl0_1640,
inference(avatar_split_clause,[],[f2070,f14427]) ).
fof(f14427,plain,
( spl0_1640
<=> ! [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_1640])]) ).
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(f14425,plain,
( spl0_1639
| ~ spl0_674
| ~ spl0_1567 ),
inference(avatar_split_clause,[],[f14038,f12774,f7014,f14423]) ).
fof(f14423,plain,
( spl0_1639
<=> ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f12774,plain,
( spl0_1567
<=> ! [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_1567])]) ).
fof(f14038,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
| ~ spl0_674
| ~ spl0_1567 ),
inference(resolution,[],[f12775,f7015]) ).
fof(f12775,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_1567 ),
inference(avatar_component_clause,[],[f12774]) ).
fof(f14421,plain,
spl0_1638,
inference(avatar_split_clause,[],[f2068,f14419]) ).
fof(f14419,plain,
( spl0_1638
<=> ! [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_1638])]) ).
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(f14417,plain,
spl0_1637,
inference(avatar_split_clause,[],[f2067,f14415]) ).
fof(f14415,plain,
( spl0_1637
<=> ! [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_1637])]) ).
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(f14413,plain,
spl0_1636,
inference(avatar_split_clause,[],[f1927,f14411]) ).
fof(f14411,plain,
( spl0_1636
<=> ! [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_1636])]) ).
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(f14409,plain,
spl0_1635,
inference(avatar_split_clause,[],[f1868,f14407]) ).
fof(f14407,plain,
( spl0_1635
<=> ! [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_1635])]) ).
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(f14405,plain,
spl0_1634,
inference(avatar_split_clause,[],[f1820,f14403]) ).
fof(f14403,plain,
( spl0_1634
<=> ! [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_1634])]) ).
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(f14401,plain,
spl0_1633,
inference(avatar_split_clause,[],[f1819,f14399]) ).
fof(f14399,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(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(f14397,plain,
spl0_1632,
inference(avatar_split_clause,[],[f1817,f14395]) ).
fof(f14395,plain,
( spl0_1632
<=> ! [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_1632])]) ).
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(f14393,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1816,f14391]) ).
fof(f14391,plain,
( spl0_1631
<=> ! [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_1631])]) ).
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(f14389,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1760,f14387]) ).
fof(f14387,plain,
( spl0_1630
<=> ! [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_1630])]) ).
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(f14385,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1756,f14383]) ).
fof(f14383,plain,
( spl0_1629
<=> ! [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_1629])]) ).
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(f14381,plain,
( spl0_1628
| ~ spl0_782
| ~ spl0_1499 ),
inference(avatar_split_clause,[],[f13179,f12484,f7493,f14379]) ).
fof(f14379,plain,
( spl0_1628
<=> ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f7493,plain,
( spl0_782
<=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f13179,plain,
( ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_782
| ~ spl0_1499 ),
inference(superposition,[],[f7494,f12485]) ).
fof(f7494,plain,
( ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ spl0_782 ),
inference(avatar_component_clause,[],[f7493]) ).
fof(f14377,plain,
spl0_1627,
inference(avatar_split_clause,[],[f1710,f14375]) ).
fof(f14375,plain,
( spl0_1627
<=> ! [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_1627])]) ).
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(f14373,plain,
spl0_1626,
inference(avatar_split_clause,[],[f1640,f14371]) ).
fof(f14371,plain,
( spl0_1626
<=> ! [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_1626])]) ).
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(f14369,plain,
spl0_1625,
inference(avatar_split_clause,[],[f1632,f14367]) ).
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(f14365,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1612,f14363]) ).
fof(f14363,plain,
( spl0_1624
<=> ! [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_1624])]) ).
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(f14361,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1600,f14359]) ).
fof(f14359,plain,
( spl0_1623
<=> ! [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_1623])]) ).
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(f14357,plain,
spl0_1622,
inference(avatar_split_clause,[],[f1596,f14355]) ).
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(f14353,plain,
spl0_1621,
inference(avatar_split_clause,[],[f1544,f14351]) ).
fof(f14351,plain,
( spl0_1621
<=> ! [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_1621])]) ).
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(f14349,plain,
spl0_1620,
inference(avatar_split_clause,[],[f1456,f14347]) ).
fof(f14347,plain,
( spl0_1620
<=> ! [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_1620])]) ).
fof(f14345,plain,
spl0_1619,
inference(avatar_split_clause,[],[f1431,f14343]) ).
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(f14341,plain,
spl0_1618,
inference(avatar_split_clause,[],[f1415,f14339]) ).
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(f14334,plain,
spl0_1617,
inference(avatar_split_clause,[],[f1414,f14332]) ).
fof(f14332,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(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(f14330,plain,
spl0_1616,
inference(avatar_split_clause,[],[f1411,f14328]) ).
fof(f14328,plain,
( spl0_1616
<=> ! [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_1616])]) ).
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(f14326,plain,
spl0_1615,
inference(avatar_split_clause,[],[f1410,f14324]) ).
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(f14322,plain,
spl0_1614,
inference(avatar_split_clause,[],[f1281,f14320]) ).
fof(f14320,plain,
( spl0_1614
<=> ! [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_1614])]) ).
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(f14318,plain,
spl0_1613,
inference(avatar_split_clause,[],[f1198,f14316]) ).
fof(f14316,plain,
( spl0_1613
<=> ! [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_1613])]) ).
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(f14314,plain,
spl0_1612,
inference(avatar_split_clause,[],[f1197,f14312]) ).
fof(f14312,plain,
( spl0_1612
<=> ! [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_1612])]) ).
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(f14310,plain,
spl0_1611,
inference(avatar_split_clause,[],[f99,f14308]) ).
fof(f14308,plain,
( spl0_1611
<=> ! [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_1611])]) ).
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(f14306,plain,
spl0_1610,
inference(avatar_split_clause,[],[f96,f14304]) ).
fof(f14304,plain,
( spl0_1610
<=> ! [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_1610])]) ).
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(f14302,plain,
spl0_1609,
inference(avatar_split_clause,[],[f59,f14300]) ).
fof(f14300,plain,
( spl0_1609
<=> ! [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_1609])]) ).
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(f14298,plain,
spl0_1608,
inference(avatar_split_clause,[],[f48,f14296]) ).
fof(f14296,plain,
( spl0_1608
<=> ! [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_1608])]) ).
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(f14294,plain,
spl0_1607,
inference(avatar_split_clause,[],[f43,f14292]) ).
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(f14290,plain,
spl0_1606,
inference(avatar_split_clause,[],[f27,f14288]) ).
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(f14171,plain,
( spl0_1605
| ~ spl0_122
| ~ spl0_1562 ),
inference(avatar_split_clause,[],[f13947,f12754,f4029,f14169]) ).
fof(f14169,plain,
( spl0_1605
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f12754,plain,
( spl0_1562
<=> ! [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_1562])]) ).
fof(f13947,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_122
| ~ spl0_1562 ),
inference(resolution,[],[f12755,f4030]) ).
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_1562 ),
inference(avatar_component_clause,[],[f12754]) ).
fof(f14017,plain,
( spl0_1604
| ~ spl0_1197
| ~ spl0_1562 ),
inference(avatar_split_clause,[],[f13941,f12754,f9609,f14015]) ).
fof(f14015,plain,
( spl0_1604
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f9609,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(f13941,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1197
| ~ spl0_1562 ),
inference(resolution,[],[f12755,f9610]) ).
fof(f9610,plain,
( ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f9609]) ).
fof(f13570,plain,
( ~ spl0_1602
| spl0_1603
| ~ spl0_120
| ~ spl0_1384 ),
inference(avatar_split_clause,[],[f11663,f10991,f4021,f13568,f13564]) ).
fof(f13564,plain,
( spl0_1602
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f13568,plain,
( spl0_1603
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f10991,plain,
( spl0_1384
<=> ! [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_1384])]) ).
fof(f11663,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_120
| ~ spl0_1384 ),
inference(resolution,[],[f10992,f4022]) ).
fof(f10992,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_1384 ),
inference(avatar_component_clause,[],[f10991]) ).
fof(f13137,plain,
( ~ spl0_1600
| spl0_1601
| ~ spl0_120
| ~ spl0_1346 ),
inference(avatar_split_clause,[],[f11441,f10836,f4021,f13135,f13131]) ).
fof(f13131,plain,
( spl0_1600
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f13135,plain,
( spl0_1601
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f10836,plain,
( spl0_1346
<=> ! [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_1346])]) ).
fof(f11441,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_120
| ~ spl0_1346 ),
inference(resolution,[],[f10837,f4022]) ).
fof(f10837,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_1346 ),
inference(avatar_component_clause,[],[f10836]) ).
fof(f12968,plain,
spl0_1599,
inference(avatar_split_clause,[],[f3339,f12966]) ).
fof(f12966,plain,
( spl0_1599
<=> ! [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_1599])]) ).
fof(f3339,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,[],[f3152,f2982]) ).
fof(f3152,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(f12964,plain,
spl0_1598,
inference(avatar_split_clause,[],[f3327,f12962]) ).
fof(f12962,plain,
( spl0_1598
<=> ! [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_1598])]) ).
fof(f3327,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,[],[f3136,f3054]) ).
fof(f3136,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(f12960,plain,
spl0_1597,
inference(avatar_split_clause,[],[f3274,f12958]) ).
fof(f3274,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,[],[f3273,f2156]) ).
fof(f3273,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,[],[f3272,f2154]) ).
fof(f3272,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(f12952,plain,
spl0_1596,
inference(avatar_split_clause,[],[f3260,f12950]) ).
fof(f3260,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(f12948,plain,
spl0_1595,
inference(avatar_split_clause,[],[f3256,f12946]) ).
fof(f3256,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,[],[f3043,f3008]) ).
fof(f3008,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(f3043,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(f12944,plain,
spl0_1594,
inference(avatar_split_clause,[],[f3162,f12942]) ).
fof(f12942,plain,
( spl0_1594
<=> ! [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_1594])]) ).
fof(f3162,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(f12940,plain,
spl0_1593,
inference(avatar_split_clause,[],[f3160,f12938]) ).
fof(f12938,plain,
( spl0_1593
<=> ! [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_1593])]) ).
fof(f3160,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(f12908,plain,
( spl0_1592
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1591 ),
inference(avatar_split_clause,[],[f12904,f12901,f11323,f10967,f7078,f6133,f12906]) ).
fof(f12901,plain,
( spl0_1591
<=> ! [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_1591])]) ).
fof(f12904,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_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1591 ),
inference(forward_demodulation,[],[f12902,f12324]) ).
fof(f12902,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_1591 ),
inference(avatar_component_clause,[],[f12901]) ).
fof(f12903,plain,
spl0_1591,
inference(avatar_split_clause,[],[f3143,f12901]) ).
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(f12899,plain,
spl0_1590,
inference(avatar_split_clause,[],[f3104,f12897]) ).
fof(f3104,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(f12891,plain,
( spl0_1589
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1588 ),
inference(avatar_split_clause,[],[f12882,f12879,f11323,f10967,f7078,f6133,f12889]) ).
fof(f12879,plain,
( spl0_1588
<=> ! [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_1588])]) ).
fof(f12882,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1588 ),
inference(forward_demodulation,[],[f12880,f12324]) ).
fof(f12880,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_1588 ),
inference(avatar_component_clause,[],[f12879]) ).
fof(f12881,plain,
spl0_1588,
inference(avatar_split_clause,[],[f3044,f12879]) ).
fof(f3044,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(f12877,plain,
spl0_1587,
inference(avatar_split_clause,[],[f3040,f12875]) ).
fof(f3040,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(f12873,plain,
spl0_1586,
inference(avatar_split_clause,[],[f3027,f12871]) ).
fof(f3027,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(f12869,plain,
spl0_1585,
inference(avatar_split_clause,[],[f3026,f12867]) ).
fof(f3026,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(f12862,plain,
( spl0_1584
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1583 ),
inference(avatar_split_clause,[],[f12858,f12855,f11323,f10967,f7078,f6133,f12860]) ).
fof(f12860,plain,
( spl0_1584
<=> ! [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_1584])]) ).
fof(f12855,plain,
( spl0_1583
<=> ! [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_1583])]) ).
fof(f12858,plain,
( ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21)
| ~ spl0_648
| ~ spl0_689
| ~ spl0_1378
| ~ spl0_1465
| ~ spl0_1583 ),
inference(forward_demodulation,[],[f12856,f12324]) ).
fof(f12856,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_1583 ),
inference(avatar_component_clause,[],[f12855]) ).
fof(f12857,plain,
spl0_1583,
inference(avatar_split_clause,[],[f3021,f12855]) ).
fof(f3021,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(f12853,plain,
spl0_1582,
inference(avatar_split_clause,[],[f2946,f12851]) ).
fof(f12851,plain,
( spl0_1582
<=> ! [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_1582])]) ).
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(f12849,plain,
spl0_1581,
inference(avatar_split_clause,[],[f2945,f12847]) ).
fof(f12847,plain,
( spl0_1581
<=> ! [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_1581])]) ).
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(f12845,plain,
spl0_1580,
inference(avatar_split_clause,[],[f2944,f12843]) ).
fof(f12843,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_OGets(X12,X86),X102,tc_Event_Oevent)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
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_1579,
inference(avatar_split_clause,[],[f2943,f12833]) ).
fof(f12833,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_OGets(X12,X86),X102,tc_Event_Oevent)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
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_1578,
inference(avatar_split_clause,[],[f2889,f12829]) ).
fof(f12829,plain,
( spl0_1578
<=> ! [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_1578])]) ).
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_1577,
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_1576,
inference(avatar_split_clause,[],[f2882,f12821]) ).
fof(f12821,plain,
( spl0_1576
<=> ! [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_1576])]) ).
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_1575,
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_1574,
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_1573,
inference(avatar_split_clause,[],[f2878,f12809]) ).
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(f12807,plain,
spl0_1572,
inference(avatar_split_clause,[],[f2876,f12805]) ).
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(f12803,plain,
spl0_1571,
inference(avatar_split_clause,[],[f2875,f12801]) ).
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(f12799,plain,
spl0_1570,
inference(avatar_split_clause,[],[f2872,f12797]) ).
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(f12784,plain,
spl0_1569,
inference(avatar_split_clause,[],[f2870,f12782]) ).
fof(f12782,plain,
( spl0_1569
<=> ! [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_1569])]) ).
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(f12780,plain,
spl0_1568,
inference(avatar_split_clause,[],[f2864,f12778]) ).
fof(f12778,plain,
( spl0_1568
<=> ! [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_1568])]) ).
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(f12776,plain,
spl0_1567,
inference(avatar_split_clause,[],[f2863,f12774]) ).
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(f12772,plain,
spl0_1566,
inference(avatar_split_clause,[],[f2861,f12770]) ).
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(f12768,plain,
spl0_1565,
inference(avatar_split_clause,[],[f2860,f12766]) ).
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(f12764,plain,
spl0_1564,
inference(avatar_split_clause,[],[f2857,f12762]) ).
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_1563,
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_1562,
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_1561,
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_1560,
inference(avatar_split_clause,[],[f2669,f12746]) ).
fof(f12746,plain,
( spl0_1560
<=> ! [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_1560])]) ).
fof(f2669,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_Oempty__Union__conv_0) ).
fof(f12743,plain,
spl0_1559,
inference(avatar_split_clause,[],[f2656,f12741]) ).
fof(f12741,plain,
( spl0_1559
<=> ! [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_1559])]) ).
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(f12739,plain,
spl0_1558,
inference(avatar_split_clause,[],[f2646,f12737]) ).
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(f12735,plain,
spl0_1557,
inference(avatar_split_clause,[],[f2645,f12733]) ).
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(f12731,plain,
spl0_1556,
inference(avatar_split_clause,[],[f2631,f12729]) ).
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(f12727,plain,
spl0_1555,
inference(avatar_split_clause,[],[f2630,f12725]) ).
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(f12723,plain,
spl0_1554,
inference(avatar_split_clause,[],[f2622,f12721]) ).
fof(f12721,plain,
( spl0_1554
<=> ! [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_1554])]) ).
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(f12719,plain,
spl0_1553,
inference(avatar_split_clause,[],[f2616,f12717]) ).
fof(f12717,plain,
( spl0_1553
<=> ! [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_1553])]) ).
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(f12715,plain,
spl0_1552,
inference(avatar_split_clause,[],[f2555,f12713]) ).
fof(f12713,plain,
( spl0_1552
<=> ! [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_1552])]) ).
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(f12711,plain,
spl0_1551,
inference(avatar_split_clause,[],[f2554,f12709]) ).
fof(f12709,plain,
( spl0_1551
<=> ! [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_1551])]) ).
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(f12707,plain,
spl0_1550,
inference(avatar_split_clause,[],[f2552,f12705]) ).
fof(f12705,plain,
( spl0_1550
<=> ! [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_1550])]) ).
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(f12698,plain,
spl0_1549,
inference(avatar_split_clause,[],[f2551,f12696]) ).
fof(f12696,plain,
( spl0_1549
<=> ! [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_1549])]) ).
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(f12694,plain,
spl0_1548,
inference(avatar_split_clause,[],[f2525,f12692]) ).
fof(f12692,plain,
( spl0_1548
<=> ! [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_1548])]) ).
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(f12690,plain,
spl0_1547,
inference(avatar_split_clause,[],[f2524,f12688]) ).
fof(f12688,plain,
( spl0_1547
<=> ! [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_1547])]) ).
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(f12686,plain,
spl0_1546,
inference(avatar_split_clause,[],[f2520,f12684]) ).
fof(f12684,plain,
( spl0_1546
<=> ! [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_1546])]) ).
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(f12682,plain,
spl0_1545,
inference(avatar_split_clause,[],[f2519,f12680]) ).
fof(f12680,plain,
( spl0_1545
<=> ! [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_1545])]) ).
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(f12678,plain,
spl0_1544,
inference(avatar_split_clause,[],[f2387,f12676]) ).
fof(f12676,plain,
( spl0_1544
<=> ! [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_1544])]) ).
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(f12674,plain,
spl0_1543,
inference(avatar_split_clause,[],[f2367,f12672]) ).
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(f12670,plain,
spl0_1542,
inference(avatar_split_clause,[],[f2365,f12668]) ).
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(f12666,plain,
spl0_1541,
inference(avatar_split_clause,[],[f2361,f12664]) ).
fof(f12664,plain,
( spl0_1541
<=> ! [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_1541])]) ).
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(f12662,plain,
spl0_1540,
inference(avatar_split_clause,[],[f2358,f12660]) ).
fof(f12660,plain,
( spl0_1540
<=> ! [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_1540])]) ).
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(f12658,plain,
( ~ spl0_1539
| ~ spl0_649
| ~ spl0_1207
| ~ spl0_1316 ),
inference(avatar_split_clause,[],[f10324,f10318,f9649,f6138,f12655]) ).
fof(f10324,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_1207
| ~ spl0_1316 ),
inference(forward_demodulation,[],[f10323,f9650]) ).
fof(f10323,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_1316 ),
inference(superposition,[],[f10319,f6140]) ).
fof(f12653,plain,
spl0_1538,
inference(avatar_split_clause,[],[f2347,f12651]) ).
fof(f12651,plain,
( spl0_1538
<=> ! [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_1538])]) ).
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(f12649,plain,
spl0_1537,
inference(avatar_split_clause,[],[f2339,f12647]) ).
fof(f12647,plain,
( spl0_1537
<=> ! [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_1537])]) ).
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(f12645,plain,
spl0_1536,
inference(avatar_split_clause,[],[f2295,f12643]) ).
fof(f12643,plain,
( spl0_1536
<=> ! [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_1536])]) ).
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(f12641,plain,
spl0_1535,
inference(avatar_split_clause,[],[f2282,f12639]) ).
fof(f12639,plain,
( spl0_1535
<=> ! [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_1535])]) ).
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(f12637,plain,
spl0_1534,
inference(avatar_split_clause,[],[f2265,f12635]) ).
fof(f12635,plain,
( spl0_1534
<=> ! [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_1534])]) ).
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(f12633,plain,
spl0_1533,
inference(avatar_split_clause,[],[f2264,f12631]) ).
fof(f12631,plain,
( spl0_1533
<=> ! [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_1533])]) ).
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(f12629,plain,
spl0_1532,
inference(avatar_split_clause,[],[f2260,f12627]) ).
fof(f12627,plain,
( spl0_1532
<=> ! [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_1532])]) ).
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(f12625,plain,
spl0_1531,
inference(avatar_split_clause,[],[f2259,f12623]) ).
fof(f12623,plain,
( spl0_1531
<=> ! [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_1531])]) ).
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(f12621,plain,
spl0_1530,
inference(avatar_split_clause,[],[f2257,f12619]) ).
fof(f12619,plain,
( spl0_1530
<=> ! [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_1530])]) ).
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(f12617,plain,
spl0_1529,
inference(avatar_split_clause,[],[f2256,f12615]) ).
fof(f12615,plain,
( spl0_1529
<=> ! [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_1529])]) ).
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(f12608,plain,
spl0_1528,
inference(avatar_split_clause,[],[f2254,f12606]) ).
fof(f12606,plain,
( spl0_1528
<=> ! [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_1528])]) ).
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(f12604,plain,
spl0_1527,
inference(avatar_split_clause,[],[f2253,f12602]) ).
fof(f12602,plain,
( spl0_1527
<=> ! [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_1527])]) ).
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(f12600,plain,
spl0_1526,
inference(avatar_split_clause,[],[f2249,f12598]) ).
fof(f12598,plain,
( spl0_1526
<=> ! [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_1526])]) ).
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(f12596,plain,
spl0_1525,
inference(avatar_split_clause,[],[f2248,f12594]) ).
fof(f12594,plain,
( spl0_1525
<=> ! [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_1525])]) ).
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(f12592,plain,
spl0_1524,
inference(avatar_split_clause,[],[f2215,f12590]) ).
fof(f12590,plain,
( spl0_1524
<=> ! [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_1524])]) ).
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(f12588,plain,
spl0_1523,
inference(avatar_split_clause,[],[f2212,f12586]) ).
fof(f12586,plain,
( spl0_1523
<=> ! [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_1523])]) ).
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(f12584,plain,
spl0_1522,
inference(avatar_split_clause,[],[f2210,f12582]) ).
fof(f12582,plain,
( spl0_1522
<=> ! [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_1522])]) ).
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(f12580,plain,
spl0_1521,
inference(avatar_split_clause,[],[f2207,f12578]) ).
fof(f12578,plain,
( spl0_1521
<=> ! [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_1521])]) ).
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(f12576,plain,
spl0_1520,
inference(avatar_split_clause,[],[f2206,f12574]) ).
fof(f12574,plain,
( spl0_1520
<=> ! [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_1520])]) ).
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(f12572,plain,
spl0_1519,
inference(avatar_split_clause,[],[f2204,f12570]) ).
fof(f12570,plain,
( spl0_1519
<=> ! [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_1519])]) ).
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(f12564,plain,
spl0_1518,
inference(avatar_split_clause,[],[f2203,f12562]) ).
fof(f12562,plain,
( spl0_1518
<=> ! [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_1518])]) ).
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(f12560,plain,
spl0_1517,
inference(avatar_split_clause,[],[f2202,f12558]) ).
fof(f12558,plain,
( spl0_1517
<=> ! [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_1517])]) ).
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(f12556,plain,
spl0_1516,
inference(avatar_split_clause,[],[f2201,f12554]) ).
fof(f12554,plain,
( spl0_1516
<=> ! [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_1516])]) ).
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(f12552,plain,
spl0_1515,
inference(avatar_split_clause,[],[f2200,f12550]) ).
fof(f12550,plain,
( spl0_1515
<=> ! [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_1515])]) ).
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(f12548,plain,
spl0_1514,
inference(avatar_split_clause,[],[f2184,f12546]) ).
fof(f12546,plain,
( spl0_1514
<=> ! [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_1514])]) ).
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(f12544,plain,
spl0_1513,
inference(avatar_split_clause,[],[f2110,f12542]) ).
fof(f12542,plain,
( spl0_1513
<=> ! [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_1513])]) ).
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(f12540,plain,
spl0_1512,
inference(avatar_split_clause,[],[f2109,f12538]) ).
fof(f12538,plain,
( spl0_1512
<=> ! [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_1512])]) ).
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(f12536,plain,
spl0_1511,
inference(avatar_split_clause,[],[f2045,f12534]) ).
fof(f12534,plain,
( spl0_1511
<=> ! [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_1511])]) ).
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(f12532,plain,
spl0_1510,
inference(avatar_split_clause,[],[f2044,f12530]) ).
fof(f12530,plain,
( spl0_1510
<=> ! [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_1510])]) ).
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(f12528,plain,
spl0_1509,
inference(avatar_split_clause,[],[f1852,f12526]) ).
fof(f12526,plain,
( spl0_1509
<=> ! [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_1509])]) ).
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_1508,
inference(avatar_split_clause,[],[f1799,f12520]) ).
fof(f12520,plain,
( spl0_1508
<=> ! [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_1508])]) ).
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_1507,
inference(avatar_split_clause,[],[f1765,f12516]) ).
fof(f12516,plain,
( spl0_1507
<=> ! [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_1507])]) ).
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_1506,
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_1505,
inference(avatar_split_clause,[],[f1742,f12508]) ).
fof(f12508,plain,
( spl0_1505
<=> ! [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_1505])]) ).
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_1504,
inference(avatar_split_clause,[],[f1702,f12504]) ).
fof(f12504,plain,
( spl0_1504
<=> ! [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_1504])]) ).
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_1503,
inference(avatar_split_clause,[],[f1604,f12500]) ).
fof(f12500,plain,
( spl0_1503
<=> ! [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_1503])]) ).
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(f12498,plain,
spl0_1502,
inference(avatar_split_clause,[],[f1591,f12496]) ).
fof(f12496,plain,
( spl0_1502
<=> ! [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_1502])]) ).
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(f12494,plain,
spl0_1501,
inference(avatar_split_clause,[],[f1589,f12492]) ).
fof(f12492,plain,
( spl0_1501
<=> ! [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_1501])]) ).
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(f12490,plain,
spl0_1500,
inference(avatar_split_clause,[],[f1581,f12488]) ).
fof(f12488,plain,
( spl0_1500
<=> ! [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_1500])]) ).
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(f12486,plain,
spl0_1499,
inference(avatar_split_clause,[],[f1580,f12484]) ).
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(f12482,plain,
spl0_1498,
inference(avatar_split_clause,[],[f1578,f12480]) ).
fof(f12480,plain,
( spl0_1498
<=> ! [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_1498])]) ).
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(f12478,plain,
spl0_1497,
inference(avatar_split_clause,[],[f1576,f12476]) ).
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(f12474,plain,
spl0_1496,
inference(avatar_split_clause,[],[f1575,f12472]) ).
fof(f12472,plain,
( spl0_1496
<=> ! [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_1496])]) ).
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(f12470,plain,
spl0_1495,
inference(avatar_split_clause,[],[f1475,f12468]) ).
fof(f12468,plain,
( spl0_1495
<=> ! [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_1495])]) ).
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(f12466,plain,
spl0_1494,
inference(avatar_split_clause,[],[f1416,f12464]) ).
fof(f12464,plain,
( spl0_1494
<=> ! [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_1494])]) ).
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(f12462,plain,
spl0_1493,
inference(avatar_split_clause,[],[f1305,f12460]) ).
fof(f12460,plain,
( spl0_1493
<=> ! [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_1493])]) ).
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(f12458,plain,
spl0_1492,
inference(avatar_split_clause,[],[f1304,f12456]) ).
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(f12454,plain,
spl0_1491,
inference(avatar_split_clause,[],[f1291,f12452]) ).
fof(f12452,plain,
( spl0_1491
<=> ! [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_1491])]) ).
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(f12450,plain,
spl0_1490,
inference(avatar_split_clause,[],[f1287,f12448]) ).
fof(f12448,plain,
( spl0_1490
<=> ! [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_1490])]) ).
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(f12446,plain,
spl0_1489,
inference(avatar_split_clause,[],[f1286,f12444]) ).
fof(f12444,plain,
( spl0_1489
<=> ! [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_1489])]) ).
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(f12442,plain,
spl0_1488,
inference(avatar_split_clause,[],[f1285,f12440]) ).
fof(f12440,plain,
( spl0_1488
<=> ! [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_1488])]) ).
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(f12438,plain,
spl0_1487,
inference(avatar_split_clause,[],[f1284,f12436]) ).
fof(f12436,plain,
( spl0_1487
<=> ! [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_1487])]) ).
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(f12434,plain,
spl0_1486,
inference(avatar_split_clause,[],[f1276,f12432]) ).
fof(f12432,plain,
( spl0_1486
<=> ! [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_1486])]) ).
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(f12430,plain,
spl0_1485,
inference(avatar_split_clause,[],[f1223,f12428]) ).
fof(f12428,plain,
( spl0_1485
<=> ! [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_1485])]) ).
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(f12426,plain,
spl0_1484,
inference(avatar_split_clause,[],[f1221,f12424]) ).
fof(f12424,plain,
( spl0_1484
<=> ! [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_1484])]) ).
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(f12422,plain,
spl0_1483,
inference(avatar_split_clause,[],[f111,f12420]) ).
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(f12418,plain,
spl0_1482,
inference(avatar_split_clause,[],[f108,f12416]) ).
fof(f12416,plain,
( spl0_1482
<=> ! [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_1482])]) ).
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(f12414,plain,
spl0_1481,
inference(avatar_split_clause,[],[f104,f12412]) ).
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(f12410,plain,
spl0_1480,
inference(avatar_split_clause,[],[f100,f12408]) ).
fof(f12408,plain,
( spl0_1480
<=> ! [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_1480])]) ).
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(f12406,plain,
spl0_1479,
inference(avatar_split_clause,[],[f97,f12404]) ).
fof(f12404,plain,
( spl0_1479
<=> ! [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_1479])]) ).
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(f12402,plain,
spl0_1478,
inference(avatar_split_clause,[],[f29,f12400]) ).
fof(f12400,plain,
( spl0_1478
<=> ! [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_1478])]) ).
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(f12270,plain,
( spl0_1477
| ~ spl0_1026
| ~ spl0_1453 ),
inference(avatar_split_clause,[],[f12227,f11275,f8693,f12268]) ).
fof(f11275,plain,
( spl0_1453
<=> ! [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_1453])]) ).
fof(f12227,plain,
( ! [X0] :
( c_in(v_KAB,c_Message_OkeysFor(c_Message_Osynth(X0)),tc_nat)
| ~ c_in(c_Message_Omsg_OKey(v_KAB),X0,tc_Message_Omsg) )
| ~ spl0_1026
| ~ spl0_1453 ),
inference(superposition,[],[f11276,f8695]) ).
fof(f11276,plain,
( ! [X88,X24] :
( c_in(c_Message_OinvKey(X24),c_Message_OkeysFor(c_Message_Osynth(X88)),tc_nat)
| ~ c_in(c_Message_Omsg_OKey(X24),X88,tc_Message_Omsg) )
| ~ spl0_1453 ),
inference(avatar_component_clause,[],[f11275]) ).
fof(f11978,plain,
( spl0_1476
| ~ spl0_661
| ~ spl0_817
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f9993,f9681,f7634,f6191,f11975]) ).
fof(f11975,plain,
( spl0_1476
<=> c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f6191,plain,
( spl0_661
<=> c_emptyset = c_Message_Oparts(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f7634,plain,
( spl0_817
<=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f9993,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_661
| ~ spl0_817
| ~ spl0_1215 ),
inference(forward_demodulation,[],[f9988,f7635]) ).
fof(f7635,plain,
( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f7634]) ).
fof(f9988,plain,
( c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_661
| ~ spl0_1215 ),
inference(superposition,[],[f9682,f6193]) ).
fof(f6193,plain,
( c_emptyset = c_Message_Oparts(c_emptyset)
| ~ spl0_661 ),
inference(avatar_component_clause,[],[f6191]) ).
fof(f11889,plain,
( spl0_1475
| ~ spl0_664
| ~ spl0_817
| ~ spl0_1214 ),
inference(avatar_split_clause,[],[f9987,f9677,f7634,f6206,f11886]) ).
fof(f11886,plain,
( spl0_1475
<=> c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f6206,plain,
( spl0_664
<=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f9987,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset))
| ~ spl0_664
| ~ spl0_817
| ~ spl0_1214 ),
inference(forward_demodulation,[],[f9982,f7635]) ).
fof(f9982,plain,
( c_Message_Oanalz(c_Message_Osynth(c_emptyset)) = c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg)
| ~ spl0_664
| ~ spl0_1214 ),
inference(superposition,[],[f9678,f6208]) ).
fof(f6208,plain,
( c_emptyset = c_Message_Oanalz(c_emptyset)
| ~ spl0_664 ),
inference(avatar_component_clause,[],[f6206]) ).
fof(f11658,plain,
( spl0_1474
| ~ spl0_728
| ~ spl0_1195 ),
inference(avatar_split_clause,[],[f9954,f9600,f7255,f11656]) ).
fof(f11656,plain,
( spl0_1474
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f7255,plain,
( spl0_728
<=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f9600,plain,
( spl0_1195
<=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f9954,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_728
| ~ spl0_1195 ),
inference(superposition,[],[f9601,f7256]) ).
fof(f7256,plain,
( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
| ~ spl0_728 ),
inference(avatar_component_clause,[],[f7255]) ).
fof(f9601,plain,
( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
| ~ spl0_1195 ),
inference(avatar_component_clause,[],[f9600]) ).
fof(f11390,plain,
( spl0_1473
| ~ spl0_1128
| ~ spl0_1335 ),
inference(avatar_split_clause,[],[f11380,f10792,f9162,f11388]) ).
fof(f11388,plain,
( spl0_1473
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f9162,plain,
( spl0_1128
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f10792,plain,
( spl0_1335
<=> ! [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_1335])]) ).
fof(f11380,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1128
| ~ spl0_1335 ),
inference(resolution,[],[f10793,f9163]) ).
fof(f9163,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1128 ),
inference(avatar_component_clause,[],[f9162]) ).
fof(f10793,plain,
( ! [X1,X12,X13] :
( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1335 ),
inference(avatar_component_clause,[],[f10792]) ).
fof(f11353,plain,
spl0_1472,
inference(avatar_split_clause,[],[f3386,f11351]) ).
fof(f11351,plain,
( spl0_1472
<=> ! [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_1472])]) ).
fof(f3386,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,[],[f3385,f2115]) ).
fof(f3385,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,[],[f3181,f2981]) ).
fof(f3181,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(f11349,plain,
spl0_1471,
inference(avatar_split_clause,[],[f3314,f11347]) ).
fof(f11347,plain,
( spl0_1471
<=> ! [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_1471])]) ).
fof(f3314,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,[],[f3313,f2156]) ).
fof(f3313,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,[],[f3312,f2154]) ).
fof(f3312,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(f11345,plain,
spl0_1470,
inference(avatar_split_clause,[],[f3307,f11343]) ).
fof(f3307,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,[],[f3306,f2156]) ).
fof(f3306,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,[],[f3305,f2154]) ).
fof(f3305,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(f11341,plain,
spl0_1469,
inference(avatar_split_clause,[],[f3120,f11339]) ).
fof(f11339,plain,
( spl0_1469
<=> ! [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_1469])]) ).
fof(f3120,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(f11337,plain,
( spl0_1468
| ~ spl0_652
| ~ spl0_1166 ),
inference(avatar_split_clause,[],[f9871,f9484,f6152,f11335]) ).
fof(f11335,plain,
( spl0_1468
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f6152,plain,
( spl0_652
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f9871,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_652
| ~ spl0_1166 ),
inference(resolution,[],[f9485,f6153]) ).
fof(f6153,plain,
( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
| ~ spl0_652 ),
inference(avatar_component_clause,[],[f6152]) ).
fof(f11333,plain,
spl0_1467,
inference(avatar_split_clause,[],[f3119,f11331]) ).
fof(f11331,plain,
( spl0_1467
<=> ! [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_1467])]) ).
fof(f3119,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(f11329,plain,
spl0_1466,
inference(avatar_split_clause,[],[f3110,f11327]) ).
fof(f11327,plain,
( spl0_1466
<=> ! [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_1466])]) ).
fof(f3110,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(f11325,plain,
spl0_1465,
inference(avatar_split_clause,[],[f3034,f11323]) ).
fof(f3034,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(f11321,plain,
spl0_1464,
inference(avatar_split_clause,[],[f3031,f11319]) ).
fof(f3031,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(f11317,plain,
spl0_1463,
inference(avatar_split_clause,[],[f3030,f11315]) ).
fof(f11315,plain,
( spl0_1463
<=> ! [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_1463])]) ).
fof(f3030,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(f11313,plain,
spl0_1462,
inference(avatar_split_clause,[],[f2935,f11311]) ).
fof(f11311,plain,
( spl0_1462
<=> ! [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_1462])]) ).
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(f11309,plain,
spl0_1461,
inference(avatar_split_clause,[],[f2897,f11307]) ).
fof(f11307,plain,
( spl0_1461
<=> ! [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_1461])]) ).
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(f11305,plain,
spl0_1460,
inference(avatar_split_clause,[],[f2893,f11303]) ).
fof(f11303,plain,
( spl0_1460
<=> ! [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_1460])]) ).
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(f11301,plain,
spl0_1459,
inference(avatar_split_clause,[],[f2892,f11299]) ).
fof(f11299,plain,
( spl0_1459
<=> ! [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_1459])]) ).
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(f11297,plain,
spl0_1458,
inference(avatar_split_clause,[],[f2851,f11295]) ).
fof(f11295,plain,
( spl0_1458
<=> ! [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_1458])]) ).
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(f11293,plain,
( spl0_1457
| ~ spl0_652
| ~ spl0_1162 ),
inference(avatar_split_clause,[],[f9861,f9467,f6152,f11291]) ).
fof(f11291,plain,
( spl0_1457
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f9467,plain,
( spl0_1162
<=> ! [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_1162])]) ).
fof(f9861,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_652
| ~ spl0_1162 ),
inference(resolution,[],[f9468,f6153]) ).
fof(f9468,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_1162 ),
inference(avatar_component_clause,[],[f9467]) ).
fof(f11289,plain,
spl0_1456,
inference(avatar_split_clause,[],[f2834,f11287]) ).
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(f11285,plain,
spl0_1455,
inference(avatar_split_clause,[],[f2833,f11283]) ).
fof(f11283,plain,
( spl0_1455
<=> ! [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_1455])]) ).
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(f11281,plain,
spl0_1454,
inference(avatar_split_clause,[],[f2796,f11279]) ).
fof(f11279,plain,
( spl0_1454
<=> ! [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_1454])]) ).
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(f11277,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2794,f11275]) ).
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(f11273,plain,
spl0_1452,
inference(avatar_split_clause,[],[f2783,f11271]) ).
fof(f11271,plain,
( spl0_1452
<=> ! [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_1452])]) ).
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(f11269,plain,
spl0_1451,
inference(avatar_split_clause,[],[f2782,f11267]) ).
fof(f11267,plain,
( spl0_1451
<=> ! [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_1451])]) ).
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(f11265,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2781,f11263]) ).
fof(f11263,plain,
( spl0_1450
<=> ! [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_1450])]) ).
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(f11261,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2774,f11259]) ).
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(f11257,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2771,f11255]) ).
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(f11253,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2768,f11251]) ).
fof(f11251,plain,
( spl0_1447
<=> ! [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_1447])]) ).
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(f11248,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2742,f11246]) ).
fof(f11246,plain,
( spl0_1446
<=> ! [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_1446])]) ).
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(f11244,plain,
spl0_1445,
inference(avatar_split_clause,[],[f2729,f11242]) ).
fof(f11242,plain,
( spl0_1445
<=> ! [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_1445])]) ).
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(f11240,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2728,f11238]) ).
fof(f11238,plain,
( spl0_1444
<=> ! [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_1444])]) ).
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(f11236,plain,
spl0_1443,
inference(avatar_split_clause,[],[f2703,f11234]) ).
fof(f11234,plain,
( spl0_1443
<=> ! [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_1443])]) ).
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(f11232,plain,
spl0_1442,
inference(avatar_split_clause,[],[f2701,f11230]) ).
fof(f11230,plain,
( spl0_1442
<=> ! [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_1442])]) ).
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(f11228,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2692,f11226]) ).
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(f11224,plain,
spl0_1440,
inference(avatar_split_clause,[],[f2688,f11222]) ).
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(f11220,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2676,f11218]) ).
fof(f11218,plain,
( spl0_1439
<=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
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(f11216,plain,
spl0_1438,
inference(avatar_split_clause,[],[f2670,f11214]) ).
fof(f11214,plain,
( spl0_1438
<=> ! [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_1438])]) ).
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(f11212,plain,
spl0_1437,
inference(avatar_split_clause,[],[f2653,f11210]) ).
fof(f11210,plain,
( spl0_1437
<=> ! [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_1437])]) ).
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(f11204,plain,
spl0_1436,
inference(avatar_split_clause,[],[f2628,f11202]) ).
fof(f11202,plain,
( spl0_1436
<=> ! [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_1436])]) ).
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(f11200,plain,
spl0_1435,
inference(avatar_split_clause,[],[f2627,f11198]) ).
fof(f11198,plain,
( spl0_1435
<=> ! [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_1435])]) ).
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(f11196,plain,
spl0_1434,
inference(avatar_split_clause,[],[f2617,f11194]) ).
fof(f11194,plain,
( spl0_1434
<=> ! [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_1434])]) ).
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(f11192,plain,
spl0_1433,
inference(avatar_split_clause,[],[f2614,f11190]) ).
fof(f11190,plain,
( spl0_1433
<=> ! [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_1433])]) ).
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(f11188,plain,
spl0_1432,
inference(avatar_split_clause,[],[f2595,f11186]) ).
fof(f11186,plain,
( spl0_1432
<=> ! [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_1432])]) ).
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(f11184,plain,
spl0_1431,
inference(avatar_split_clause,[],[f2594,f11182]) ).
fof(f11182,plain,
( spl0_1431
<=> ! [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_1431])]) ).
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(f11180,plain,
spl0_1430,
inference(avatar_split_clause,[],[f2592,f11178]) ).
fof(f11178,plain,
( spl0_1430
<=> ! [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_1430])]) ).
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(f11176,plain,
spl0_1429,
inference(avatar_split_clause,[],[f2591,f11174]) ).
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(f11172,plain,
spl0_1428,
inference(avatar_split_clause,[],[f2581,f11170]) ).
fof(f11170,plain,
( spl0_1428
<=> ! [X13,X12,X1] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
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(f11168,plain,
spl0_1427,
inference(avatar_split_clause,[],[f2570,f11166]) ).
fof(f11166,plain,
( spl0_1427
<=> ! [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_1427])]) ).
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(f11164,plain,
spl0_1426,
inference(avatar_split_clause,[],[f2569,f11162]) ).
fof(f11162,plain,
( spl0_1426
<=> ! [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_1426])]) ).
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(f11160,plain,
spl0_1425,
inference(avatar_split_clause,[],[f2568,f11158]) ).
fof(f11158,plain,
( spl0_1425
<=> ! [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_1425])]) ).
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(f11156,plain,
spl0_1424,
inference(avatar_split_clause,[],[f2559,f11154]) ).
fof(f11154,plain,
( spl0_1424
<=> ! [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_1424])]) ).
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(f11152,plain,
spl0_1423,
inference(avatar_split_clause,[],[f2558,f11150]) ).
fof(f11150,plain,
( spl0_1423
<=> ! [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_1423])]) ).
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(f11148,plain,
spl0_1422,
inference(avatar_split_clause,[],[f2557,f11146]) ).
fof(f11146,plain,
( spl0_1422
<=> ! [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_1422])]) ).
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(f11144,plain,
spl0_1421,
inference(avatar_split_clause,[],[f2550,f11142]) ).
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(f11140,plain,
spl0_1420,
inference(avatar_split_clause,[],[f2546,f11138]) ).
fof(f11138,plain,
( spl0_1420
<=> ! [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_1420])]) ).
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(f11136,plain,
spl0_1419,
inference(avatar_split_clause,[],[f2543,f11134]) ).
fof(f11134,plain,
( spl0_1419
<=> ! [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_1419])]) ).
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(f11132,plain,
spl0_1418,
inference(avatar_split_clause,[],[f2537,f11130]) ).
fof(f11130,plain,
( spl0_1418
<=> ! [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_1418])]) ).
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(f11128,plain,
spl0_1417,
inference(avatar_split_clause,[],[f2536,f11126]) ).
fof(f11126,plain,
( spl0_1417
<=> ! [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_1417])]) ).
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(f11121,plain,
spl0_1416,
inference(avatar_split_clause,[],[f2535,f11119]) ).
fof(f11119,plain,
( spl0_1416
<=> ! [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_1416])]) ).
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(f11117,plain,
spl0_1415,
inference(avatar_split_clause,[],[f2531,f11115]) ).
fof(f11115,plain,
( spl0_1415
<=> ! [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_1415])]) ).
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(f11113,plain,
spl0_1414,
inference(avatar_split_clause,[],[f2530,f11111]) ).
fof(f11111,plain,
( spl0_1414
<=> ! [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_1414])]) ).
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(f11109,plain,
spl0_1413,
inference(avatar_split_clause,[],[f2529,f11107]) ).
fof(f11107,plain,
( spl0_1413
<=> ! [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_1413])]) ).
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(f11105,plain,
spl0_1412,
inference(avatar_split_clause,[],[f2523,f11103]) ).
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(f11101,plain,
spl0_1411,
inference(avatar_split_clause,[],[f2518,f11099]) ).
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(f11097,plain,
spl0_1410,
inference(avatar_split_clause,[],[f2517,f11095]) ).
fof(f11095,plain,
( spl0_1410
<=> ! [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_1410])]) ).
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(f11093,plain,
spl0_1409,
inference(avatar_split_clause,[],[f2516,f11091]) ).
fof(f11091,plain,
( spl0_1409
<=> ! [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_1409])]) ).
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(f11089,plain,
spl0_1408,
inference(avatar_split_clause,[],[f2515,f11087]) ).
fof(f11087,plain,
( spl0_1408
<=> ! [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_1408])]) ).
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(f11085,plain,
spl0_1407,
inference(avatar_split_clause,[],[f2514,f11083]) ).
fof(f11083,plain,
( spl0_1407
<=> ! [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_1407])]) ).
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(f11081,plain,
spl0_1406,
inference(avatar_split_clause,[],[f2302,f11079]) ).
fof(f11079,plain,
( spl0_1406
<=> ! [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_1406])]) ).
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(f11077,plain,
spl0_1405,
inference(avatar_split_clause,[],[f2301,f11075]) ).
fof(f11075,plain,
( spl0_1405
<=> ! [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_1405])]) ).
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(f11073,plain,
spl0_1404,
inference(avatar_split_clause,[],[f2300,f11071]) ).
fof(f11071,plain,
( spl0_1404
<=> ! [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_1404])]) ).
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(f11069,plain,
spl0_1403,
inference(avatar_split_clause,[],[f2299,f11067]) ).
fof(f11067,plain,
( spl0_1403
<=> ! [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_1403])]) ).
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(f11065,plain,
spl0_1402,
inference(avatar_split_clause,[],[f2296,f11063]) ).
fof(f11063,plain,
( spl0_1402
<=> ! [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_1402])]) ).
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(f11061,plain,
spl0_1401,
inference(avatar_split_clause,[],[f2289,f11059]) ).
fof(f11059,plain,
( spl0_1401
<=> ! [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_1401])]) ).
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(f11057,plain,
spl0_1400,
inference(avatar_split_clause,[],[f2288,f11055]) ).
fof(f11055,plain,
( spl0_1400
<=> ! [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_1400])]) ).
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(f11053,plain,
spl0_1399,
inference(avatar_split_clause,[],[f2287,f11051]) ).
fof(f11051,plain,
( spl0_1399
<=> ! [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_1399])]) ).
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(f11049,plain,
spl0_1398,
inference(avatar_split_clause,[],[f2286,f11047]) ).
fof(f11047,plain,
( spl0_1398
<=> ! [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_1398])]) ).
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(f11045,plain,
spl0_1397,
inference(avatar_split_clause,[],[f2283,f11043]) ).
fof(f11043,plain,
( spl0_1397
<=> ! [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_1397])]) ).
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(f11041,plain,
spl0_1396,
inference(avatar_split_clause,[],[f2277,f11039]) ).
fof(f11039,plain,
( spl0_1396
<=> ! [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_1396])]) ).
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(f11037,plain,
spl0_1395,
inference(avatar_split_clause,[],[f2276,f11035]) ).
fof(f11035,plain,
( spl0_1395
<=> ! [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_1395])]) ).
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(f11033,plain,
spl0_1394,
inference(avatar_split_clause,[],[f2275,f11031]) ).
fof(f11031,plain,
( spl0_1394
<=> ! [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_1394])]) ).
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(f11029,plain,
spl0_1393,
inference(avatar_split_clause,[],[f2274,f11027]) ).
fof(f11027,plain,
( spl0_1393
<=> ! [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_1393])]) ).
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(f11025,plain,
spl0_1392,
inference(avatar_split_clause,[],[f2234,f11023]) ).
fof(f11023,plain,
( spl0_1392
<=> ! [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_1392])]) ).
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(f11021,plain,
spl0_1391,
inference(avatar_split_clause,[],[f2233,f11019]) ).
fof(f11019,plain,
( spl0_1391
<=> ! [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_1391])]) ).
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(f11017,plain,
spl0_1390,
inference(avatar_split_clause,[],[f2230,f11015]) ).
fof(f11015,plain,
( spl0_1390
<=> ! [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_1390])]) ).
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(f11013,plain,
spl0_1389,
inference(avatar_split_clause,[],[f2229,f11011]) ).
fof(f11011,plain,
( spl0_1389
<=> ! [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_1389])]) ).
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(f11009,plain,
spl0_1388,
inference(avatar_split_clause,[],[f2227,f11007]) ).
fof(f11007,plain,
( spl0_1388
<=> ! [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_1388])]) ).
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(f11005,plain,
spl0_1387,
inference(avatar_split_clause,[],[f2224,f11003]) ).
fof(f11003,plain,
( spl0_1387
<=> ! [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_1387])]) ).
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(f11001,plain,
spl0_1386,
inference(avatar_split_clause,[],[f2223,f10999]) ).
fof(f10999,plain,
( spl0_1386
<=> ! [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_1386])]) ).
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(f10997,plain,
spl0_1385,
inference(avatar_split_clause,[],[f2222,f10995]) ).
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(f10993,plain,
spl0_1384,
inference(avatar_split_clause,[],[f2221,f10991]) ).
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(f10989,plain,
spl0_1383,
inference(avatar_split_clause,[],[f2167,f10987]) ).
fof(f10987,plain,
( spl0_1383
<=> ! [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_1383])]) ).
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(f10985,plain,
spl0_1382,
inference(avatar_split_clause,[],[f2166,f10983]) ).
fof(f10983,plain,
( spl0_1382
<=> ! [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_1382])]) ).
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(f10981,plain,
spl0_1381,
inference(avatar_split_clause,[],[f2086,f10979]) ).
fof(f10979,plain,
( spl0_1381
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
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(f10977,plain,
spl0_1380,
inference(avatar_split_clause,[],[f2081,f10975]) ).
fof(f10975,plain,
( spl0_1380
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
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(f10973,plain,
spl0_1379,
inference(avatar_split_clause,[],[f2065,f10971]) ).
fof(f10971,plain,
( spl0_1379
<=> ! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
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(f10969,plain,
spl0_1378,
inference(avatar_split_clause,[],[f1850,f10967]) ).
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(f10965,plain,
spl0_1377,
inference(avatar_split_clause,[],[f1813,f10963]) ).
fof(f10963,plain,
( spl0_1377
<=> ! [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_1377])]) ).
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(f10961,plain,
( spl0_1376
| ~ spl0_719
| ~ spl0_800
| ~ spl0_1121 ),
inference(avatar_split_clause,[],[f9333,f9084,f7565,f7216,f10958]) ).
fof(f9333,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_719
| ~ spl0_800
| ~ spl0_1121 ),
inference(forward_demodulation,[],[f9330,f7218]) ).
fof(f9330,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_800
| ~ spl0_1121 ),
inference(superposition,[],[f9085,f7567]) ).
fof(f10956,plain,
spl0_1375,
inference(avatar_split_clause,[],[f1807,f10954]) ).
fof(f10954,plain,
( spl0_1375
<=> ! [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_1375])]) ).
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(f10952,plain,
spl0_1374,
inference(avatar_split_clause,[],[f1806,f10950]) ).
fof(f10950,plain,
( spl0_1374
<=> ! [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_1374])]) ).
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(f10948,plain,
spl0_1373,
inference(avatar_split_clause,[],[f1784,f10946]) ).
fof(f10946,plain,
( spl0_1373
<=> ! [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_1373])]) ).
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(f10944,plain,
spl0_1372,
inference(avatar_split_clause,[],[f1743,f10942]) ).
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(f10940,plain,
spl0_1371,
inference(avatar_split_clause,[],[f1737,f10938]) ).
fof(f10938,plain,
( spl0_1371
<=> ! [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_1371])]) ).
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(f10936,plain,
spl0_1370,
inference(avatar_split_clause,[],[f1626,f10934]) ).
fof(f10934,plain,
( spl0_1370
<=> ! [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_1370])]) ).
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(f10932,plain,
spl0_1369,
inference(avatar_split_clause,[],[f1625,f10930]) ).
fof(f10930,plain,
( spl0_1369
<=> ! [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_1369])]) ).
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(f10928,plain,
spl0_1368,
inference(avatar_split_clause,[],[f1610,f10926]) ).
fof(f10926,plain,
( spl0_1368
<=> ! [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_1368])]) ).
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(f10924,plain,
spl0_1367,
inference(avatar_split_clause,[],[f1552,f10922]) ).
fof(f10922,plain,
( spl0_1367
<=> ! [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_1367])]) ).
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(f10920,plain,
spl0_1366,
inference(avatar_split_clause,[],[f1530,f10918]) ).
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(f10916,plain,
spl0_1365,
inference(avatar_split_clause,[],[f1493,f10914]) ).
fof(f10914,plain,
( spl0_1365
<=> ! [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_1365])]) ).
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(f10912,plain,
spl0_1364,
inference(avatar_split_clause,[],[f1492,f10910]) ).
fof(f10910,plain,
( spl0_1364
<=> ! [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_1364])]) ).
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(f10908,plain,
spl0_1363,
inference(avatar_split_clause,[],[f1485,f10906]) ).
fof(f10906,plain,
( spl0_1363
<=> ! [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_1363])]) ).
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(f10903,plain,
( spl0_1362
| ~ spl0_919
| ~ spl0_1361 ),
inference(avatar_split_clause,[],[f10899,f10896,f8115,f10901]) ).
fof(f10901,plain,
( spl0_1362
<=> ! [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_1362])]) ).
fof(f8115,plain,
( spl0_919
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f10896,plain,
( spl0_1361
<=> ! [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_1361])]) ).
fof(f10899,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_919
| ~ spl0_1361 ),
inference(forward_demodulation,[],[f10897,f8117]) ).
fof(f8117,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f8115]) ).
fof(f10897,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_1361 ),
inference(avatar_component_clause,[],[f10896]) ).
fof(f10898,plain,
spl0_1361,
inference(avatar_split_clause,[],[f1484,f10896]) ).
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(f10894,plain,
spl0_1360,
inference(avatar_split_clause,[],[f1477,f10892]) ).
fof(f10892,plain,
( spl0_1360
<=> ! [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_1360])]) ).
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(f10890,plain,
spl0_1359,
inference(avatar_split_clause,[],[f1476,f10888]) ).
fof(f10888,plain,
( spl0_1359
<=> ! [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_1359])]) ).
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(f10886,plain,
spl0_1358,
inference(avatar_split_clause,[],[f1457,f10884]) ).
fof(f10884,plain,
( spl0_1358
<=> ! [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_1358])]) ).
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(f10882,plain,
spl0_1357,
inference(avatar_split_clause,[],[f1442,f10880]) ).
fof(f10880,plain,
( spl0_1357
<=> ! [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_1357])]) ).
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(f10878,plain,
( spl0_1355
| ~ spl0_1356
| ~ spl0_802
| ~ spl0_1080 ),
inference(avatar_split_clause,[],[f9270,f8918,f7574,f10875,f10872]) ).
fof(f10872,plain,
( spl0_1355
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f10875,plain,
( spl0_1356
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f7574,plain,
( spl0_802
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f8918,plain,
( spl0_1080
<=> ! [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_1080])]) ).
fof(f9270,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_802
| ~ spl0_1080 ),
inference(superposition,[],[f8919,f7575]) ).
fof(f7575,plain,
( ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat)
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f7574]) ).
fof(f8919,plain,
( ! [X3,X0] :
( ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_1080 ),
inference(avatar_component_clause,[],[f8918]) ).
fof(f10870,plain,
spl0_1354,
inference(avatar_split_clause,[],[f1413,f10868]) ).
fof(f10868,plain,
( spl0_1354
<=> ! [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_1354])]) ).
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(f10866,plain,
spl0_1353,
inference(avatar_split_clause,[],[f1412,f10864]) ).
fof(f10864,plain,
( spl0_1353
<=> ! [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_1353])]) ).
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(f10862,plain,
spl0_1352,
inference(avatar_split_clause,[],[f1409,f10860]) ).
fof(f10860,plain,
( spl0_1352
<=> ! [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_1352])]) ).
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(f10858,plain,
spl0_1351,
inference(avatar_split_clause,[],[f1408,f10856]) ).
fof(f10856,plain,
( spl0_1351
<=> ! [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_1351])]) ).
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(f10854,plain,
spl0_1350,
inference(avatar_split_clause,[],[f1406,f10852]) ).
fof(f10852,plain,
( spl0_1350
<=> ! [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_1350])]) ).
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(f10850,plain,
spl0_1349,
inference(avatar_split_clause,[],[f1400,f10848]) ).
fof(f10848,plain,
( spl0_1349
<=> ! [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_1349])]) ).
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(f10846,plain,
spl0_1348,
inference(avatar_split_clause,[],[f1399,f10844]) ).
fof(f10844,plain,
( spl0_1348
<=> ! [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_1348])]) ).
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(f10842,plain,
spl0_1347,
inference(avatar_split_clause,[],[f1398,f10840]) ).
fof(f10840,plain,
( spl0_1347
<=> ! [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_1347])]) ).
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(f10838,plain,
spl0_1346,
inference(avatar_split_clause,[],[f1397,f10836]) ).
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(f10834,plain,
spl0_1345,
inference(avatar_split_clause,[],[f1361,f10832]) ).
fof(f10832,plain,
( spl0_1345
<=> ! [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_1345])]) ).
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(f10830,plain,
spl0_1344,
inference(avatar_split_clause,[],[f1356,f10828]) ).
fof(f10828,plain,
( spl0_1344
<=> ! [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_1344])]) ).
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(f10826,plain,
spl0_1343,
inference(avatar_split_clause,[],[f1342,f10824]) ).
fof(f10824,plain,
( spl0_1343
<=> ! [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_1343])]) ).
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(f10822,plain,
spl0_1342,
inference(avatar_split_clause,[],[f1341,f10820]) ).
fof(f10820,plain,
( spl0_1342
<=> ! [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_1342])]) ).
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(f10818,plain,
spl0_1341,
inference(avatar_split_clause,[],[f1243,f10816]) ).
fof(f10816,plain,
( spl0_1341
<=> ! [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_1341])]) ).
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(f10814,plain,
spl0_1340,
inference(avatar_split_clause,[],[f1233,f10812]) ).
fof(f10812,plain,
( spl0_1340
<=> ! [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_1340])]) ).
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(f10810,plain,
spl0_1339,
inference(avatar_split_clause,[],[f1232,f10808]) ).
fof(f10808,plain,
( spl0_1339
<=> ! [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_1339])]) ).
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(f10806,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1191,f10804]) ).
fof(f10804,plain,
( spl0_1338
<=> ! [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_1338])]) ).
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(f10802,plain,
spl0_1337,
inference(avatar_split_clause,[],[f1189,f10800]) ).
fof(f10800,plain,
( spl0_1337
<=> ! [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_1337])]) ).
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(f10798,plain,
spl0_1336,
inference(avatar_split_clause,[],[f1185,f10796]) ).
fof(f10796,plain,
( spl0_1336
<=> ! [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_1336])]) ).
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(f10794,plain,
spl0_1335,
inference(avatar_split_clause,[],[f110,f10792]) ).
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(f10790,plain,
( spl0_1334
| ~ spl0_768
| ~ spl0_1044 ),
inference(avatar_split_clause,[],[f9181,f8770,f7437,f10788]) ).
fof(f10788,plain,
( spl0_1334
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f7437,plain,
( spl0_768
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f8770,plain,
( spl0_1044
<=> ! [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_1044])]) ).
fof(f9181,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_768
| ~ spl0_1044 ),
inference(superposition,[],[f8771,f7438]) ).
fof(f7438,plain,
( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
| ~ spl0_768 ),
inference(avatar_component_clause,[],[f7437]) ).
fof(f8771,plain,
( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
| ~ spl0_1044 ),
inference(avatar_component_clause,[],[f8770]) ).
fof(f10786,plain,
spl0_1333,
inference(avatar_split_clause,[],[f109,f10784]) ).
fof(f10784,plain,
( spl0_1333
<=> ! [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_1333])]) ).
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(f10782,plain,
spl0_1332,
inference(avatar_split_clause,[],[f49,f10780]) ).
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(f10778,plain,
spl0_1331,
inference(avatar_split_clause,[],[f2,f10776]) ).
fof(f10776,plain,
( spl0_1331
<=> ! [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_1331])]) ).
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(f10774,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1,f10772]) ).
fof(f10772,plain,
( spl0_1330
<=> ! [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_1330])]) ).
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(f10661,plain,
( ~ spl0_1328
| spl0_1329
| ~ spl0_790
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10585,f10209,f7525,f10659,f10655]) ).
fof(f10655,plain,
( spl0_1328
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f10659,plain,
( spl0_1329
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f10585,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_790
| ~ spl0_1289 ),
inference(trivial_inequality_removal,[],[f10578]) ).
fof(f10578,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_790
| ~ spl0_1289 ),
inference(superposition,[],[f10210,f7526]) ).
fof(f10447,plain,
( spl0_1327
| ~ spl0_59
| ~ spl0_1024 ),
inference(avatar_split_clause,[],[f8697,f8556,f3725,f10444]) ).
fof(f8556,plain,
( spl0_1024
<=> ! [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_1024])]) ).
fof(f8697,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1024 ),
inference(resolution,[],[f8557,f3727]) ).
fof(f8557,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
| ~ spl0_1024 ),
inference(avatar_component_clause,[],[f8556]) ).
fof(f10397,plain,
( spl0_1326
| ~ spl0_897
| ~ spl0_1000 ),
inference(avatar_split_clause,[],[f8665,f8457,f7967,f10394]) ).
fof(f10394,plain,
( spl0_1326
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f8665,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_897
| ~ spl0_1000 ),
inference(superposition,[],[f7968,f8459]) ).
fof(f10390,plain,
( spl0_1325
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1248 ),
inference(avatar_split_clause,[],[f10047,f10044,f8897,f3725,f10388]) ).
fof(f10044,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(f10047,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_59
| ~ spl0_1075
| ~ spl0_1248 ),
inference(forward_demodulation,[],[f10045,f9261]) ).
fof(f10045,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,[],[f10044]) ).
fof(f10356,plain,
spl0_1324,
inference(avatar_split_clause,[],[f3331,f10354]) ).
fof(f10354,plain,
( spl0_1324
<=> ! [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_1324])]) ).
fof(f3331,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,[],[f3145,f2982]) ).
fof(f3145,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(f10352,plain,
( spl0_1323
| ~ spl0_94
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f8651,f8404,f3900,f10350]) ).
fof(f10350,plain,
( spl0_1323
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f3900,plain,
( spl0_94
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f8404,plain,
( spl0_987
<=> ! [X1,X3] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f8651,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_94
| ~ spl0_987 ),
inference(resolution,[],[f8405,f3902]) ).
fof(f3902,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f3900]) ).
fof(f8405,plain,
( ! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 )
| ~ spl0_987 ),
inference(avatar_component_clause,[],[f8404]) ).
fof(f10348,plain,
spl0_1322,
inference(avatar_split_clause,[],[f3330,f10346]) ).
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,[],[f3144,f2982]) ).
fof(f3144,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(f10344,plain,
spl0_1321,
inference(avatar_split_clause,[],[f3324,f10342]) ).
fof(f10342,plain,
( spl0_1321
<=> ! [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_1321])]) ).
fof(f3324,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,[],[f3131,f2982]) ).
fof(f3131,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(f10340,plain,
spl0_1320,
inference(avatar_split_clause,[],[f3259,f10338]) ).
fof(f3259,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,[],[f3052,f2982]) ).
fof(f3052,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(f10336,plain,
spl0_1319,
inference(avatar_split_clause,[],[f3255,f10334]) ).
fof(f3255,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,[],[f3038,f3034]) ).
fof(f3038,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(f10332,plain,
spl0_1318,
inference(avatar_split_clause,[],[f3251,f10330]) ).
fof(f10330,plain,
( spl0_1318
<=> ! [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_1318])]) ).
fof(f3251,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,[],[f3036,f3008]) ).
fof(f3036,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(f10328,plain,
spl0_1317,
inference(avatar_split_clause,[],[f3037,f10326]) ).
fof(f3037,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(f10320,plain,
( spl0_1316
| ~ spl0_1315 ),
inference(avatar_split_clause,[],[f10316,f10313,f10318]) ).
fof(f10313,plain,
( spl0_1315
<=> ! [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_1315])]) ).
fof(f10316,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_1315 ),
inference(forward_demodulation,[],[f10314,f3034]) ).
fof(f10314,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_1315 ),
inference(avatar_component_clause,[],[f10313]) ).
fof(f10315,plain,
spl0_1315,
inference(avatar_split_clause,[],[f3025,f10313]) ).
fof(f3025,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(f10311,plain,
spl0_1314,
inference(avatar_split_clause,[],[f2890,f10309]) ).
fof(f10309,plain,
( spl0_1314
<=> ! [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_1314])]) ).
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(f10307,plain,
( spl0_1313
| ~ spl0_60
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f8650,f8404,f3730,f10305]) ).
fof(f3730,plain,
( spl0_60
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f8650,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_60
| ~ spl0_987 ),
inference(resolution,[],[f8405,f3732]) ).
fof(f3732,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f3730]) ).
fof(f10303,plain,
spl0_1312,
inference(avatar_split_clause,[],[f2885,f10301]) ).
fof(f10301,plain,
( spl0_1312
<=> ! [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_1312])]) ).
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(f10299,plain,
spl0_1311,
inference(avatar_split_clause,[],[f2843,f10297]) ).
fof(f10297,plain,
( spl0_1311
<=> ! [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_1311])]) ).
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(f10295,plain,
spl0_1310,
inference(avatar_split_clause,[],[f2831,f10293]) ).
fof(f10293,plain,
( spl0_1310
<=> ! [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_1310])]) ).
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(f10291,plain,
spl0_1309,
inference(avatar_split_clause,[],[f2793,f10289]) ).
fof(f10289,plain,
( spl0_1309
<=> ! [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_1309])]) ).
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(f10287,plain,
spl0_1308,
inference(avatar_split_clause,[],[f2715,f10285]) ).
fof(f10285,plain,
( spl0_1308
<=> ! [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_1308])]) ).
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(f10283,plain,
spl0_1307,
inference(avatar_split_clause,[],[f2713,f10281]) ).
fof(f10281,plain,
( spl0_1307
<=> ! [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_1307])]) ).
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(f10279,plain,
spl0_1306,
inference(avatar_split_clause,[],[f2685,f10277]) ).
fof(f10277,plain,
( spl0_1306
<=> ! [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_1306])]) ).
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(f10275,plain,
spl0_1305,
inference(avatar_split_clause,[],[f2642,f10273]) ).
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(f10271,plain,
spl0_1304,
inference(avatar_split_clause,[],[f2641,f10269]) ).
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(f10267,plain,
spl0_1303,
inference(avatar_split_clause,[],[f2583,f10265]) ).
fof(f10265,plain,
( spl0_1303
<=> ! [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_1303])]) ).
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(f10263,plain,
( spl0_1302
| ~ spl0_94
| ~ spl0_985 ),
inference(avatar_split_clause,[],[f8649,f8395,f3900,f10261]) ).
fof(f10261,plain,
( spl0_1302
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f8395,plain,
( spl0_985
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f8649,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_94
| ~ spl0_985 ),
inference(resolution,[],[f8396,f3902]) ).
fof(f8396,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) )
| ~ spl0_985 ),
inference(avatar_component_clause,[],[f8395]) ).
fof(f10259,plain,
spl0_1301,
inference(avatar_split_clause,[],[f2582,f10257]) ).
fof(f10257,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(f10255,plain,
spl0_1300,
inference(avatar_split_clause,[],[f2545,f10253]) ).
fof(f10253,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(f10251,plain,
spl0_1299,
inference(avatar_split_clause,[],[f2542,f10249]) ).
fof(f10249,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(f10247,plain,
spl0_1298,
inference(avatar_split_clause,[],[f2522,f10245]) ).
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(f10243,plain,
spl0_1297,
inference(avatar_split_clause,[],[f2271,f10241]) ).
fof(f10241,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(f10239,plain,
spl0_1296,
inference(avatar_split_clause,[],[f2270,f10237]) ).
fof(f10237,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(f10235,plain,
spl0_1295,
inference(avatar_split_clause,[],[f2252,f10233]) ).
fof(f10233,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(f10231,plain,
spl0_1294,
inference(avatar_split_clause,[],[f2245,f10229]) ).
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(f10227,plain,
spl0_1293,
inference(avatar_split_clause,[],[f2244,f10225]) ).
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(f10223,plain,
spl0_1292,
inference(avatar_split_clause,[],[f2240,f10221]) ).
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(f10219,plain,
( spl0_1291
| ~ spl0_60
| ~ spl0_985 ),
inference(avatar_split_clause,[],[f8648,f8395,f3730,f10217]) ).
fof(f10217,plain,
( spl0_1291
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f8648,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_985 ),
inference(resolution,[],[f8396,f3732]) ).
fof(f10215,plain,
spl0_1290,
inference(avatar_split_clause,[],[f2239,f10213]) ).
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(f10211,plain,
spl0_1289,
inference(avatar_split_clause,[],[f2199,f10209]) ).
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(f10207,plain,
spl0_1288,
inference(avatar_split_clause,[],[f2183,f10205]) ).
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(f10203,plain,
spl0_1287,
inference(avatar_split_clause,[],[f2181,f10201]) ).
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(f10199,plain,
spl0_1286,
inference(avatar_split_clause,[],[f2179,f10197]) ).
fof(f10197,plain,
( spl0_1286
<=> ! [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_1286])]) ).
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(f10195,plain,
spl0_1285,
inference(avatar_split_clause,[],[f2178,f10193]) ).
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(f10191,plain,
spl0_1284,
inference(avatar_split_clause,[],[f2147,f10189]) ).
fof(f10189,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(f10187,plain,
spl0_1283,
inference(avatar_split_clause,[],[f2127,f10185]) ).
fof(f10183,plain,
spl0_1282,
inference(avatar_split_clause,[],[f2104,f10181]) ).
fof(f10181,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(f10179,plain,
spl0_1281,
inference(avatar_split_clause,[],[f2103,f10177]) ).
fof(f10177,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(f10175,plain,
( spl0_1280
| ~ spl0_98
| ~ spl0_982 ),
inference(avatar_split_clause,[],[f8644,f8383,f3920,f10173]) ).
fof(f10173,plain,
( spl0_1280
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f8383,plain,
( spl0_982
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f8644,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_98
| ~ spl0_982 ),
inference(resolution,[],[f8384,f3922]) ).
fof(f8384,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 )
| ~ spl0_982 ),
inference(avatar_component_clause,[],[f8383]) ).
fof(f10171,plain,
spl0_1279,
inference(avatar_split_clause,[],[f2079,f10169]) ).
fof(f10169,plain,
( spl0_1279
<=> ! [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_1279])]) ).
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(f10167,plain,
spl0_1278,
inference(avatar_split_clause,[],[f2078,f10165]) ).
fof(f10165,plain,
( spl0_1278
<=> ! [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_1278])]) ).
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(f10163,plain,
spl0_1277,
inference(avatar_split_clause,[],[f2030,f10161]) ).
fof(f10161,plain,
( spl0_1277
<=> ! [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_1277])]) ).
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(f10159,plain,
spl0_1276,
inference(avatar_split_clause,[],[f2029,f10157]) ).
fof(f10157,plain,
( spl0_1276
<=> ! [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_1276])]) ).
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(f10155,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1851,f10153]) ).
fof(f10153,plain,
( spl0_1275
<=> ! [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_1275])]) ).
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(f10151,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1814,f10149]) ).
fof(f10149,plain,
( spl0_1274
<=> ! [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_1274])]) ).
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(f10147,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1761,f10145]) ).
fof(f10145,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(f10143,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1731,f10141]) ).
fof(f10141,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(f10139,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1712,f10137]) ).
fof(f10137,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(f10135,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1613,f10133]) ).
fof(f10133,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(f10131,plain,
( spl0_1269
| ~ spl0_34
| ~ spl0_982 ),
inference(avatar_split_clause,[],[f8643,f8383,f3600,f10129]) ).
fof(f10129,plain,
( spl0_1269
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f8643,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_34
| ~ spl0_982 ),
inference(resolution,[],[f8384,f3602]) ).
fof(f10127,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1609,f10125]) ).
fof(f10125,plain,
( spl0_1268
<=> ! [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_1268])]) ).
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(f10123,plain,
spl0_1267,
inference(avatar_split_clause,[],[f1608,f10121]) ).
fof(f10121,plain,
( spl0_1267
<=> ! [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_1267])]) ).
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(f10119,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1595,f10117]) ).
fof(f10117,plain,
( spl0_1266
<=> ! [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_1266])]) ).
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(f10115,plain,
spl0_1265,
inference(avatar_split_clause,[],[f1594,f10113]) ).
fof(f10113,plain,
( spl0_1265
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
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(f10111,plain,
spl0_1264,
inference(avatar_split_clause,[],[f1593,f10109]) ).
fof(f10109,plain,
( spl0_1264
<=> ! [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_1264])]) ).
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(f10107,plain,
spl0_1263,
inference(avatar_split_clause,[],[f1584,f10105]) ).
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(f10103,plain,
spl0_1262,
inference(avatar_split_clause,[],[f1583,f10101]) ).
fof(f10101,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(f10099,plain,
spl0_1261,
inference(avatar_split_clause,[],[f1582,f10097]) ).
fof(f10097,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(f10095,plain,
spl0_1260,
inference(avatar_split_clause,[],[f1539,f10093]) ).
fof(f10093,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(f10091,plain,
spl0_1259,
inference(avatar_split_clause,[],[f1463,f10089]) ).
fof(f10089,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(f10087,plain,
( spl0_1258
| ~ spl0_98
| ~ spl0_981 ),
inference(avatar_split_clause,[],[f8642,f8379,f3920,f10085]) ).
fof(f10085,plain,
( spl0_1258
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f8379,plain,
( spl0_981
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f8642,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_98
| ~ spl0_981 ),
inference(resolution,[],[f8380,f3922]) ).
fof(f8380,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 )
| ~ spl0_981 ),
inference(avatar_component_clause,[],[f8379]) ).
fof(f10083,plain,
spl0_1257,
inference(avatar_split_clause,[],[f1462,f10081]) ).
fof(f10081,plain,
( spl0_1257
<=> ! [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_1257])]) ).
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(f10079,plain,
spl0_1256,
inference(avatar_split_clause,[],[f1455,f10077]) ).
fof(f10077,plain,
( spl0_1256
<=> ! [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_1256])]) ).
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(f10075,plain,
spl0_1255,
inference(avatar_split_clause,[],[f1454,f10073]) ).
fof(f10073,plain,
( spl0_1255
<=> ! [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_1255])]) ).
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(f10071,plain,
spl0_1254,
inference(avatar_split_clause,[],[f1418,f10069]) ).
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(f10067,plain,
spl0_1253,
inference(avatar_split_clause,[],[f1354,f10065]) ).
fof(f10065,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(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(f10063,plain,
spl0_1252,
inference(avatar_split_clause,[],[f1353,f10061]) ).
fof(f10061,plain,
( spl0_1252
<=> ! [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_1252])]) ).
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(f10059,plain,
spl0_1251,
inference(avatar_split_clause,[],[f1352,f10057]) ).
fof(f10057,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(f10055,plain,
spl0_1250,
inference(avatar_split_clause,[],[f1351,f10053]) ).
fof(f10053,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(f10051,plain,
spl0_1249,
inference(avatar_split_clause,[],[f1348,f10049]) ).
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(f10046,plain,
spl0_1248,
inference(avatar_split_clause,[],[f1345,f10044]) ).
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(f10042,plain,
( spl0_1247
| ~ spl0_34
| ~ spl0_981 ),
inference(avatar_split_clause,[],[f8641,f8379,f3600,f10040]) ).
fof(f10040,plain,
( spl0_1247
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f8641,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_34
| ~ spl0_981 ),
inference(resolution,[],[f8380,f3602]) ).
fof(f10038,plain,
spl0_1246,
inference(avatar_split_clause,[],[f1310,f10036]) ).
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(f10034,plain,
spl0_1245,
inference(avatar_split_clause,[],[f1307,f10032]) ).
fof(f10032,plain,
( spl0_1245
<=> ! [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_1245])]) ).
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(f10030,plain,
spl0_1244,
inference(avatar_split_clause,[],[f1236,f10028]) ).
fof(f10028,plain,
( spl0_1244
<=> ! [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_1244])]) ).
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(f10026,plain,
spl0_1243,
inference(avatar_split_clause,[],[f1234,f10024]) ).
fof(f10024,plain,
( spl0_1243
<=> ! [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_1243])]) ).
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(f10022,plain,
spl0_1242,
inference(avatar_split_clause,[],[f1178,f10020]) ).
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(f10018,plain,
spl0_1241,
inference(avatar_split_clause,[],[f1166,f10016]) ).
fof(f10016,plain,
( spl0_1241
<=> ! [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_1241])]) ).
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(f10003,plain,
( spl0_1240
| ~ spl0_71
| ~ spl0_977 ),
inference(avatar_split_clause,[],[f8635,f8363,f3785,f10001]) ).
fof(f10001,plain,
( spl0_1240
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f3785,plain,
( spl0_71
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f8363,plain,
( spl0_977
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f8635,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_71
| ~ spl0_977 ),
inference(resolution,[],[f8364,f3787]) ).
fof(f3787,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f3785]) ).
fof(f8364,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 )
| ~ spl0_977 ),
inference(avatar_component_clause,[],[f8363]) ).
fof(f9981,plain,
( spl0_1239
| ~ spl0_22
| ~ spl0_977 ),
inference(avatar_split_clause,[],[f8634,f8363,f3540,f9979]) ).
fof(f9979,plain,
( spl0_1239
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f3540,plain,
( spl0_22
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f8634,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_22
| ~ spl0_977 ),
inference(resolution,[],[f8364,f3542]) ).
fof(f3542,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f3540]) ).
fof(f9961,plain,
( spl0_1238
| ~ spl0_71
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f8633,f8359,f3785,f9959]) ).
fof(f9959,plain,
( spl0_1238
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f8359,plain,
( spl0_976
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f8633,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_71
| ~ spl0_976 ),
inference(resolution,[],[f8360,f3787]) ).
fof(f8360,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 )
| ~ spl0_976 ),
inference(avatar_component_clause,[],[f8359]) ).
fof(f9948,plain,
( spl0_1237
| ~ spl0_22
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f8632,f8359,f3540,f9946]) ).
fof(f9946,plain,
( spl0_1237
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f8632,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_22
| ~ spl0_976 ),
inference(resolution,[],[f8360,f3542]) ).
fof(f9924,plain,
( spl0_1236
| ~ spl0_16
| ~ spl0_975 ),
inference(avatar_split_clause,[],[f8631,f8355,f3510,f9922]) ).
fof(f9922,plain,
( spl0_1236
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f8355,plain,
( spl0_975
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f8631,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_16
| ~ spl0_975 ),
inference(resolution,[],[f8356,f3512]) ).
fof(f8356,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) )
| ~ spl0_975 ),
inference(avatar_component_clause,[],[f8355]) ).
fof(f9870,plain,
( spl0_1235
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1165 ),
inference(avatar_split_clause,[],[f9482,f9479,f8897,f3725,f9868]) ).
fof(f9868,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(f9479,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(f9482,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1075
| ~ spl0_1165 ),
inference(forward_demodulation,[],[f9480,f9261]) ).
fof(f9480,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,[],[f9479]) ).
fof(f9834,plain,
( spl0_1234
| spl0_687
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f9807,f9422,f7069,f9831]) ).
fof(f9831,plain,
( spl0_1234
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f7069,plain,
( spl0_687
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f9422,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(f9807,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_687
| ~ spl0_1151 ),
inference(resolution,[],[f9423,f7071]) ).
fof(f7071,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_687 ),
inference(avatar_component_clause,[],[f7069]) ).
fof(f9423,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,[],[f9422]) ).
fof(f9802,plain,
( spl0_1233
| ~ spl0_16
| ~ spl0_974 ),
inference(avatar_split_clause,[],[f8630,f8351,f3510,f9800]) ).
fof(f9800,plain,
( spl0_1233
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f8351,plain,
( spl0_974
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f8630,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_16
| ~ spl0_974 ),
inference(resolution,[],[f8352,f3512]) ).
fof(f8352,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 )
| ~ spl0_974 ),
inference(avatar_component_clause,[],[f8351]) ).
fof(f9757,plain,
spl0_1232,
inference(avatar_split_clause,[],[f3381,f9755]) ).
fof(f9755,plain,
( spl0_1232
<=> ! [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_1232])]) ).
fof(f3381,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,[],[f3380]) ).
fof(f3380,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,[],[f3379,f2115]) ).
fof(f3379,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,[],[f3177,f2981]) ).
fof(f3177,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(f9753,plain,
spl0_1231,
inference(avatar_split_clause,[],[f3262,f9751]) ).
fof(f9751,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(f3262,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,[],[f3261,f3259]) ).
fof(f3261,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,[],[f3066,f2982]) ).
fof(f3066,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(f9749,plain,
spl0_1230,
inference(avatar_split_clause,[],[f3258,f9747]) ).
fof(f9747,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(f3258,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f3046,f2982]) ).
fof(f3046,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(f9745,plain,
spl0_1229,
inference(avatar_split_clause,[],[f3257,f9743]) ).
fof(f9743,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(f3257,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f3045,f2982]) ).
fof(f3045,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(f9741,plain,
spl0_1228,
inference(avatar_split_clause,[],[f3126,f9739]) ).
fof(f9739,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(f3126,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(f9737,plain,
( spl0_1227
| ~ spl0_649
| ~ spl0_1207
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f9724,f9719,f9649,f6138,f9734]) ).
fof(f9734,plain,
( spl0_1227
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f9724,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_1207
| ~ spl0_1224 ),
inference(forward_demodulation,[],[f9723,f9650]) ).
fof(f9723,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_1224 ),
inference(superposition,[],[f9720,f6140]) ).
fof(f9732,plain,
spl0_1226,
inference(avatar_split_clause,[],[f3112,f9730]) ).
fof(f9730,plain,
( spl0_1226
<=> ! [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_1226])]) ).
fof(f3112,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(f9728,plain,
spl0_1225,
inference(avatar_split_clause,[],[f3039,f9726]) ).
fof(f9726,plain,
( spl0_1225
<=> ! [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_1225])]) ).
fof(f3039,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(f9721,plain,
( spl0_1224
| ~ spl0_1223 ),
inference(avatar_split_clause,[],[f9717,f9714,f9719]) ).
fof(f9714,plain,
( spl0_1223
<=> ! [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_1223])]) ).
fof(f9717,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_1223 ),
inference(forward_demodulation,[],[f9715,f3034]) ).
fof(f9715,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_1223 ),
inference(avatar_component_clause,[],[f9714]) ).
fof(f9716,plain,
spl0_1223,
inference(avatar_split_clause,[],[f3023,f9714]) ).
fof(f3023,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(f9712,plain,
spl0_1222,
inference(avatar_split_clause,[],[f3015,f9710]) ).
fof(f9710,plain,
( spl0_1222
<=> ! [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_1222])]) ).
fof(f3015,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,[],[f2818,f2837]) ).
fof(f2818,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_OHPair__neqs__6_0) ).
fof(f9708,plain,
( spl0_1221
| ~ spl0_817
| ~ spl0_1220 ),
inference(avatar_split_clause,[],[f9704,f9701,f7634,f9706]) ).
fof(f9706,plain,
( spl0_1221
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f9701,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(f9704,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1)
| ~ spl0_817
| ~ spl0_1220 ),
inference(forward_demodulation,[],[f9702,f7635]) ).
fof(f9702,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,[],[f9701]) ).
fof(f9703,plain,
spl0_1220,
inference(avatar_split_clause,[],[f2983,f9701]) ).
fof(f2983,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(f9699,plain,
spl0_1219,
inference(avatar_split_clause,[],[f2920,f9697]) ).
fof(f9697,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(f9695,plain,
( spl0_1218
| ~ spl0_11
| ~ spl0_973 ),
inference(avatar_split_clause,[],[f8628,f8347,f3485,f9693]) ).
fof(f9693,plain,
( spl0_1218
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f3485,plain,
( spl0_11
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f8347,plain,
( spl0_973
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f8628,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_11
| ~ spl0_973 ),
inference(resolution,[],[f8348,f3487]) ).
fof(f3487,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f8348,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 )
| ~ spl0_973 ),
inference(avatar_component_clause,[],[f8347]) ).
fof(f9691,plain,
spl0_1217,
inference(avatar_split_clause,[],[f2919,f9689]) ).
fof(f9689,plain,
( spl0_1217
<=> ! [X4,X111,X12,X27] :
( X4 = X27
| c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
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(f9687,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2898,f9685]) ).
fof(f9685,plain,
( spl0_1216
<=> ! [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_1216])]) ).
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(f9683,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2883,f9681]) ).
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(f9679,plain,
spl0_1214,
inference(avatar_split_clause,[],[f2865,f9677]) ).
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(f9675,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2852,f9673]) ).
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(f9671,plain,
spl0_1212,
inference(avatar_split_clause,[],[f2800,f9669]) ).
fof(f9669,plain,
( spl0_1212
<=> ! [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_1212])]) ).
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(f9667,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2787,f9665]) ).
fof(f9665,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(f9663,plain,
spl0_1210,
inference(avatar_split_clause,[],[f2786,f9661]) ).
fof(f9661,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(f9659,plain,
spl0_1209,
inference(avatar_split_clause,[],[f2785,f9657]) ).
fof(f9657,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(f9655,plain,
spl0_1208,
inference(avatar_split_clause,[],[f2784,f9653]) ).
fof(f9653,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(f9651,plain,
( spl0_1207
| ~ spl0_11
| ~ spl0_972 ),
inference(avatar_split_clause,[],[f8626,f8343,f3485,f9649]) ).
fof(f8343,plain,
( spl0_972
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f8626,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_11
| ~ spl0_972 ),
inference(resolution,[],[f8344,f3487]) ).
fof(f8344,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 )
| ~ spl0_972 ),
inference(avatar_component_clause,[],[f8343]) ).
fof(f9647,plain,
spl0_1206,
inference(avatar_split_clause,[],[f2759,f9645]) ).
fof(f9645,plain,
( spl0_1206
<=> ! [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_1206])]) ).
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(f9643,plain,
spl0_1205,
inference(avatar_split_clause,[],[f2758,f9641]) ).
fof(f9641,plain,
( spl0_1205
<=> ! [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_1205])]) ).
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(f9639,plain,
spl0_1204,
inference(avatar_split_clause,[],[f2757,f9637]) ).
fof(f9637,plain,
( spl0_1204
<=> ! [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_1204])]) ).
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(f9635,plain,
spl0_1203,
inference(avatar_split_clause,[],[f2756,f9633]) ).
fof(f9633,plain,
( spl0_1203
<=> ! [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_1203])]) ).
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(f9631,plain,
spl0_1202,
inference(avatar_split_clause,[],[f2748,f9629]) ).
fof(f9629,plain,
( spl0_1202
<=> ! [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_1202])]) ).
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(f9627,plain,
spl0_1201,
inference(avatar_split_clause,[],[f2671,f9625]) ).
fof(f9625,plain,
( spl0_1201
<=> ! [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_1201])]) ).
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(f9623,plain,
spl0_1200,
inference(avatar_split_clause,[],[f2654,f9621]) ).
fof(f9621,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(f9619,plain,
spl0_1199,
inference(avatar_split_clause,[],[f2618,f9617]) ).
fof(f9617,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(f9615,plain,
spl0_1198,
inference(avatar_split_clause,[],[f2615,f9613]) ).
fof(f9613,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(f9611,plain,
spl0_1197,
inference(avatar_split_clause,[],[f2388,f9609]) ).
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(f9607,plain,
( spl0_1196
| ~ spl0_718
| ~ spl0_913
| ~ spl0_968 ),
inference(avatar_split_clause,[],[f8612,f8327,f8032,f7211,f9604]) ).
fof(f9604,plain,
( spl0_1196
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f8327,plain,
( spl0_968
<=> ! [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_968])]) ).
fof(f8612,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_718
| ~ spl0_913
| ~ spl0_968 ),
inference(forward_demodulation,[],[f8610,f7213]) ).
fof(f8610,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_913
| ~ spl0_968 ),
inference(superposition,[],[f8328,f8034]) ).
fof(f8328,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
| ~ spl0_968 ),
inference(avatar_component_clause,[],[f8327]) ).
fof(f9602,plain,
spl0_1195,
inference(avatar_split_clause,[],[f2383,f9600]) ).
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(f9598,plain,
spl0_1194,
inference(avatar_split_clause,[],[f2366,f9596]) ).
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(f9594,plain,
spl0_1193,
inference(avatar_split_clause,[],[f2364,f9592]) ).
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(f9590,plain,
spl0_1192,
inference(avatar_split_clause,[],[f2342,f9588]) ).
fof(f9588,plain,
( spl0_1192
<=> ! [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_1192])]) ).
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(f9586,plain,
spl0_1191,
inference(avatar_split_clause,[],[f2341,f9584]) ).
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(f9582,plain,
spl0_1190,
inference(avatar_split_clause,[],[f2294,f9580]) ).
fof(f9580,plain,
( spl0_1190
<=> ! [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_1190])]) ).
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(f9578,plain,
spl0_1189,
inference(avatar_split_clause,[],[f2281,f9576]) ).
fof(f9576,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(f9574,plain,
spl0_1188,
inference(avatar_split_clause,[],[f2247,f9572]) ).
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(f9570,plain,
spl0_1187,
inference(avatar_split_clause,[],[f2225,f9568]) ).
fof(f9568,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(f2225,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__equal__0__iff__equal_0) ).
fof(f9566,plain,
spl0_1186,
inference(avatar_split_clause,[],[f2213,f9564]) ).
fof(f9564,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(f9562,plain,
( spl0_1185
| ~ spl0_89
| ~ spl0_949 ),
inference(avatar_split_clause,[],[f8584,f8250,f3875,f9560]) ).
fof(f9560,plain,
( spl0_1185
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f3875,plain,
( spl0_89
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f8250,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(f8584,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_89
| ~ spl0_949 ),
inference(resolution,[],[f8251,f3877]) ).
fof(f3877,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f3875]) ).
fof(f8251,plain,
( ! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 )
| ~ spl0_949 ),
inference(avatar_component_clause,[],[f8250]) ).
fof(f9558,plain,
spl0_1184,
inference(avatar_split_clause,[],[f2211,f9556]) ).
fof(f9556,plain,
( spl0_1184
<=> ! [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_1184])]) ).
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(f9554,plain,
spl0_1183,
inference(avatar_split_clause,[],[f2197,f9552]) ).
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(f9550,plain,
spl0_1182,
inference(avatar_split_clause,[],[f2172,f9548]) ).
fof(f9548,plain,
( spl0_1182
<=> ! [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_1182])]) ).
fof(f2172,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__0__eq_0) ).
fof(f9546,plain,
spl0_1181,
inference(avatar_split_clause,[],[f2171,f9544]) ).
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(f9542,plain,
spl0_1180,
inference(avatar_split_clause,[],[f2039,f9540]) ).
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(f9538,plain,
spl0_1179,
inference(avatar_split_clause,[],[f2038,f9536]) ).
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(f9534,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1849,f9532]) ).
fof(f1849,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__number__of__0_2) ).
fof(f9530,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1832,f9528]) ).
fof(f9528,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(f9526,plain,
spl0_1176,
inference(avatar_split_clause,[],[f1803,f9524]) ).
fof(f9524,plain,
( spl0_1176
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f1803,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
fof(f9522,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1759,f9520]) ).
fof(f9520,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(f9518,plain,
( spl0_1174
| ~ spl0_31
| ~ spl0_949 ),
inference(avatar_split_clause,[],[f8583,f8250,f3585,f9516]) ).
fof(f9516,plain,
( spl0_1174
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f3585,plain,
( spl0_31
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f8583,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_31
| ~ spl0_949 ),
inference(resolution,[],[f8251,f3587]) ).
fof(f3587,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f3585]) ).
fof(f9514,plain,
spl0_1173,
inference(avatar_split_clause,[],[f1730,f9512]) ).
fof(f9512,plain,
( spl0_1173
<=> ! [X25,X1,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
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(f9510,plain,
spl0_1172,
inference(avatar_split_clause,[],[f1603,f9508]) ).
fof(f9508,plain,
( spl0_1172
<=> ! [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_1172])]) ).
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(f9506,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1548,f9504]) ).
fof(f9504,plain,
( spl0_1171
<=> ! [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_1171])]) ).
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(f9502,plain,
spl0_1170,
inference(avatar_split_clause,[],[f1541,f9500]) ).
fof(f9500,plain,
( spl0_1170
<=> ! [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_1170])]) ).
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(f9498,plain,
spl0_1169,
inference(avatar_split_clause,[],[f1540,f9496]) ).
fof(f9496,plain,
( spl0_1169
<=> ! [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_1169])]) ).
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(f9494,plain,
spl0_1168,
inference(avatar_split_clause,[],[f1509,f9492]) ).
fof(f9492,plain,
( spl0_1168
<=> ! [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_1168])]) ).
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(f9490,plain,
spl0_1167,
inference(avatar_split_clause,[],[f1488,f9488]) ).
fof(f9488,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(f9486,plain,
spl0_1166,
inference(avatar_split_clause,[],[f1487,f9484]) ).
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(f9481,plain,
spl0_1165,
inference(avatar_split_clause,[],[f1467,f9479]) ).
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(f9477,plain,
spl0_1164,
inference(avatar_split_clause,[],[f1440,f9475]) ).
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(f9473,plain,
( spl0_1163
| ~ spl0_96
| ~ spl0_948 ),
inference(avatar_split_clause,[],[f8581,f8246,f3910,f9471]) ).
fof(f9471,plain,
( spl0_1163
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f3910,plain,
( spl0_96
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f8246,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(f8581,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_96
| ~ spl0_948 ),
inference(resolution,[],[f8247,f3912]) ).
fof(f3912,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f3910]) ).
fof(f8247,plain,
( ! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 )
| ~ spl0_948 ),
inference(avatar_component_clause,[],[f8246]) ).
fof(f9469,plain,
spl0_1162,
inference(avatar_split_clause,[],[f1439,f9467]) ).
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(f9465,plain,
spl0_1161,
inference(avatar_split_clause,[],[f1430,f9463]) ).
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(f9461,plain,
spl0_1160,
inference(avatar_split_clause,[],[f1429,f9459]) ).
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(f9457,plain,
spl0_1159,
inference(avatar_split_clause,[],[f1428,f9455]) ).
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(f9453,plain,
spl0_1158,
inference(avatar_split_clause,[],[f1427,f9451]) ).
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(f9449,plain,
spl0_1157,
inference(avatar_split_clause,[],[f1426,f9447]) ).
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(f9445,plain,
spl0_1156,
inference(avatar_split_clause,[],[f1425,f9443]) ).
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(f9441,plain,
spl0_1155,
inference(avatar_split_clause,[],[f1407,f9439]) ).
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(f9437,plain,
spl0_1154,
inference(avatar_split_clause,[],[f1404,f9435]) ).
fof(f9435,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(f9433,plain,
spl0_1153,
inference(avatar_split_clause,[],[f1390,f9431]) ).
fof(f9431,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(f9428,plain,
spl0_1152,
inference(avatar_split_clause,[],[f1389,f9426]) ).
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(f9424,plain,
spl0_1151,
inference(avatar_split_clause,[],[f1279,f9422]) ).
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(f9420,plain,
spl0_1150,
inference(avatar_split_clause,[],[f1275,f9418]) ).
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(f9416,plain,
spl0_1149,
inference(avatar_split_clause,[],[f1265,f9414]) ).
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(f9412,plain,
spl0_1148,
inference(avatar_split_clause,[],[f1235,f9410]) ).
fof(f9410,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(f9408,plain,
spl0_1147,
inference(avatar_split_clause,[],[f1224,f9406]) ).
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(f9404,plain,
spl0_1146,
inference(avatar_split_clause,[],[f1216,f9402]) ).
fof(f9402,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(f9400,plain,
spl0_1145,
inference(avatar_split_clause,[],[f1200,f9398]) ).
fof(f9398,plain,
( spl0_1145
<=> ! [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_1145])]) ).
fof(f1200,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_OScons__not__Leaf_0) ).
fof(f9396,plain,
spl0_1144,
inference(avatar_split_clause,[],[f1199,f9394]) ).
fof(f9394,plain,
( spl0_1144
<=> ! [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_1144])]) ).
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(f9392,plain,
spl0_1143,
inference(avatar_split_clause,[],[f1196,f9390]) ).
fof(f9390,plain,
( spl0_1143
<=> ! [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_1143])]) ).
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(f9388,plain,
( spl0_1142
| ~ spl0_917
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9240,f8885,f8065,f9386]) ).
fof(f9386,plain,
( spl0_1142
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f8065,plain,
( spl0_917
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f9240,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_917
| ~ spl0_1072 ),
inference(resolution,[],[f8886,f8066]) ).
fof(f8066,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f8065]) ).
fof(f9384,plain,
spl0_1141,
inference(avatar_split_clause,[],[f1180,f9382]) ).
fof(f9382,plain,
( spl0_1141
<=> ! [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_1141])]) ).
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(f9380,plain,
spl0_1140,
inference(avatar_split_clause,[],[f1179,f9378]) ).
fof(f9378,plain,
( spl0_1140
<=> ! [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_1140])]) ).
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(f9376,plain,
spl0_1139,
inference(avatar_split_clause,[],[f1175,f9374]) ).
fof(f9374,plain,
( spl0_1139
<=> ! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
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(f9372,plain,
spl0_1138,
inference(avatar_split_clause,[],[f1170,f9370]) ).
fof(f9370,plain,
( spl0_1138
<=> ! [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_1138])]) ).
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(f9368,plain,
spl0_1137,
inference(avatar_split_clause,[],[f1169,f9366]) ).
fof(f9366,plain,
( spl0_1137
<=> ! [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_1137])]) ).
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(f9364,plain,
spl0_1136,
inference(avatar_split_clause,[],[f1168,f9362]) ).
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(f9360,plain,
spl0_1135,
inference(avatar_split_clause,[],[f105,f9358]) ).
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(f9356,plain,
spl0_1134,
inference(avatar_split_clause,[],[f103,f9354]) ).
fof(f9354,plain,
( spl0_1134
<=> ! [X13,X12,X1] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
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(f9352,plain,
spl0_1133,
inference(avatar_split_clause,[],[f102,f9350]) ).
fof(f9350,plain,
( spl0_1133
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
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(f9325,plain,
( ~ spl0_1132
| spl0_7
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f9307,f9015,f3465,f9322]) ).
fof(f9322,plain,
( spl0_1132
<=> c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f9015,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(f9307,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)
| spl0_7
| ~ spl0_1104 ),
inference(resolution,[],[f9016,f3467]) ).
fof(f9016,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,[],[f9015]) ).
fof(f9295,plain,
( spl0_1131
| ~ spl0_819
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f9279,f8959,f7642,f9293]) ).
fof(f9293,plain,
( spl0_1131
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f9279,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_819
| ~ spl0_1090 ),
inference(superposition,[],[f7643,f8960]) ).
fof(f9256,plain,
( spl0_1130
| ~ spl0_819
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9226,f8845,f7642,f9254]) ).
fof(f9254,plain,
( spl0_1130
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f9226,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_819
| ~ spl0_1062 ),
inference(superposition,[],[f7643,f8846]) ).
fof(f9223,plain,
( spl0_1129
| ~ spl0_32
| ~ spl0_948 ),
inference(avatar_split_clause,[],[f8580,f8246,f3590,f9221]) ).
fof(f9221,plain,
( spl0_1129
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f3590,plain,
( spl0_32
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f8580,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_32
| ~ spl0_948 ),
inference(resolution,[],[f8247,f3592]) ).
fof(f3592,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f3590]) ).
fof(f9164,plain,
( ~ spl0_81
| spl0_1128
| ~ spl0_685
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8579,f8238,f7061,f9162,f3835]) ).
fof(f3835,plain,
( spl0_81
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f7061,plain,
( spl0_685
<=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f8238,plain,
( spl0_946
<=> ! [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_946])]) ).
fof(f8579,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_685
| ~ spl0_946 ),
inference(superposition,[],[f8239,f7062]) ).
fof(f7062,plain,
( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
| ~ spl0_685 ),
inference(avatar_component_clause,[],[f7061]) ).
fof(f8239,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_946 ),
inference(avatar_component_clause,[],[f8238]) ).
fof(f9122,plain,
( spl0_1127
| ~ spl0_844
| ~ spl0_862 ),
inference(avatar_split_clause,[],[f8080,f7827,f7755,f9120]) ).
fof(f9120,plain,
( spl0_1127
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f8080,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_844
| ~ spl0_862 ),
inference(resolution,[],[f7828,f7756]) ).
fof(f9106,plain,
spl0_1126,
inference(avatar_split_clause,[],[f3332,f9104]) ).
fof(f3332,plain,
! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3147,f2982]) ).
fof(f3147,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(f9102,plain,
spl0_1125,
inference(avatar_split_clause,[],[f3325,f9100]) ).
fof(f3325,plain,
! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3134,f2982]) ).
fof(f3134,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(f9098,plain,
spl0_1124,
inference(avatar_split_clause,[],[f3317,f9096]) ).
fof(f9096,plain,
( spl0_1124
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f3317,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ),
inference(forward_demodulation,[],[f3123,f2982]) ).
fof(f3123,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,[],[f2063,f2544]) ).
fof(f2063,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_Omult__eq__1__iff_1) ).
fof(f9094,plain,
spl0_1123,
inference(avatar_split_clause,[],[f3315,f9092]) ).
fof(f9092,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,[],[f3121,f2982]) ).
fof(f3121,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(f9090,plain,
spl0_1122,
inference(avatar_split_clause,[],[f3029,f9088]) ).
fof(f9088,plain,
( spl0_1122
<=> ! [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_1122])]) ).
fof(f3029,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(f9086,plain,
spl0_1121,
inference(avatar_split_clause,[],[f3028,f9084]) ).
fof(f3028,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(f9082,plain,
( spl0_1120
| ~ spl0_843
| ~ spl0_862 ),
inference(avatar_split_clause,[],[f8079,f7827,f7751,f9080]) ).
fof(f9080,plain,
( spl0_1120
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f8079,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_843
| ~ spl0_862 ),
inference(resolution,[],[f7828,f7752]) ).
fof(f9078,plain,
spl0_1119,
inference(avatar_split_clause,[],[f3013,f9076]) ).
fof(f9076,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(f3013,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(f9074,plain,
spl0_1118,
inference(avatar_split_clause,[],[f3012,f9072]) ).
fof(f9072,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(f3012,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(f9070,plain,
spl0_1117,
inference(avatar_split_clause,[],[f3011,f9068]) ).
fof(f9068,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(f3011,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(f9066,plain,
spl0_1116,
inference(avatar_split_clause,[],[f3005,f9064]) ).
fof(f9064,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(f3005,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(f9062,plain,
spl0_1115,
inference(avatar_split_clause,[],[f2997,f9060]) ).
fof(f9060,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(f2997,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,f2837]) ).
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(f9058,plain,
spl0_1114,
inference(avatar_split_clause,[],[f2995,f9056]) ).
fof(f9056,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(f2995,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,f2837]) ).
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(f9054,plain,
spl0_1113,
inference(avatar_split_clause,[],[f2993,f9052]) ).
fof(f9052,plain,
( spl0_1113
<=> ! [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_1113])]) ).
fof(f2993,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,f2837]) ).
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(f9050,plain,
spl0_1112,
inference(avatar_split_clause,[],[f2991,f9048]) ).
fof(f9048,plain,
( spl0_1112
<=> ! [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_1112])]) ).
fof(f2991,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,f2837]) ).
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(f9046,plain,
spl0_1111,
inference(avatar_split_clause,[],[f2989,f9044]) ).
fof(f9044,plain,
( spl0_1111
<=> ! [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_1111])]) ).
fof(f2989,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,f2837]) ).
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(f9042,plain,
spl0_1110,
inference(avatar_split_clause,[],[f2932,f9040]) ).
fof(f9040,plain,
( spl0_1110
<=> ! [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_1110])]) ).
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(f9038,plain,
( spl0_1109
| ~ spl0_648
| ~ spl0_859 ),
inference(avatar_split_clause,[],[f8072,f7815,f6133,f9035]) ).
fof(f9035,plain,
( spl0_1109
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f7815,plain,
( spl0_859
<=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f8072,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_648
| ~ spl0_859 ),
inference(superposition,[],[f7816,f6135]) ).
fof(f7816,plain,
( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
| ~ spl0_859 ),
inference(avatar_component_clause,[],[f7815]) ).
fof(f9033,plain,
spl0_1108,
inference(avatar_split_clause,[],[f2931,f9031]) ).
fof(f9031,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(f9029,plain,
spl0_1107,
inference(avatar_split_clause,[],[f2930,f9027]) ).
fof(f9027,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(f9025,plain,
spl0_1106,
inference(avatar_split_clause,[],[f2916,f9023]) ).
fof(f9023,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(f9021,plain,
spl0_1105,
inference(avatar_split_clause,[],[f2886,f9019]) ).
fof(f9019,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(f9017,plain,
spl0_1104,
inference(avatar_split_clause,[],[f2847,f9015]) ).
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(f9013,plain,
spl0_1103,
inference(avatar_split_clause,[],[f2767,f9011]) ).
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(f9009,plain,
spl0_1102,
inference(avatar_split_clause,[],[f2750,f9007]) ).
fof(f9007,plain,
( spl0_1102
<=> ! [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_1102])]) ).
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(f9005,plain,
spl0_1101,
inference(avatar_split_clause,[],[f2749,f9003]) ).
fof(f9003,plain,
( spl0_1101
<=> ! [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_1101])]) ).
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(f9001,plain,
spl0_1100,
inference(avatar_split_clause,[],[f2747,f8999]) ).
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(f8997,plain,
spl0_1099,
inference(avatar_split_clause,[],[f2746,f8995]) ).
fof(f8995,plain,
( spl0_1099
<=> ! [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_1099])]) ).
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(f8993,plain,
spl0_1098,
inference(avatar_split_clause,[],[f2744,f8991]) ).
fof(f8991,plain,
( spl0_1098
<=> ! [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_1098])]) ).
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(f8989,plain,
spl0_1097,
inference(avatar_split_clause,[],[f2718,f8987]) ).
fof(f8987,plain,
( spl0_1097
<=> ! [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_1097])]) ).
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(f8985,plain,
spl0_1096,
inference(avatar_split_clause,[],[f2717,f8983]) ).
fof(f8983,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(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(f8981,plain,
spl0_1095,
inference(avatar_split_clause,[],[f2704,f8979]) ).
fof(f8979,plain,
( spl0_1095
<=> ! [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_1095])]) ).
fof(f2704,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_OInr__not__Inl_0) ).
fof(f8977,plain,
spl0_1094,
inference(avatar_split_clause,[],[f2667,f8975]) ).
fof(f8975,plain,
( spl0_1094
<=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
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(f8973,plain,
spl0_1093,
inference(avatar_split_clause,[],[f2659,f8971]) ).
fof(f8971,plain,
( spl0_1093
<=> ! [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_1093])]) ).
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(f8969,plain,
spl0_1092,
inference(avatar_split_clause,[],[f2636,f8967]) ).
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(f8965,plain,
spl0_1091,
inference(avatar_split_clause,[],[f2635,f8963]) ).
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(f8961,plain,
spl0_1090,
inference(avatar_split_clause,[],[f2626,f8959]) ).
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(f8957,plain,
spl0_1089,
inference(avatar_split_clause,[],[f2390,f8955]) ).
fof(f8955,plain,
( spl0_1089
<=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
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(f8953,plain,
( ~ spl0_59
| spl0_1088
| ~ spl0_877
| ~ spl0_986 ),
inference(avatar_split_clause,[],[f8621,f8399,f7887,f8950,f3725]) ).
fof(f8950,plain,
( spl0_1088
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f7887,plain,
( spl0_877
<=> ! [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_877])]) ).
fof(f8399,plain,
( spl0_986
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f8621,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_877
| ~ spl0_986 ),
inference(superposition,[],[f7888,f8401]) ).
fof(f8401,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_986 ),
inference(avatar_component_clause,[],[f8399]) ).
fof(f7888,plain,
( ! [X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_877 ),
inference(avatar_component_clause,[],[f7887]) ).
fof(f8948,plain,
spl0_1087,
inference(avatar_split_clause,[],[f2389,f8946]) ).
fof(f8946,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(f8944,plain,
spl0_1086,
inference(avatar_split_clause,[],[f2382,f8942]) ).
fof(f8942,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(f8940,plain,
spl0_1085,
inference(avatar_split_clause,[],[f2298,f8938]) ).
fof(f8938,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(f8936,plain,
spl0_1084,
inference(avatar_split_clause,[],[f2297,f8934]) ).
fof(f8934,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(f8932,plain,
spl0_1083,
inference(avatar_split_clause,[],[f2293,f8930]) ).
fof(f8930,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(f8928,plain,
spl0_1082,
inference(avatar_split_clause,[],[f2285,f8926]) ).
fof(f8926,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(f8924,plain,
spl0_1081,
inference(avatar_split_clause,[],[f2284,f8922]) ).
fof(f8922,plain,
( spl0_1081
<=> ! [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_1081])]) ).
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(f8920,plain,
spl0_1080,
inference(avatar_split_clause,[],[f2280,f8918]) ).
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(f8916,plain,
spl0_1079,
inference(avatar_split_clause,[],[f2216,f8914]) ).
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(f8912,plain,
spl0_1078,
inference(avatar_split_clause,[],[f2154,f8910]) ).
fof(f8907,plain,
spl0_1077,
inference(avatar_split_clause,[],[f2150,f8905]) ).
fof(f8905,plain,
( spl0_1077
<=> ! [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_1077])]) ).
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(f8903,plain,
spl0_1076,
inference(avatar_split_clause,[],[f2136,f8901]) ).
fof(f8901,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_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
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(f8899,plain,
spl0_1075,
inference(avatar_split_clause,[],[f2118,f8897]) ).
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(f8895,plain,
spl0_1074,
inference(avatar_split_clause,[],[f2032,f8893]) ).
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(f8891,plain,
spl0_1073,
inference(avatar_split_clause,[],[f2031,f8889]) ).
fof(f8889,plain,
( spl0_1073
<=> ! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
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(f8887,plain,
spl0_1072,
inference(avatar_split_clause,[],[f1786,f8885]) ).
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(f8883,plain,
spl0_1071,
inference(avatar_split_clause,[],[f1758,f8881]) ).
fof(f8881,plain,
( spl0_1071
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
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(f8879,plain,
spl0_1070,
inference(avatar_split_clause,[],[f1757,f8877]) ).
fof(f8877,plain,
( spl0_1070
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
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(f8875,plain,
spl0_1069,
inference(avatar_split_clause,[],[f1754,f8873]) ).
fof(f8873,plain,
( spl0_1069
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
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(f8871,plain,
spl0_1068,
inference(avatar_split_clause,[],[f1746,f8869]) ).
fof(f8869,plain,
( spl0_1068
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
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(f8867,plain,
( spl0_1067
| ~ spl0_741
| ~ spl0_1046 ),
inference(avatar_split_clause,[],[f8821,f8778,f7311,f8865]) ).
fof(f8865,plain,
( spl0_1067
<=> ! [X0] :
( v_KAB != X0
| v_KAB = c_Message_OinvKey(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f8778,plain,
( spl0_1046
<=> ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_KAB = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f8821,plain,
( ! [X0] :
( v_KAB != X0
| v_KAB = c_Message_OinvKey(X0) )
| ~ spl0_741
| ~ spl0_1046 ),
inference(superposition,[],[f8779,f7312]) ).
fof(f8779,plain,
( ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_KAB = X0 )
| ~ spl0_1046 ),
inference(avatar_component_clause,[],[f8778]) ).
fof(f8863,plain,
spl0_1066,
inference(avatar_split_clause,[],[f1744,f8861]) ).
fof(f8861,plain,
( spl0_1066
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
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(f8859,plain,
spl0_1065,
inference(avatar_split_clause,[],[f1740,f8857]) ).
fof(f8857,plain,
( spl0_1065
<=> ! [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_1065])]) ).
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(f8855,plain,
spl0_1064,
inference(avatar_split_clause,[],[f1720,f8853]) ).
fof(f8853,plain,
( spl0_1064
<=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
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(f8851,plain,
spl0_1063,
inference(avatar_split_clause,[],[f1692,f8849]) ).
fof(f8849,plain,
( spl0_1063
<=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
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(f8847,plain,
spl0_1062,
inference(avatar_split_clause,[],[f1639,f8845]) ).
fof(f8843,plain,
spl0_1061,
inference(avatar_split_clause,[],[f1607,f8841]) ).
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(f8839,plain,
spl0_1060,
inference(avatar_split_clause,[],[f1597,f8837]) ).
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(f8835,plain,
spl0_1059,
inference(avatar_split_clause,[],[f1565,f8833]) ).
fof(f8833,plain,
( spl0_1059
<=> ! [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_1059])]) ).
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(f8831,plain,
spl0_1058,
inference(avatar_split_clause,[],[f1564,f8829]) ).
fof(f8829,plain,
( spl0_1058
<=> ! [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_1058])]) ).
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(f8827,plain,
spl0_1057,
inference(avatar_split_clause,[],[f1563,f8825]) ).
fof(f8825,plain,
( spl0_1057
<=> ! [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_1057])]) ).
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(f8820,plain,
spl0_1056,
inference(avatar_split_clause,[],[f1560,f8818]) ).
fof(f8818,plain,
( spl0_1056
<=> ! [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_1056])]) ).
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(f8816,plain,
spl0_1055,
inference(avatar_split_clause,[],[f1559,f8814]) ).
fof(f8814,plain,
( spl0_1055
<=> ! [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_1055])]) ).
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(f8812,plain,
spl0_1054,
inference(avatar_split_clause,[],[f1556,f8810]) ).
fof(f8810,plain,
( spl0_1054
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
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(f8808,plain,
spl0_1053,
inference(avatar_split_clause,[],[f1555,f8806]) ).
fof(f8806,plain,
( spl0_1053
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
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(f8804,plain,
spl0_1052,
inference(avatar_split_clause,[],[f1553,f8802]) ).
fof(f8802,plain,
( spl0_1052
<=> ! [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_1052])]) ).
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(f8800,plain,
spl0_1051,
inference(avatar_split_clause,[],[f1528,f8798]) ).
fof(f8798,plain,
( spl0_1051
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
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(f8796,plain,
spl0_1050,
inference(avatar_split_clause,[],[f1527,f8794]) ).
fof(f8794,plain,
( spl0_1050
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f1527,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_Oappend__is__Nil__conv_0) ).
fof(f8792,plain,
spl0_1049,
inference(avatar_split_clause,[],[f1497,f8790]) ).
fof(f8790,plain,
( spl0_1049
<=> ! [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_1049])]) ).
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(f8788,plain,
spl0_1048,
inference(avatar_split_clause,[],[f1496,f8786]) ).
fof(f8786,plain,
( spl0_1048
<=> ! [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_1048])]) ).
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(f8784,plain,
spl0_1047,
inference(avatar_split_clause,[],[f1483,f8782]) ).
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(f8780,plain,
( spl0_1046
| ~ spl0_1004
| ~ spl0_1026 ),
inference(avatar_split_clause,[],[f8734,f8693,f8474,f8778]) ).
fof(f8734,plain,
( ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_KAB = X0 )
| ~ spl0_1004
| ~ spl0_1026 ),
inference(superposition,[],[f8475,f8695]) ).
fof(f8776,plain,
spl0_1045,
inference(avatar_split_clause,[],[f1471,f8774]) ).
fof(f8774,plain,
( spl0_1045
<=> ! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
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(f8772,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1441,f8770]) ).
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(f8768,plain,
spl0_1043,
inference(avatar_split_clause,[],[f1423,f8766]) ).
fof(f8766,plain,
( spl0_1043
<=> ! [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_1043])]) ).
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(f8764,plain,
spl0_1042,
inference(avatar_split_clause,[],[f1422,f8762]) ).
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(f8760,plain,
spl0_1041,
inference(avatar_split_clause,[],[f1421,f8758]) ).
fof(f8758,plain,
( spl0_1041
<=> ! [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_1041])]) ).
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(f8756,plain,
spl0_1040,
inference(avatar_split_clause,[],[f1420,f8754]) ).
fof(f8754,plain,
( spl0_1040
<=> ! [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_1040])]) ).
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(f8752,plain,
spl0_1039,
inference(avatar_split_clause,[],[f1380,f8750]) ).
fof(f8750,plain,
( spl0_1039
<=> ! [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_1039])]) ).
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(f8748,plain,
spl0_1038,
inference(avatar_split_clause,[],[f1379,f8746]) ).
fof(f8746,plain,
( spl0_1038
<=> ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
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(f8744,plain,
spl0_1037,
inference(avatar_split_clause,[],[f1349,f8742]) ).
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(f8740,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1244,f8738]) ).
fof(f8738,plain,
( spl0_1036
<=> ! [X5,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f1244,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__empty2_0) ).
fof(f8733,plain,
spl0_1035,
inference(avatar_split_clause,[],[f1242,f8731]) ).
fof(f8731,plain,
( spl0_1035
<=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
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(f8729,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1240,f8727]) ).
fof(f8727,plain,
( spl0_1034
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
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(f8725,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1238,f8723]) ).
fof(f8723,plain,
( spl0_1033
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
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(f8721,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1195,f8719]) ).
fof(f8719,plain,
( spl0_1032
<=> ! [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_1032])]) ).
fof(f1195,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_ONumb__not__Leaf_0) ).
fof(f8717,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1192,f8715]) ).
fof(f8715,plain,
( spl0_1031
<=> ! [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_1031])]) ).
fof(f1192,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_OIn1__not__In0_0) ).
fof(f8713,plain,
spl0_1030,
inference(avatar_split_clause,[],[f63,f8711]) ).
fof(f8711,plain,
( spl0_1030
<=> ! [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_1030])]) ).
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(f8709,plain,
spl0_1029,
inference(avatar_split_clause,[],[f62,f8707]) ).
fof(f8707,plain,
( spl0_1029
<=> ! [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_1029])]) ).
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(f8705,plain,
spl0_1028,
inference(avatar_split_clause,[],[f35,f8703]) ).
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(f8701,plain,
spl0_1027,
inference(avatar_split_clause,[],[f34,f8699]) ).
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(f8696,plain,
( spl0_1026
| ~ spl0_3
| ~ spl0_1013 ),
inference(avatar_split_clause,[],[f8688,f8511,f3445,f8693]) ).
fof(f8511,plain,
( spl0_1013
<=> ! [X3] :
( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f8688,plain,
( v_KAB = c_Message_OinvKey(v_KAB)
| ~ spl0_3
| ~ spl0_1013 ),
inference(resolution,[],[f8512,f3447]) ).
fof(f8512,plain,
( ! [X3] :
( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(X3) = X3 )
| ~ spl0_1013 ),
inference(avatar_component_clause,[],[f8511]) ).
fof(f8675,plain,
( ~ spl0_1025
| ~ spl0_819
| ~ spl0_1000 ),
inference(avatar_split_clause,[],[f8666,f8457,f7642,f8672]) ).
fof(f8672,plain,
( spl0_1025
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f8666,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_819
| ~ spl0_1000 ),
inference(superposition,[],[f7643,f8459]) ).
fof(f8558,plain,
spl0_1024,
inference(avatar_split_clause,[],[f3304,f8556]) ).
fof(f3304,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(f8554,plain,
spl0_1023,
inference(avatar_split_clause,[],[f3250,f8552]) ).
fof(f8552,plain,
( spl0_1023
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f3250,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f3033,f2982]) ).
fof(f3033,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(f8550,plain,
spl0_1022,
inference(avatar_split_clause,[],[f3249,f8548]) ).
fof(f3249,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f3032,f2982]) ).
fof(f3032,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(f8546,plain,
spl0_1021,
inference(avatar_split_clause,[],[f3017,f8544]) ).
fof(f3017,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(f8542,plain,
spl0_1020,
inference(avatar_split_clause,[],[f2988,f8540]) ).
fof(f8540,plain,
( spl0_1020
<=> ! [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_1020])]) ).
fof(f2988,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(f8538,plain,
spl0_1019,
inference(avatar_split_clause,[],[f2986,f8536]) ).
fof(f8536,plain,
( spl0_1019
<=> ! [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_1019])]) ).
fof(f2986,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(f8534,plain,
( spl0_1018
| ~ spl0_47
| ~ spl0_887 ),
inference(avatar_split_clause,[],[f8119,f7927,f3665,f8531]) ).
fof(f8531,plain,
( spl0_1018
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f7927,plain,
( spl0_887
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f8119,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_47
| ~ spl0_887 ),
inference(resolution,[],[f7928,f3667]) ).
fof(f3667,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f3665]) ).
fof(f7928,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) )
| ~ spl0_887 ),
inference(avatar_component_clause,[],[f7927]) ).
fof(f8529,plain,
spl0_1017,
inference(avatar_split_clause,[],[f2927,f8527]) ).
fof(f8527,plain,
( spl0_1017
<=> ! [X0,X3] :
( X0 = X3
| c_Public_OshrK(X0) != c_Public_OshrK(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
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(f8525,plain,
spl0_1016,
inference(avatar_split_clause,[],[f2925,f8523]) ).
fof(f8523,plain,
( spl0_1016
<=> ! [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_1016])]) ).
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(f8521,plain,
spl0_1015,
inference(avatar_split_clause,[],[f2922,f8519]) ).
fof(f8519,plain,
( spl0_1015
<=> ! [X4,X27,X12,X111] : c_Message_OinvKey(c_Public_OpublicKey(X27,X12)) != c_Public_OpublicKey(X4,X111) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f2922,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_OpublicKey__neq__privateKey_0) ).
fof(f8517,plain,
spl0_1014,
inference(avatar_split_clause,[],[f2921,f8515]) ).
fof(f8515,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(f8513,plain,
spl0_1013,
inference(avatar_split_clause,[],[f2899,f8511]) ).
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(f8509,plain,
spl0_1012,
inference(avatar_split_clause,[],[f2788,f8507]) ).
fof(f8507,plain,
( spl0_1012
<=> ! [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_1012])]) ).
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(f8505,plain,
spl0_1011,
inference(avatar_split_clause,[],[f2778,f8503]) ).
fof(f8503,plain,
( spl0_1011
<=> ! [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_1011])]) ).
fof(f2778,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__4_0) ).
fof(f8501,plain,
spl0_1010,
inference(avatar_split_clause,[],[f2775,f8499]) ).
fof(f8499,plain,
( spl0_1010
<=> ! [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_1010])]) ).
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(f8497,plain,
spl0_1009,
inference(avatar_split_clause,[],[f2755,f8495]) ).
fof(f8495,plain,
( spl0_1009
<=> ! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
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(f8493,plain,
spl0_1008,
inference(avatar_split_clause,[],[f2754,f8491]) ).
fof(f8491,plain,
( spl0_1008
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
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(f8488,plain,
spl0_1007,
inference(avatar_split_clause,[],[f2753,f8486]) ).
fof(f8486,plain,
( spl0_1007
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
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(f8484,plain,
spl0_1006,
inference(avatar_split_clause,[],[f2752,f8482]) ).
fof(f8482,plain,
( spl0_1006
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
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(f8480,plain,
spl0_1005,
inference(avatar_split_clause,[],[f2751,f8478]) ).
fof(f8478,plain,
( spl0_1005
<=> ! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
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(f8476,plain,
spl0_1004,
inference(avatar_split_clause,[],[f2741,f8474]) ).
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(f8472,plain,
spl0_1003,
inference(avatar_split_clause,[],[f2736,f8470]) ).
fof(f8470,plain,
( spl0_1003
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
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(f8468,plain,
spl0_1002,
inference(avatar_split_clause,[],[f2699,f8466]) ).
fof(f8466,plain,
( spl0_1002
<=> ! [X12,X1] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
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(f8464,plain,
spl0_1001,
inference(avatar_split_clause,[],[f2660,f8462]) ).
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(f8460,plain,
spl0_1000,
inference(avatar_split_clause,[],[f2534,f8457]) ).
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(f8455,plain,
spl0_999,
inference(avatar_split_clause,[],[f2492,f8453]) ).
fof(f8453,plain,
( spl0_999
<=> ! [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_999])]) ).
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(f8451,plain,
spl0_998,
inference(avatar_split_clause,[],[f2491,f8449]) ).
fof(f8449,plain,
( spl0_998
<=> ! [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_998])]) ).
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(f8447,plain,
( spl0_997
| ~ spl0_47
| ~ spl0_886 ),
inference(avatar_split_clause,[],[f8113,f7923,f3665,f8444]) ).
fof(f8444,plain,
( spl0_997
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f7923,plain,
( spl0_886
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f8113,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_47
| ~ spl0_886 ),
inference(resolution,[],[f7924,f3667]) ).
fof(f7924,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) )
| ~ spl0_886 ),
inference(avatar_component_clause,[],[f7923]) ).
fof(f8442,plain,
spl0_996,
inference(avatar_split_clause,[],[f2474,f8440]) ).
fof(f8440,plain,
( spl0_996
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
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(f8438,plain,
spl0_995,
inference(avatar_split_clause,[],[f2473,f8436]) ).
fof(f8436,plain,
( spl0_995
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
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(f8434,plain,
spl0_994,
inference(avatar_split_clause,[],[f2470,f8432]) ).
fof(f8432,plain,
( spl0_994
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
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(f8430,plain,
spl0_993,
inference(avatar_split_clause,[],[f2469,f8428]) ).
fof(f8428,plain,
( spl0_993
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
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(f8426,plain,
spl0_992,
inference(avatar_split_clause,[],[f2379,f8424]) ).
fof(f8424,plain,
( spl0_992
<=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
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(f8422,plain,
spl0_991,
inference(avatar_split_clause,[],[f2377,f8420]) ).
fof(f8420,plain,
( spl0_991
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
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(f8418,plain,
spl0_990,
inference(avatar_split_clause,[],[f2371,f8416]) ).
fof(f8416,plain,
( spl0_990
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
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(f8414,plain,
spl0_989,
inference(avatar_split_clause,[],[f2369,f8412]) ).
fof(f8412,plain,
( spl0_989
<=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
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(f8410,plain,
spl0_988,
inference(avatar_split_clause,[],[f2357,f8408]) ).
fof(f8408,plain,
( spl0_988
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
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(f8406,plain,
spl0_987,
inference(avatar_split_clause,[],[f2354,f8404]) ).
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(f8402,plain,
( spl0_986
| ~ spl0_59
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f8110,f7911,f3725,f8399]) ).
fof(f7911,plain,
( spl0_883
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f8110,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_883 ),
inference(resolution,[],[f7912,f3727]) ).
fof(f7912,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f7911]) ).
fof(f8397,plain,
spl0_985,
inference(avatar_split_clause,[],[f2353,f8395]) ).
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(f8393,plain,
spl0_984,
inference(avatar_split_clause,[],[f2292,f8391]) ).
fof(f8391,plain,
( spl0_984
<=> ! [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_984])]) ).
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(f8389,plain,
spl0_983,
inference(avatar_split_clause,[],[f2291,f8387]) ).
fof(f8387,plain,
( spl0_983
<=> ! [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_983])]) ).
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(f8385,plain,
spl0_982,
inference(avatar_split_clause,[],[f2267,f8383]) ).
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(f8381,plain,
spl0_981,
inference(avatar_split_clause,[],[f2262,f8379]) ).
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(f8377,plain,
spl0_980,
inference(avatar_split_clause,[],[f2251,f8375]) ).
fof(f8375,plain,
( spl0_980
<=> ! [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_980])]) ).
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(f8373,plain,
spl0_979,
inference(avatar_split_clause,[],[f2250,f8371]) ).
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(f8369,plain,
spl0_978,
inference(avatar_split_clause,[],[f2241,f8367]) ).
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(f8365,plain,
spl0_977,
inference(avatar_split_clause,[],[f2218,f8363]) ).
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(f8361,plain,
spl0_976,
inference(avatar_split_clause,[],[f2217,f8359]) ).
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(f8357,plain,
spl0_975,
inference(avatar_split_clause,[],[f2205,f8355]) ).
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(f8353,plain,
spl0_974,
inference(avatar_split_clause,[],[f2198,f8351]) ).
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(f8349,plain,
spl0_973,
inference(avatar_split_clause,[],[f2196,f8347]) ).
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(f8345,plain,
spl0_972,
inference(avatar_split_clause,[],[f2185,f8343]) ).
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(f8341,plain,
spl0_971,
inference(avatar_split_clause,[],[f2182,f8339]) ).
fof(f8339,plain,
( spl0_971
<=> ! [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_971])]) ).
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(f8337,plain,
spl0_970,
inference(avatar_split_clause,[],[f2180,f8335]) ).
fof(f8335,plain,
( spl0_970
<=> ! [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_970])]) ).
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(f8333,plain,
spl0_969,
inference(avatar_split_clause,[],[f2177,f8331]) ).
fof(f8331,plain,
( spl0_969
<=> ! [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_969])]) ).
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(f8329,plain,
spl0_968,
inference(avatar_split_clause,[],[f2153,f8327]) ).
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(f8325,plain,
spl0_967,
inference(avatar_split_clause,[],[f1865,f8323]) ).
fof(f8323,plain,
( spl0_967
<=> ! [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_967])]) ).
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(f8321,plain,
spl0_966,
inference(avatar_split_clause,[],[f1818,f8319]) ).
fof(f8319,plain,
( spl0_966
<=> ! [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_966])]) ).
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(f8317,plain,
spl0_965,
inference(avatar_split_clause,[],[f1815,f8315]) ).
fof(f8315,plain,
( spl0_965
<=> ! [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_965])]) ).
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(f8313,plain,
spl0_964,
inference(avatar_split_clause,[],[f1805,f8311]) ).
fof(f8311,plain,
( spl0_964
<=> ! [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_964])]) ).
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(f8309,plain,
spl0_963,
inference(avatar_split_clause,[],[f1779,f8307]) ).
fof(f8307,plain,
( spl0_963
<=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
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(f8305,plain,
spl0_962,
inference(avatar_split_clause,[],[f1752,f8303]) ).
fof(f8303,plain,
( spl0_962
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f1752,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__empty_0) ).
fof(f8301,plain,
spl0_961,
inference(avatar_split_clause,[],[f1735,f8299]) ).
fof(f8299,plain,
( spl0_961
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
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(f8297,plain,
spl0_960,
inference(avatar_split_clause,[],[f1717,f8295]) ).
fof(f8295,plain,
( spl0_960
<=> ! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1717,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__right__iff_0) ).
fof(f8293,plain,
spl0_959,
inference(avatar_split_clause,[],[f1588,f8291]) ).
fof(f8291,plain,
( spl0_959
<=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
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(f8289,plain,
spl0_958,
inference(avatar_split_clause,[],[f1579,f8287]) ).
fof(f8287,plain,
( spl0_958
<=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
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(f8285,plain,
spl0_957,
inference(avatar_split_clause,[],[f1562,f8283]) ).
fof(f8283,plain,
( spl0_957
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
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(f8281,plain,
spl0_956,
inference(avatar_split_clause,[],[f1561,f8279]) ).
fof(f8279,plain,
( spl0_956
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
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(f8277,plain,
( ~ spl0_954
| spl0_955
| ~ spl0_717
| ~ spl0_877 ),
inference(avatar_split_clause,[],[f8109,f7887,f7206,f8274,f8270]) ).
fof(f8270,plain,
( spl0_954
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f8274,plain,
( spl0_955
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f8109,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_717
| ~ spl0_877 ),
inference(superposition,[],[f7888,f7208]) ).
fof(f8268,plain,
spl0_953,
inference(avatar_split_clause,[],[f1550,f8266]) ).
fof(f8266,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(f8264,plain,
spl0_952,
inference(avatar_split_clause,[],[f1549,f8262]) ).
fof(f8262,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(f8260,plain,
spl0_951,
inference(avatar_split_clause,[],[f1537,f8258]) ).
fof(f8258,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(f8256,plain,
spl0_950,
inference(avatar_split_clause,[],[f1513,f8254]) ).
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(f8252,plain,
spl0_949,
inference(avatar_split_clause,[],[f1499,f8250]) ).
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(f8248,plain,
spl0_948,
inference(avatar_split_clause,[],[f1498,f8246]) ).
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(f8244,plain,
spl0_947,
inference(avatar_split_clause,[],[f1490,f8242]) ).
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(f8240,plain,
spl0_946,
inference(avatar_split_clause,[],[f1419,f8238]) ).
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(f8236,plain,
spl0_945,
inference(avatar_split_clause,[],[f1392,f8234]) ).
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(f8232,plain,
spl0_944,
inference(avatar_split_clause,[],[f1385,f8230]) ).
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(f8228,plain,
spl0_943,
inference(avatar_split_clause,[],[f1376,f8226]) ).
fof(f8226,plain,
( spl0_943
<=> ! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
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(f8224,plain,
spl0_942,
inference(avatar_split_clause,[],[f1375,f8222]) ).
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(f8220,plain,
spl0_941,
inference(avatar_split_clause,[],[f1308,f8218]) ).
fof(f8218,plain,
( spl0_941
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
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(f8216,plain,
spl0_940,
inference(avatar_split_clause,[],[f1298,f8214]) ).
fof(f8214,plain,
( spl0_940
<=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
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(f8212,plain,
spl0_939,
inference(avatar_split_clause,[],[f1297,f8210]) ).
fof(f8210,plain,
( spl0_939
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
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(f8208,plain,
spl0_938,
inference(avatar_split_clause,[],[f1177,f8206]) ).
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(f8204,plain,
spl0_937,
inference(avatar_split_clause,[],[f1171,f8202]) ).
fof(f8202,plain,
( spl0_937
<=> ! [X1,X40] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
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(f8199,plain,
spl0_936,
inference(avatar_split_clause,[],[f1167,f8197]) ).
fof(f8197,plain,
( spl0_936
<=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
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(f8195,plain,
spl0_935,
inference(avatar_split_clause,[],[f252,f8193]) ).
fof(f8193,plain,
( spl0_935
<=> ! [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_935])]) ).
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(f8191,plain,
spl0_934,
inference(avatar_split_clause,[],[f246,f8189]) ).
fof(f8189,plain,
( spl0_934
<=> ! [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_934])]) ).
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(f8187,plain,
( spl0_933
| ~ spl0_55
| ~ spl0_870 ),
inference(avatar_split_clause,[],[f8084,f7859,f3705,f8184]) ).
fof(f8184,plain,
( spl0_933
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f3705,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f7859,plain,
( spl0_870
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f8084,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_55
| ~ spl0_870 ),
inference(resolution,[],[f7860,f3707]) ).
fof(f3707,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f3705]) ).
fof(f7860,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) )
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f7859]) ).
fof(f8182,plain,
spl0_932,
inference(avatar_split_clause,[],[f196,f8180]) ).
fof(f8180,plain,
( spl0_932
<=> ! [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_932])]) ).
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(f8178,plain,
spl0_931,
inference(avatar_split_clause,[],[f94,f8176]) ).
fof(f8176,plain,
( spl0_931
<=> ! [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_931])]) ).
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(f8174,plain,
spl0_930,
inference(avatar_split_clause,[],[f93,f8172]) ).
fof(f8172,plain,
( spl0_930
<=> ! [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_930])]) ).
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(f8170,plain,
spl0_929,
inference(avatar_split_clause,[],[f92,f8168]) ).
fof(f8168,plain,
( spl0_929
<=> ! [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_929])]) ).
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(f8166,plain,
spl0_928,
inference(avatar_split_clause,[],[f91,f8164]) ).
fof(f8164,plain,
( spl0_928
<=> ! [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_928])]) ).
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(f8162,plain,
spl0_927,
inference(avatar_split_clause,[],[f89,f8160]) ).
fof(f8160,plain,
( spl0_927
<=> ! [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_927])]) ).
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(f8158,plain,
spl0_926,
inference(avatar_split_clause,[],[f88,f8156]) ).
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(f8154,plain,
spl0_925,
inference(avatar_split_clause,[],[f87,f8152]) ).
fof(f8152,plain,
( spl0_925
<=> ! [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_925])]) ).
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(f8150,plain,
spl0_924,
inference(avatar_split_clause,[],[f86,f8148]) ).
fof(f8148,plain,
( spl0_924
<=> ! [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_924])]) ).
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(f8146,plain,
spl0_923,
inference(avatar_split_clause,[],[f37,f8144]) ).
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(f8142,plain,
( spl0_922
| ~ spl0_28
| ~ spl0_869 ),
inference(avatar_split_clause,[],[f8082,f7855,f3570,f8139]) ).
fof(f8139,plain,
( spl0_922
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f3570,plain,
( spl0_28
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f7855,plain,
( spl0_869
<=> ! [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_869])]) ).
fof(f8082,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_28
| ~ spl0_869 ),
inference(resolution,[],[f7856,f3572]) ).
fof(f3572,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3570]) ).
fof(f7856,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) )
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f7855]) ).
fof(f8132,plain,
( spl0_921
| ~ spl0_29
| ~ spl0_861 ),
inference(avatar_split_clause,[],[f8076,f7823,f3575,f8129]) ).
fof(f8129,plain,
( spl0_921
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f7823,plain,
( spl0_861
<=> ! [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_861])]) ).
fof(f8076,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_29
| ~ spl0_861 ),
inference(resolution,[],[f7824,f3577]) ).
fof(f7824,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) )
| ~ spl0_861 ),
inference(avatar_component_clause,[],[f7823]) ).
fof(f8127,plain,
( spl0_920
| ~ spl0_57
| ~ spl0_860 ),
inference(avatar_split_clause,[],[f8075,f7819,f3715,f8124]) ).
fof(f8124,plain,
( spl0_920
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f7819,plain,
( spl0_860
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f8075,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_860 ),
inference(resolution,[],[f7820,f3717]) ).
fof(f7820,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) )
| ~ spl0_860 ),
inference(avatar_component_clause,[],[f7819]) ).
fof(f8118,plain,
( spl0_919
| ~ spl0_649
| ~ spl0_857 ),
inference(avatar_split_clause,[],[f8069,f7807,f6138,f8115]) ).
fof(f8069,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_857 ),
inference(superposition,[],[f7808,f6140]) ).
fof(f8108,plain,
( spl0_918
| ~ spl0_648
| ~ spl0_857 ),
inference(avatar_split_clause,[],[f8068,f7807,f6133,f8105]) ).
fof(f8105,plain,
( spl0_918
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f8068,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_857 ),
inference(superposition,[],[f7808,f6135]) ).
fof(f8067,plain,
( spl0_917
| ~ spl0_840
| ~ spl0_851 ),
inference(avatar_split_clause,[],[f8058,f7783,f7729,f8065]) ).
fof(f7729,plain,
( spl0_840
<=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f8058,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_840
| ~ spl0_851 ),
inference(superposition,[],[f7784,f7730]) ).
fof(f7730,plain,
( ! [X3] : c_div(X3,c_1,tc_nat) = X3
| ~ spl0_840 ),
inference(avatar_component_clause,[],[f7729]) ).
fof(f8047,plain,
spl0_916,
inference(avatar_split_clause,[],[f3329,f8045]) ).
fof(f8045,plain,
( spl0_916
<=> ! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f3329,plain,
! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f3328,f2982]) ).
fof(f3328,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,[],[f3141,f2982]) ).
fof(f3141,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(f8043,plain,
spl0_915,
inference(avatar_split_clause,[],[f3237,f8041]) ).
fof(f8041,plain,
( spl0_915
<=> ! [X13,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f3237,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1),
inference(forward_demodulation,[],[f3004,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(f3004,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(f8039,plain,
spl0_914,
inference(avatar_split_clause,[],[f3008,f8037]) ).
fof(f8035,plain,
spl0_913,
inference(avatar_split_clause,[],[f3006,f8032]) ).
fof(f3006,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(f8030,plain,
spl0_912,
inference(avatar_split_clause,[],[f3002,f8028]) ).
fof(f8028,plain,
( spl0_912
<=> ! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(X32,c_List_Olist_ONil))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f3002,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(f8026,plain,
spl0_911,
inference(avatar_split_clause,[],[f2982,f8023]) ).
fof(f8023,plain,
( spl0_911
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f8021,plain,
spl0_910,
inference(avatar_split_clause,[],[f2978,f8019]) ).
fof(f8019,plain,
( spl0_910
<=> ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f2978,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(f8017,plain,
spl0_909,
inference(avatar_split_clause,[],[f2928,f8015]) ).
fof(f8015,plain,
( spl0_909
<=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Message_OinvKey(c_Public_OpublicKey(X27,X32)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
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(f8013,plain,
spl0_908,
inference(avatar_split_clause,[],[f2926,f8011]) ).
fof(f8011,plain,
( spl0_908
<=> ! [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_908])]) ).
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(f8009,plain,
spl0_907,
inference(avatar_split_clause,[],[f2910,f8007]) ).
fof(f8007,plain,
( spl0_907
<=> ! [X27,X12] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X27,X12)),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
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(f8005,plain,
spl0_906,
inference(avatar_split_clause,[],[f2906,f8003]) ).
fof(f8003,plain,
( spl0_906
<=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__rec(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
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(f8001,plain,
spl0_905,
inference(avatar_split_clause,[],[f2905,f7999]) ).
fof(f7999,plain,
( spl0_905
<=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__rec(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
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(f7997,plain,
spl0_904,
inference(avatar_split_clause,[],[f2902,f7995]) ).
fof(f7995,plain,
( spl0_904
<=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__case(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
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(f7993,plain,
spl0_903,
inference(avatar_split_clause,[],[f2901,f7991]) ).
fof(f7991,plain,
( spl0_903
<=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__case(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
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(f7989,plain,
spl0_902,
inference(avatar_split_clause,[],[f2891,f7987]) ).
fof(f7987,plain,
( spl0_902
<=> ! [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_902])]) ).
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(f7985,plain,
spl0_901,
inference(avatar_split_clause,[],[f2790,f7983]) ).
fof(f7983,plain,
( spl0_901
<=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_ONotes(X94,X96),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
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(f7981,plain,
spl0_900,
inference(avatar_split_clause,[],[f2789,f7979]) ).
fof(f7979,plain,
( spl0_900
<=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_OGets(X94,X96),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
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(f7977,plain,
spl0_899,
inference(avatar_split_clause,[],[f2780,f7975]) ).
fof(f7975,plain,
( spl0_899
<=> ! [X96,X97,X94,X95] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2780,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__6_0) ).
fof(f7973,plain,
spl0_898,
inference(avatar_split_clause,[],[f2705,f7971]) ).
fof(f7971,plain,
( spl0_898
<=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
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(f7969,plain,
spl0_897,
inference(avatar_split_clause,[],[f2684,f7967]) ).
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(f7965,plain,
spl0_896,
inference(avatar_split_clause,[],[f2668,f7963]) ).
fof(f7963,plain,
( spl0_896
<=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
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(f7961,plain,
spl0_895,
inference(avatar_split_clause,[],[f2648,f7959]) ).
fof(f7959,plain,
( spl0_895
<=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
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(f7957,plain,
spl0_894,
inference(avatar_split_clause,[],[f2590,f7955]) ).
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(f7953,plain,
spl0_893,
inference(avatar_split_clause,[],[f2588,f7951]) ).
fof(f7951,plain,
( spl0_893
<=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
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(f7949,plain,
spl0_892,
inference(avatar_split_clause,[],[f2587,f7947]) ).
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(f7945,plain,
spl0_891,
inference(avatar_split_clause,[],[f2549,f7943]) ).
fof(f7943,plain,
( spl0_891
<=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
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(f7941,plain,
spl0_890,
inference(avatar_split_clause,[],[f2394,f7939]) ).
fof(f7939,plain,
( spl0_890
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
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(f7937,plain,
spl0_889,
inference(avatar_split_clause,[],[f2374,f7935]) ).
fof(f7935,plain,
( spl0_889
<=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
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(f7933,plain,
spl0_888,
inference(avatar_split_clause,[],[f2372,f7931]) ).
fof(f7931,plain,
( spl0_888
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
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(f7929,plain,
spl0_887,
inference(avatar_split_clause,[],[f2243,f7927]) ).
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(f7925,plain,
spl0_886,
inference(avatar_split_clause,[],[f2238,f7923]) ).
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(f7921,plain,
spl0_885,
inference(avatar_split_clause,[],[f2220,f7919]) ).
fof(f7919,plain,
( spl0_885
<=> ! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
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(f7917,plain,
spl0_884,
inference(avatar_split_clause,[],[f2176,f7915]) ).
fof(f7915,plain,
( spl0_884
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f2176,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__eq__0_1) ).
fof(f7913,plain,
spl0_883,
inference(avatar_split_clause,[],[f2169,f7911]) ).
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(f7909,plain,
spl0_882,
inference(avatar_split_clause,[],[f2162,f7907]) ).
fof(f7907,plain,
( spl0_882
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
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(f7905,plain,
spl0_881,
inference(avatar_split_clause,[],[f2161,f7903]) ).
fof(f7903,plain,
( spl0_881
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
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(f7901,plain,
spl0_880,
inference(avatar_split_clause,[],[f2158,f7899]) ).
fof(f7899,plain,
( spl0_880
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
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(f7897,plain,
spl0_879,
inference(avatar_split_clause,[],[f2157,f7895]) ).
fof(f7895,plain,
( spl0_879
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
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(f7893,plain,
spl0_878,
inference(avatar_split_clause,[],[f2144,f7891]) ).
fof(f7891,plain,
( spl0_878
<=> ! [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_878])]) ).
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(f7889,plain,
spl0_877,
inference(avatar_split_clause,[],[f2143,f7887]) ).
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(f7885,plain,
spl0_876,
inference(avatar_split_clause,[],[f2089,f7883]) ).
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(f7881,plain,
spl0_875,
inference(avatar_split_clause,[],[f2088,f7879]) ).
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(f7877,plain,
spl0_874,
inference(avatar_split_clause,[],[f2087,f7875]) ).
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(f7873,plain,
spl0_873,
inference(avatar_split_clause,[],[f2048,f7871]) ).
fof(f7871,plain,
( spl0_873
<=> ! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
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(f7869,plain,
spl0_872,
inference(avatar_split_clause,[],[f2042,f7867]) ).
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(f7865,plain,
spl0_871,
inference(avatar_split_clause,[],[f2040,f7863]) ).
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(f7861,plain,
spl0_870,
inference(avatar_split_clause,[],[f1812,f7859]) ).
fof(f1812,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__eq__0__iff_1) ).
fof(f7857,plain,
spl0_869,
inference(avatar_split_clause,[],[f1808,f7855]) ).
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(f7853,plain,
spl0_868,
inference(avatar_split_clause,[],[f1790,f7851]) ).
fof(f7851,plain,
( spl0_868
<=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
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(f7849,plain,
spl0_867,
inference(avatar_split_clause,[],[f1788,f7847]) ).
fof(f7847,plain,
( spl0_867
<=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
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(f7845,plain,
spl0_866,
inference(avatar_split_clause,[],[f1732,f7843]) ).
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(f7841,plain,
spl0_865,
inference(avatar_split_clause,[],[f1711,f7839]) ).
fof(f7839,plain,
( spl0_865
<=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
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(f7837,plain,
spl0_864,
inference(avatar_split_clause,[],[f1631,f7835]) ).
fof(f7835,plain,
( spl0_864
<=> ! [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_864])]) ).
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(f7833,plain,
spl0_863,
inference(avatar_split_clause,[],[f1542,f7831]) ).
fof(f7831,plain,
( spl0_863
<=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
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(f7829,plain,
spl0_862,
inference(avatar_split_clause,[],[f1478,f7827]) ).
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(f7825,plain,
spl0_861,
inference(avatar_split_clause,[],[f1401,f7823]) ).
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(f7821,plain,
spl0_860,
inference(avatar_split_clause,[],[f1396,f7819]) ).
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(f7817,plain,
spl0_859,
inference(avatar_split_clause,[],[f1387,f7815]) ).
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(f7813,plain,
spl0_858,
inference(avatar_split_clause,[],[f1373,f7811]) ).
fof(f7811,plain,
( spl0_858
<=> ! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
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(f7809,plain,
spl0_857,
inference(avatar_split_clause,[],[f1367,f7807]) ).
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(f7805,plain,
spl0_856,
inference(avatar_split_clause,[],[f1253,f7803]) ).
fof(f7803,plain,
( spl0_856
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
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(f7801,plain,
spl0_855,
inference(avatar_split_clause,[],[f1252,f7799]) ).
fof(f7799,plain,
( spl0_855
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
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(f7797,plain,
spl0_854,
inference(avatar_split_clause,[],[f1249,f7795]) ).
fof(f7795,plain,
( spl0_854
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
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(f7793,plain,
spl0_853,
inference(avatar_split_clause,[],[f1248,f7791]) ).
fof(f7791,plain,
( spl0_853
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
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(f7789,plain,
spl0_852,
inference(avatar_split_clause,[],[f1225,f7787]) ).
fof(f7787,plain,
( spl0_852
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
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(f7785,plain,
spl0_851,
inference(avatar_split_clause,[],[f1215,f7783]) ).
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(f7781,plain,
spl0_850,
inference(avatar_split_clause,[],[f1202,f7779]) ).
fof(f7779,plain,
( spl0_850
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
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(f7777,plain,
spl0_849,
inference(avatar_split_clause,[],[f1181,f7775]) ).
fof(f7775,plain,
( spl0_849
<=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
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(f7773,plain,
spl0_848,
inference(avatar_split_clause,[],[f95,f7771]) ).
fof(f7771,plain,
( spl0_848
<=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
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(f7769,plain,
spl0_847,
inference(avatar_split_clause,[],[f90,f7767]) ).
fof(f7767,plain,
( spl0_847
<=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
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(f7765,plain,
spl0_846,
inference(avatar_split_clause,[],[f61,f7763]) ).
fof(f7763,plain,
( spl0_846
<=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
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(f7761,plain,
spl0_845,
inference(avatar_split_clause,[],[f45,f7759]) ).
fof(f7759,plain,
( spl0_845
<=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
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(f7757,plain,
spl0_844,
inference(avatar_split_clause,[],[f42,f7755]) ).
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(f7753,plain,
spl0_843,
inference(avatar_split_clause,[],[f41,f7751]) ).
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(f7749,plain,
spl0_842,
inference(avatar_split_clause,[],[f26,f7747]) ).
fof(f7747,plain,
( spl0_842
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
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(f7745,plain,
spl0_841,
inference(avatar_split_clause,[],[f25,f7743]) ).
fof(f7743,plain,
( spl0_841
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
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(f7731,plain,
spl0_840,
inference(avatar_split_clause,[],[f3247,f7729]) ).
fof(f3247,plain,
! [X3] : c_div(X3,c_1,tc_nat) = X3,
inference(forward_demodulation,[],[f3022,f2982]) ).
fof(f3022,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(f7727,plain,
spl0_839,
inference(avatar_split_clause,[],[f3245,f7724]) ).
fof(f7724,plain,
( spl0_839
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f3245,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f3019,f2982]) ).
fof(f3019,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,[],[f2094,f2544]) ).
fof(f2094,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
fof(f7722,plain,
spl0_838,
inference(avatar_split_clause,[],[f3243,f7720]) ).
fof(f3243,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat),
inference(forward_demodulation,[],[f3018,f2982]) ).
fof(f3018,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(f7718,plain,
spl0_837,
inference(avatar_split_clause,[],[f3242,f7715]) ).
fof(f3242,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(f7713,plain,
spl0_836,
inference(avatar_split_clause,[],[f3240,f7711]) ).
fof(f3240,plain,
! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3,
inference(forward_demodulation,[],[f3010,f1729]) ).
fof(f1729,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
fof(f3010,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(f7709,plain,
spl0_835,
inference(avatar_split_clause,[],[f3238,f7706]) ).
fof(f3238,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f3007,f2156]) ).
fof(f3007,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(f7704,plain,
spl0_834,
inference(avatar_split_clause,[],[f2929,f7702]) ).
fof(f7702,plain,
( spl0_834
<=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Public_OpublicKey(X27,X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
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(f7700,plain,
spl0_833,
inference(avatar_split_clause,[],[f2911,f7698]) ).
fof(f7698,plain,
( spl0_833
<=> ! [X27,X12] : ~ c_in(c_Public_OpublicKey(X27,X12),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
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(f7696,plain,
spl0_832,
inference(avatar_split_clause,[],[f2900,f7694]) ).
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(f7692,plain,
spl0_831,
inference(avatar_split_clause,[],[f2895,f7690]) ).
fof(f7690,plain,
( spl0_831
<=> ! [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_831])]) ).
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(f7688,plain,
spl0_830,
inference(avatar_split_clause,[],[f2871,f7686]) ).
fof(f7686,plain,
( spl0_830
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
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(f7684,plain,
spl0_829,
inference(avatar_split_clause,[],[f2869,f7682]) ).
fof(f7682,plain,
( spl0_829
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
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(f7680,plain,
spl0_828,
inference(avatar_split_clause,[],[f2862,f7678]) ).
fof(f7678,plain,
( spl0_828
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
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(f7676,plain,
spl0_827,
inference(avatar_split_clause,[],[f2854,f7674]) ).
fof(f7674,plain,
( spl0_827
<=> ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
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(f7672,plain,
spl0_826,
inference(avatar_split_clause,[],[f2845,f7670]) ).
fof(f7670,plain,
( spl0_826
<=> ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
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(f7668,plain,
spl0_825,
inference(avatar_split_clause,[],[f2803,f7666]) ).
fof(f7666,plain,
( spl0_825
<=> ! [X12,X88] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
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(f7664,plain,
spl0_824,
inference(avatar_split_clause,[],[f2763,f7662]) ).
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(f7660,plain,
spl0_823,
inference(avatar_split_clause,[],[f2762,f7658]) ).
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(f7656,plain,
spl0_822,
inference(avatar_split_clause,[],[f2761,f7654]) ).
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(f7652,plain,
spl0_821,
inference(avatar_split_clause,[],[f2760,f7650]) ).
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(f7648,plain,
spl0_820,
inference(avatar_split_clause,[],[f2738,f7646]) ).
fof(f7646,plain,
( spl0_820
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
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(f7644,plain,
spl0_819,
inference(avatar_split_clause,[],[f2687,f7642]) ).
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(f7640,plain,
spl0_818,
inference(avatar_split_clause,[],[f2639,f7638]) ).
fof(f7638,plain,
( spl0_818
<=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
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(f7636,plain,
spl0_817,
inference(avatar_split_clause,[],[f2638,f7634]) ).
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(f7632,plain,
spl0_816,
inference(avatar_split_clause,[],[f2634,f7630]) ).
fof(f2634,axiom,
! [X3,X1] : c_union(X3,X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7628,plain,
spl0_815,
inference(avatar_split_clause,[],[f2633,f7626]) ).
fof(f7626,plain,
( spl0_815
<=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
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(f7624,plain,
spl0_814,
inference(avatar_split_clause,[],[f2632,f7622]) ).
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(f7620,plain,
spl0_813,
inference(avatar_split_clause,[],[f2580,f7618]) ).
fof(f7618,plain,
( spl0_813
<=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
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(f7616,plain,
spl0_812,
inference(avatar_split_clause,[],[f2576,f7614]) ).
fof(f7614,plain,
( spl0_812
<=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
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(f7612,plain,
spl0_811,
inference(avatar_split_clause,[],[f2511,f7610]) ).
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(f7608,plain,
spl0_810,
inference(avatar_split_clause,[],[f2499,f7606]) ).
fof(f7606,plain,
( spl0_810
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
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(f7604,plain,
spl0_809,
inference(avatar_split_clause,[],[f2494,f7602]) ).
fof(f7602,plain,
( spl0_809
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
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(f7600,plain,
spl0_808,
inference(avatar_split_clause,[],[f2493,f7598]) ).
fof(f7598,plain,
( spl0_808
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
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(f7596,plain,
spl0_807,
inference(avatar_split_clause,[],[f2381,f7594]) ).
fof(f7594,plain,
( spl0_807
<=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
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(f7592,plain,
spl0_806,
inference(avatar_split_clause,[],[f2380,f7590]) ).
fof(f7590,plain,
( spl0_806
<=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
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(f7588,plain,
spl0_805,
inference(avatar_split_clause,[],[f2378,f7586]) ).
fof(f7586,plain,
( spl0_805
<=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
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(f7584,plain,
spl0_804,
inference(avatar_split_clause,[],[f2370,f7582]) ).
fof(f7582,plain,
( spl0_804
<=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
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(f7580,plain,
spl0_803,
inference(avatar_split_clause,[],[f2368,f7578]) ).
fof(f7578,plain,
( spl0_803
<=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
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(f7576,plain,
spl0_802,
inference(avatar_split_clause,[],[f2344,f7574]) ).
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(f7572,plain,
spl0_801,
inference(avatar_split_clause,[],[f2269,f7570]) ).
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(f7568,plain,
spl0_800,
inference(avatar_split_clause,[],[f2156,f7565]) ).
fof(f7563,plain,
spl0_799,
inference(avatar_split_clause,[],[f2102,f7561]) ).
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(f7559,plain,
spl0_798,
inference(avatar_split_clause,[],[f2100,f7557]) ).
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(f7555,plain,
spl0_797,
inference(avatar_split_clause,[],[f2098,f7553]) ).
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(f7551,plain,
spl0_796,
inference(avatar_split_clause,[],[f2056,f7549]) ).
fof(f7549,plain,
( spl0_796
<=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
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(f7547,plain,
spl0_795,
inference(avatar_split_clause,[],[f2054,f7545]) ).
fof(f7545,plain,
( spl0_795
<=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
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(f7543,plain,
spl0_794,
inference(avatar_split_clause,[],[f2053,f7541]) ).
fof(f7541,plain,
( spl0_794
<=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
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(f7539,plain,
spl0_793,
inference(avatar_split_clause,[],[f2051,f7537]) ).
fof(f7537,plain,
( spl0_793
<=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
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(f7535,plain,
spl0_792,
inference(avatar_split_clause,[],[f2050,f7533]) ).
fof(f7533,plain,
( spl0_792
<=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
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(f7531,plain,
spl0_791,
inference(avatar_split_clause,[],[f2041,f7529]) ).
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(f7527,plain,
spl0_790,
inference(avatar_split_clause,[],[f2034,f7525]) ).
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(f7523,plain,
spl0_789,
inference(avatar_split_clause,[],[f2026,f7521]) ).
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(f7519,plain,
spl0_788,
inference(avatar_split_clause,[],[f1763,f7517]) ).
fof(f7517,plain,
( spl0_788
<=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
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(f7515,plain,
spl0_787,
inference(avatar_split_clause,[],[f1762,f7513]) ).
fof(f7513,plain,
( spl0_787
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
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(f7511,plain,
spl0_786,
inference(avatar_split_clause,[],[f1747,f7509]) ).
fof(f1747,axiom,
! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
fof(f7507,plain,
spl0_785,
inference(avatar_split_clause,[],[f1741,f7505]) ).
fof(f7505,plain,
( spl0_785
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
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(f7503,plain,
spl0_784,
inference(avatar_split_clause,[],[f1722,f7501]) ).
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(f7499,plain,
spl0_783,
inference(avatar_split_clause,[],[f1719,f7497]) ).
fof(f7497,plain,
( spl0_783
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
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(f7495,plain,
spl0_782,
inference(avatar_split_clause,[],[f1707,f7493]) ).
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(f7491,plain,
spl0_781,
inference(avatar_split_clause,[],[f1689,f7489]) ).
fof(f1689,axiom,
! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
fof(f7487,plain,
spl0_780,
inference(avatar_split_clause,[],[f1628,f7485]) ).
fof(f7485,plain,
( spl0_780
<=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
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(f7483,plain,
spl0_779,
inference(avatar_split_clause,[],[f1624,f7481]) ).
fof(f7481,plain,
( spl0_779
<=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1624,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__2_0) ).
fof(f7479,plain,
spl0_778,
inference(avatar_split_clause,[],[f1615,f7477]) ).
fof(f7477,plain,
( spl0_778
<=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
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(f7475,plain,
spl0_777,
inference(avatar_split_clause,[],[f1598,f7473]) ).
fof(f7473,plain,
( spl0_777
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
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(f7471,plain,
spl0_776,
inference(avatar_split_clause,[],[f1569,f7469]) ).
fof(f7469,plain,
( spl0_776
<=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
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(f7467,plain,
spl0_775,
inference(avatar_split_clause,[],[f1568,f7465]) ).
fof(f7465,plain,
( spl0_775
<=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
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(f7463,plain,
spl0_774,
inference(avatar_split_clause,[],[f1494,f7461]) ).
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(f7459,plain,
spl0_773,
inference(avatar_split_clause,[],[f1491,f7457]) ).
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(f7455,plain,
spl0_772,
inference(avatar_split_clause,[],[f1489,f7453]) ).
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(f7451,plain,
spl0_771,
inference(avatar_split_clause,[],[f1474,f7449]) ).
fof(f7449,plain,
( spl0_771
<=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
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(f7447,plain,
spl0_770,
inference(avatar_split_clause,[],[f1466,f7445]) ).
fof(f7445,plain,
( spl0_770
<=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
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(f7443,plain,
spl0_769,
inference(avatar_split_clause,[],[f1464,f7441]) ).
fof(f7441,plain,
( spl0_769
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
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(f7439,plain,
spl0_768,
inference(avatar_split_clause,[],[f1432,f7437]) ).
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(f7435,plain,
spl0_767,
inference(avatar_split_clause,[],[f1364,f7433]) ).
fof(f7433,plain,
( spl0_767
<=> ! [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_767])]) ).
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(f7431,plain,
spl0_766,
inference(avatar_split_clause,[],[f1363,f7429]) ).
fof(f7429,plain,
( spl0_766
<=> ! [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_766])]) ).
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(f7427,plain,
spl0_765,
inference(avatar_split_clause,[],[f1358,f7425]) ).
fof(f7425,plain,
( spl0_765
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
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(f7423,plain,
spl0_764,
inference(avatar_split_clause,[],[f1357,f7421]) ).
fof(f7421,plain,
( spl0_764
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
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(f7419,plain,
spl0_763,
inference(avatar_split_clause,[],[f1350,f7416]) ).
fof(f7416,plain,
( spl0_763
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
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(f7414,plain,
spl0_762,
inference(avatar_split_clause,[],[f1247,f7412]) ).
fof(f7412,plain,
( spl0_762
<=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f1247,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__empty_1) ).
fof(f7410,plain,
spl0_761,
inference(avatar_split_clause,[],[f1241,f7408]) ).
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(f7406,plain,
spl0_760,
inference(avatar_split_clause,[],[f1230,f7404]) ).
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(f7402,plain,
spl0_759,
inference(avatar_split_clause,[],[f1213,f7400]) ).
fof(f7400,plain,
( spl0_759
<=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
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(f7398,plain,
spl0_758,
inference(avatar_split_clause,[],[f1212,f7396]) ).
fof(f7396,plain,
( spl0_758
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
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(f7394,plain,
spl0_757,
inference(avatar_split_clause,[],[f1211,f7392]) ).
fof(f7392,plain,
( spl0_757
<=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
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(f7390,plain,
spl0_756,
inference(avatar_split_clause,[],[f1183,f7388]) ).
fof(f7388,plain,
( spl0_756
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
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(f7386,plain,
spl0_755,
inference(avatar_split_clause,[],[f1182,f7384]) ).
fof(f7384,plain,
( spl0_755
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
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(f7382,plain,
spl0_754,
inference(avatar_split_clause,[],[f1176,f7380]) ).
fof(f7380,plain,
( spl0_754
<=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
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(f7378,plain,
spl0_753,
inference(avatar_split_clause,[],[f68,f7376]) ).
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(f7374,plain,
spl0_752,
inference(avatar_split_clause,[],[f2975,f7371]) ).
fof(f2975,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_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
fof(f7369,plain,
spl0_751,
inference(avatar_split_clause,[],[f2973,f7366]) ).
fof(f2973,axiom,
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_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f7363,plain,
( spl0_750
| ~ spl0_648
| ~ spl0_690 ),
inference(avatar_split_clause,[],[f7346,f7082,f6133,f7360]) ).
fof(f7360,plain,
( spl0_750
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f7346,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_690 ),
inference(superposition,[],[f7083,f6135]) ).
fof(f7357,plain,
( ~ spl0_749
| ~ spl0_649
| ~ spl0_688 ),
inference(avatar_split_clause,[],[f7343,f7074,f6138,f7354]) ).
fof(f7354,plain,
( spl0_749
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f7074,plain,
( spl0_688
<=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f7343,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_688 ),
inference(superposition,[],[f7075,f6140]) ).
fof(f7075,plain,
( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
| ~ spl0_688 ),
inference(avatar_component_clause,[],[f7074]) ).
fof(f7352,plain,
( ~ spl0_748
| ~ spl0_648
| ~ spl0_688 ),
inference(avatar_split_clause,[],[f7342,f7074,f6133,f7349]) ).
fof(f7349,plain,
( spl0_748
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f7342,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_688 ),
inference(superposition,[],[f7075,f6135]) ).
fof(f7341,plain,
spl0_747,
inference(avatar_split_clause,[],[f3244,f7338]) ).
fof(f7338,plain,
( spl0_747
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f3244,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(f7336,plain,
spl0_746,
inference(avatar_split_clause,[],[f3239,f7334]) ).
fof(f7334,plain,
( spl0_746
<=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f3239,plain,
! [X3] : c_Binomial_Obinomial(X3,c_1) = X3,
inference(forward_demodulation,[],[f3009,f2982]) ).
fof(f3009,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(f7332,plain,
spl0_745,
inference(avatar_split_clause,[],[f2981,f7329]) ).
fof(f7327,plain,
spl0_744,
inference(avatar_split_clause,[],[f2923,f7325]) ).
fof(f7325,plain,
( spl0_744
<=> ! [X86] : c_in(c_Public_OshrK(X86),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
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(f7323,plain,
spl0_743,
inference(avatar_split_clause,[],[f2908,f7320]) ).
fof(f7320,plain,
( spl0_743
<=> c_0 = c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
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(f7318,plain,
spl0_742,
inference(avatar_split_clause,[],[f2907,f7315]) ).
fof(f7315,plain,
( spl0_742
<=> c_0 = c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
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(f7313,plain,
spl0_741,
inference(avatar_split_clause,[],[f2740,f7311]) ).
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(f7309,plain,
spl0_740,
inference(avatar_split_clause,[],[f2739,f7306]) ).
fof(f7306,plain,
( spl0_740
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
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(f7304,plain,
spl0_739,
inference(avatar_split_clause,[],[f2737,f7301]) ).
fof(f7301,plain,
( spl0_739
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
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(f7299,plain,
spl0_738,
inference(avatar_split_clause,[],[f2714,f7297]) ).
fof(f7297,plain,
( spl0_738
<=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
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(f7295,plain,
spl0_737,
inference(avatar_split_clause,[],[f2698,f7293]) ).
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(f7291,plain,
spl0_736,
inference(avatar_split_clause,[],[f2691,f7289]) ).
fof(f7289,plain,
( spl0_736
<=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
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(f7287,plain,
spl0_735,
inference(avatar_split_clause,[],[f2651,f7285]) ).
fof(f7285,plain,
( spl0_735
<=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f2651,axiom,
! [X1] : c_emptyset = c_Union(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f7283,plain,
spl0_734,
inference(avatar_split_clause,[],[f2649,f7281]) ).
fof(f7281,plain,
( spl0_734
<=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2649,axiom,
! [X1] : c_UNIV = c_Union(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f7279,plain,
spl0_733,
inference(avatar_split_clause,[],[f2625,f7277]) ).
fof(f7277,plain,
( spl0_733
<=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2625,axiom,
! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f7275,plain,
spl0_732,
inference(avatar_split_clause,[],[f2619,f7273]) ).
fof(f7273,plain,
( spl0_732
<=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f2619,axiom,
! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f7271,plain,
spl0_731,
inference(avatar_split_clause,[],[f2612,f7269]) ).
fof(f7269,plain,
( spl0_731
<=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2612,axiom,
! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f7267,plain,
spl0_730,
inference(avatar_split_clause,[],[f2567,f7264]) ).
fof(f7264,plain,
( spl0_730
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
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(f7262,plain,
spl0_729,
inference(avatar_split_clause,[],[f2528,f7259]) ).
fof(f7259,plain,
( spl0_729
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
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(f7257,plain,
spl0_728,
inference(avatar_split_clause,[],[f2386,f7255]) ).
fof(f7253,plain,
spl0_727,
inference(avatar_split_clause,[],[f2164,f7250]) ).
fof(f7250,plain,
( spl0_727
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
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(f7248,plain,
spl0_726,
inference(avatar_split_clause,[],[f2163,f7245]) ).
fof(f7245,plain,
( spl0_726
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
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(f7243,plain,
spl0_725,
inference(avatar_split_clause,[],[f2152,f7241]) ).
fof(f7241,plain,
( spl0_725
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
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(f7239,plain,
spl0_724,
inference(avatar_split_clause,[],[f2151,f7237]) ).
fof(f7237,plain,
( spl0_724
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
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(f7235,plain,
spl0_723,
inference(avatar_split_clause,[],[f2135,f7233]) ).
fof(f7233,plain,
( spl0_723
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
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(f7231,plain,
spl0_722,
inference(avatar_split_clause,[],[f2130,f7229]) ).
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(f7227,plain,
spl0_721,
inference(avatar_split_clause,[],[f2115,f7225]) ).
fof(f7225,plain,
( spl0_721
<=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f7223,plain,
spl0_720,
inference(avatar_split_clause,[],[f2114,f7221]) ).
fof(f7219,plain,
spl0_719,
inference(avatar_split_clause,[],[f2106,f7216]) ).
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(f7214,plain,
spl0_718,
inference(avatar_split_clause,[],[f2105,f7211]) ).
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(f7209,plain,
spl0_717,
inference(avatar_split_clause,[],[f1866,f7206]) ).
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(f7204,plain,
spl0_716,
inference(avatar_split_clause,[],[f1785,f7202]) ).
fof(f7202,plain,
( spl0_716
<=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
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(f7200,plain,
spl0_715,
inference(avatar_split_clause,[],[f1778,f7198]) ).
fof(f7198,plain,
( spl0_715
<=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
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(f7196,plain,
spl0_714,
inference(avatar_split_clause,[],[f1751,f7194]) ).
fof(f7194,plain,
( spl0_714
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1751,axiom,
! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
fof(f7192,plain,
spl0_713,
inference(avatar_split_clause,[],[f1736,f7190]) ).
fof(f7190,plain,
( spl0_713
<=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
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(f7188,plain,
spl0_712,
inference(avatar_split_clause,[],[f1729,f7186]) ).
fof(f7186,plain,
( spl0_712
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f7184,plain,
spl0_711,
inference(avatar_split_clause,[],[f1716,f7182]) ).
fof(f7182,plain,
( spl0_711
<=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f1716,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__iff_1) ).
fof(f7180,plain,
spl0_710,
inference(avatar_split_clause,[],[f1688,f7177]) ).
fof(f7177,plain,
( spl0_710
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
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(f7175,plain,
spl0_709,
inference(avatar_split_clause,[],[f1687,f7172]) ).
fof(f7172,plain,
( spl0_709
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
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(f7170,plain,
spl0_708,
inference(avatar_split_clause,[],[f1686,f7167]) ).
fof(f7167,plain,
( spl0_708
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
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(f7165,plain,
spl0_707,
inference(avatar_split_clause,[],[f1685,f7162]) ).
fof(f7162,plain,
( spl0_707
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
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(f7160,plain,
spl0_706,
inference(avatar_split_clause,[],[f1684,f7157]) ).
fof(f7157,plain,
( spl0_706
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
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(f7155,plain,
spl0_705,
inference(avatar_split_clause,[],[f1683,f7152]) ).
fof(f7152,plain,
( spl0_705
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
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(f7150,plain,
spl0_704,
inference(avatar_split_clause,[],[f1682,f7147]) ).
fof(f7147,plain,
( spl0_704
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
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(f7145,plain,
spl0_703,
inference(avatar_split_clause,[],[f1681,f7142]) ).
fof(f7142,plain,
( spl0_703
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
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(f7140,plain,
spl0_702,
inference(avatar_split_clause,[],[f1680,f7137]) ).
fof(f7137,plain,
( spl0_702
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
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(f7135,plain,
spl0_701,
inference(avatar_split_clause,[],[f1679,f7132]) ).
fof(f7132,plain,
( spl0_701
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
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(f7130,plain,
spl0_700,
inference(avatar_split_clause,[],[f1678,f7127]) ).
fof(f7127,plain,
( spl0_700
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
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(f7125,plain,
spl0_699,
inference(avatar_split_clause,[],[f1677,f7122]) ).
fof(f7122,plain,
( spl0_699
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
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(f7120,plain,
spl0_698,
inference(avatar_split_clause,[],[f1676,f7117]) ).
fof(f7117,plain,
( spl0_698
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
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(f7115,plain,
spl0_697,
inference(avatar_split_clause,[],[f1675,f7112]) ).
fof(f7112,plain,
( spl0_697
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
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(f7110,plain,
spl0_696,
inference(avatar_split_clause,[],[f1674,f7107]) ).
fof(f7107,plain,
( spl0_696
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
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(f7105,plain,
spl0_695,
inference(avatar_split_clause,[],[f1673,f7102]) ).
fof(f7102,plain,
( spl0_695
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
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(f7100,plain,
spl0_694,
inference(avatar_split_clause,[],[f1638,f7098]) ).
fof(f7098,plain,
( spl0_694
<=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
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(f7096,plain,
spl0_693,
inference(avatar_split_clause,[],[f1567,f7094]) ).
fof(f7094,plain,
( spl0_693
<=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
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(f7092,plain,
spl0_692,
inference(avatar_split_clause,[],[f1543,f7090]) ).
fof(f7090,plain,
( spl0_692
<=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
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(f7088,plain,
spl0_691,
inference(avatar_split_clause,[],[f1536,f7086]) ).
fof(f7086,plain,
( spl0_691
<=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
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(f7084,plain,
spl0_690,
inference(avatar_split_clause,[],[f1424,f7082]) ).
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(f7080,plain,
spl0_689,
inference(avatar_split_clause,[],[f1384,f7078]) ).
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(f7076,plain,
spl0_688,
inference(avatar_split_clause,[],[f1378,f7074]) ).
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(f7072,plain,
~ spl0_687,
inference(avatar_split_clause,[],[f1309,f7069]) ).
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(f7067,plain,
spl0_686,
inference(avatar_split_clause,[],[f1296,f7065]) ).
fof(f7065,plain,
( spl0_686
<=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1296,axiom,
! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f7063,plain,
spl0_685,
inference(avatar_split_clause,[],[f1295,f7061]) ).
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(f7059,plain,
spl0_684,
inference(avatar_split_clause,[],[f1278,f7057]) ).
fof(f7057,plain,
( spl0_684
<=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
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(f7055,plain,
spl0_683,
inference(avatar_split_clause,[],[f1255,f7052]) ).
fof(f7052,plain,
( spl0_683
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
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(f7050,plain,
spl0_682,
inference(avatar_split_clause,[],[f1254,f7047]) ).
fof(f7047,plain,
( spl0_682
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
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(f7045,plain,
spl0_681,
inference(avatar_split_clause,[],[f1184,f7042]) ).
fof(f7042,plain,
( spl0_681
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
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(f7040,plain,
spl0_680,
inference(avatar_split_clause,[],[f1173,f7038]) ).
fof(f7038,plain,
( spl0_680
<=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f1173,axiom,
! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f7036,plain,
spl0_679,
inference(avatar_split_clause,[],[f1172,f7034]) ).
fof(f7034,plain,
( spl0_679
<=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
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(f7032,plain,
spl0_678,
inference(avatar_split_clause,[],[f1165,f7030]) ).
fof(f7030,plain,
( spl0_678
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
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(f7028,plain,
spl0_677,
inference(avatar_split_clause,[],[f1164,f7026]) ).
fof(f7026,plain,
( spl0_677
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
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(f7024,plain,
spl0_676,
inference(avatar_split_clause,[],[f250,f7022]) ).
fof(f7022,plain,
( spl0_676
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
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(f7020,plain,
spl0_675,
inference(avatar_split_clause,[],[f128,f7018]) ).
fof(f7018,plain,
( spl0_675
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
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(f7016,plain,
spl0_674,
inference(avatar_split_clause,[],[f112,f7014]) ).
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(f7012,plain,
spl0_673,
inference(avatar_split_clause,[],[f101,f7010]) ).
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(f7008,plain,
spl0_672,
inference(avatar_split_clause,[],[f44,f7006]) ).
fof(f7006,plain,
( spl0_672
<=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
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(f7004,plain,
spl0_671,
inference(avatar_split_clause,[],[f28,f7002]) ).
fof(f7002,plain,
( spl0_671
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
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(f7000,plain,
( ~ spl0_670
| ~ spl0_649
| ~ spl0_651 ),
inference(avatar_split_clause,[],[f6990,f6148,f6138,f6997]) ).
fof(f6997,plain,
( spl0_670
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f6148,plain,
( spl0_651
<=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f6990,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_651 ),
inference(superposition,[],[f6149,f6140]) ).
fof(f6149,plain,
( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_651 ),
inference(avatar_component_clause,[],[f6148]) ).
fof(f6995,plain,
( ~ spl0_669
| ~ spl0_648
| ~ spl0_651 ),
inference(avatar_split_clause,[],[f6989,f6148,f6133,f6992]) ).
fof(f6992,plain,
( spl0_669
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f6989,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_648
| ~ spl0_651 ),
inference(superposition,[],[f6149,f6135]) ).
fof(f6228,plain,
spl0_668,
inference(avatar_split_clause,[],[f3254,f6225]) ).
fof(f3254,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(f6223,plain,
spl0_667,
inference(avatar_split_clause,[],[f3235,f6221]) ).
fof(f6221,plain,
( spl0_667
<=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f3235,plain,
! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat),
inference(forward_demodulation,[],[f2985,f2982]) ).
fof(f2985,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(f6219,plain,
spl0_666,
inference(avatar_split_clause,[],[f3234,f6216]) ).
fof(f6216,plain,
( spl0_666
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
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(f6214,plain,
spl0_665,
inference(avatar_split_clause,[],[f3233,f6211]) ).
fof(f3233,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2984,f2982]) ).
fof(f2984,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(f6209,plain,
spl0_664,
inference(avatar_split_clause,[],[f2853,f6206]) ).
fof(f2853,axiom,
c_emptyset = c_Message_Oanalz(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
fof(f6204,plain,
spl0_663,
inference(avatar_split_clause,[],[f2773,f6201]) ).
fof(f6201,plain,
( spl0_663
<=> c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
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(f6199,plain,
~ spl0_662,
inference(avatar_split_clause,[],[f2772,f6196]) ).
fof(f6196,plain,
( spl0_662
<=> c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
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(f6194,plain,
spl0_661,
inference(avatar_split_clause,[],[f2770,f6191]) ).
fof(f2770,axiom,
c_emptyset = c_Message_Oparts(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
fof(f6189,plain,
spl0_660,
inference(avatar_split_clause,[],[f2743,f6186]) ).
fof(f2743,axiom,
c_emptyset = c_Message_OkeysFor(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
fof(f6184,plain,
spl0_659,
inference(avatar_split_clause,[],[f2735,f6182]) ).
fof(f6182,plain,
( spl0_659
<=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2735,axiom,
! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).
fof(f6180,plain,
spl0_658,
inference(avatar_split_clause,[],[f2730,f6178]) ).
fof(f6178,plain,
( spl0_658
<=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f2730,axiom,
! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).
fof(f6176,plain,
spl0_657,
inference(avatar_split_clause,[],[f2672,f6174]) ).
fof(f2672,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f6172,plain,
spl0_656,
inference(avatar_split_clause,[],[f2155,f6169]) ).
fof(f6169,plain,
( spl0_656
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
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(f6167,plain,
spl0_655,
inference(avatar_split_clause,[],[f2091,f6165]) ).
fof(f6165,plain,
( spl0_655
<=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2091,axiom,
! [X21] : ~ c_less(X21,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f6163,plain,
spl0_654,
inference(avatar_split_clause,[],[f2049,f6160]) ).
fof(f2049,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f6158,plain,
spl0_653,
inference(avatar_split_clause,[],[f1709,f6156]) ).
fof(f6156,plain,
( spl0_653
<=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
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(f6154,plain,
spl0_652,
inference(avatar_split_clause,[],[f1482,f6152]) ).
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(f6150,plain,
spl0_651,
inference(avatar_split_clause,[],[f1393,f6148]) ).
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(f6146,plain,
spl0_650,
inference(avatar_split_clause,[],[f1386,f6143]) ).
fof(f6143,plain,
( spl0_650
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f1386,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f6141,plain,
spl0_649,
inference(avatar_split_clause,[],[f1374,f6138]) ).
fof(f6136,plain,
spl0_648,
inference(avatar_split_clause,[],[f1371,f6133]) ).
fof(f1371,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f6131,plain,
spl0_647,
inference(avatar_split_clause,[],[f1229,f6129]) ).
fof(f6129,plain,
( spl0_647
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
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(f6127,plain,
spl0_646,
inference(avatar_split_clause,[],[f1159,f6125]) ).
fof(f6125,plain,
( spl0_646
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
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(f6123,plain,
spl0_645,
inference(avatar_split_clause,[],[f1158,f6121]) ).
fof(f6121,plain,
( spl0_645
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
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(f6119,plain,
spl0_644,
inference(avatar_split_clause,[],[f1157,f6117]) ).
fof(f6117,plain,
( spl0_644
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
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(f6115,plain,
spl0_643,
inference(avatar_split_clause,[],[f1156,f6113]) ).
fof(f6113,plain,
( spl0_643
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
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(f6111,plain,
spl0_642,
inference(avatar_split_clause,[],[f1155,f6109]) ).
fof(f6109,plain,
( spl0_642
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
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(f6107,plain,
spl0_641,
inference(avatar_split_clause,[],[f1154,f6105]) ).
fof(f6105,plain,
( spl0_641
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
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(f6103,plain,
spl0_640,
inference(avatar_split_clause,[],[f1153,f6101]) ).
fof(f6101,plain,
( spl0_640
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
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(f6099,plain,
spl0_639,
inference(avatar_split_clause,[],[f1148,f6097]) ).
fof(f6097,plain,
( spl0_639
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
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(f6095,plain,
spl0_638,
inference(avatar_split_clause,[],[f1147,f6093]) ).
fof(f6093,plain,
( spl0_638
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
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(f6091,plain,
spl0_637,
inference(avatar_split_clause,[],[f1146,f6089]) ).
fof(f6089,plain,
( spl0_637
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
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(f6087,plain,
spl0_636,
inference(avatar_split_clause,[],[f1145,f6085]) ).
fof(f6085,plain,
( spl0_636
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
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(f6083,plain,
spl0_635,
inference(avatar_split_clause,[],[f1144,f6081]) ).
fof(f6081,plain,
( spl0_635
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
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(f6079,plain,
spl0_634,
inference(avatar_split_clause,[],[f1143,f6077]) ).
fof(f6077,plain,
( spl0_634
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
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(f6075,plain,
spl0_633,
inference(avatar_split_clause,[],[f1140,f6073]) ).
fof(f6073,plain,
( spl0_633
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
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(f6071,plain,
spl0_632,
inference(avatar_split_clause,[],[f1139,f6069]) ).
fof(f6069,plain,
( spl0_632
<=> ! [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_632])]) ).
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(f6067,plain,
spl0_631,
inference(avatar_split_clause,[],[f1138,f6065]) ).
fof(f6065,plain,
( spl0_631
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
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(f6063,plain,
spl0_630,
inference(avatar_split_clause,[],[f1135,f6061]) ).
fof(f6061,plain,
( spl0_630
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
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(f6059,plain,
spl0_629,
inference(avatar_split_clause,[],[f1132,f6057]) ).
fof(f6057,plain,
( spl0_629
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
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(f6055,plain,
spl0_628,
inference(avatar_split_clause,[],[f1131,f6053]) ).
fof(f6053,plain,
( spl0_628
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
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(f6051,plain,
spl0_627,
inference(avatar_split_clause,[],[f1130,f6049]) ).
fof(f6049,plain,
( spl0_627
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
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(f6047,plain,
spl0_626,
inference(avatar_split_clause,[],[f1129,f6045]) ).
fof(f6045,plain,
( spl0_626
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
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(f6043,plain,
spl0_625,
inference(avatar_split_clause,[],[f1126,f6041]) ).
fof(f6041,plain,
( spl0_625
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
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(f6039,plain,
spl0_624,
inference(avatar_split_clause,[],[f1125,f6037]) ).
fof(f6037,plain,
( spl0_624
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
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(f6035,plain,
spl0_623,
inference(avatar_split_clause,[],[f1120,f6033]) ).
fof(f6033,plain,
( spl0_623
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
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(f6031,plain,
spl0_622,
inference(avatar_split_clause,[],[f1117,f6029]) ).
fof(f6029,plain,
( spl0_622
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
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(f6027,plain,
spl0_621,
inference(avatar_split_clause,[],[f1116,f6025]) ).
fof(f6025,plain,
( spl0_621
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
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(f6023,plain,
spl0_620,
inference(avatar_split_clause,[],[f1115,f6021]) ).
fof(f6021,plain,
( spl0_620
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
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(f6019,plain,
spl0_619,
inference(avatar_split_clause,[],[f1113,f6017]) ).
fof(f6017,plain,
( spl0_619
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
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(f6015,plain,
spl0_618,
inference(avatar_split_clause,[],[f1107,f6013]) ).
fof(f6013,plain,
( spl0_618
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
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(f6011,plain,
spl0_617,
inference(avatar_split_clause,[],[f1099,f6009]) ).
fof(f6009,plain,
( spl0_617
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
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(f6007,plain,
spl0_616,
inference(avatar_split_clause,[],[f1098,f6005]) ).
fof(f6005,plain,
( spl0_616
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
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(f6003,plain,
spl0_615,
inference(avatar_split_clause,[],[f1097,f6001]) ).
fof(f6001,plain,
( spl0_615
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
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(f5999,plain,
spl0_614,
inference(avatar_split_clause,[],[f1096,f5997]) ).
fof(f5997,plain,
( spl0_614
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
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(f5995,plain,
spl0_613,
inference(avatar_split_clause,[],[f1095,f5993]) ).
fof(f5993,plain,
( spl0_613
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
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(f5991,plain,
spl0_612,
inference(avatar_split_clause,[],[f1093,f5989]) ).
fof(f5989,plain,
( spl0_612
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
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(f5987,plain,
spl0_611,
inference(avatar_split_clause,[],[f1092,f5985]) ).
fof(f5985,plain,
( spl0_611
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
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(f5983,plain,
spl0_610,
inference(avatar_split_clause,[],[f1091,f5981]) ).
fof(f5981,plain,
( spl0_610
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
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(f5979,plain,
spl0_609,
inference(avatar_split_clause,[],[f1090,f5977]) ).
fof(f5977,plain,
( spl0_609
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
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(f5975,plain,
spl0_608,
inference(avatar_split_clause,[],[f1089,f5973]) ).
fof(f5973,plain,
( spl0_608
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
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(f5971,plain,
spl0_607,
inference(avatar_split_clause,[],[f1084,f5969]) ).
fof(f5969,plain,
( spl0_607
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
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(f5967,plain,
spl0_606,
inference(avatar_split_clause,[],[f1083,f5965]) ).
fof(f5965,plain,
( spl0_606
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
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(f5963,plain,
spl0_605,
inference(avatar_split_clause,[],[f1082,f5961]) ).
fof(f5961,plain,
( spl0_605
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
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(f5959,plain,
spl0_604,
inference(avatar_split_clause,[],[f1080,f5957]) ).
fof(f5957,plain,
( spl0_604
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
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(f5955,plain,
spl0_603,
inference(avatar_split_clause,[],[f1078,f5953]) ).
fof(f5953,plain,
( spl0_603
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
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(f5951,plain,
spl0_602,
inference(avatar_split_clause,[],[f1073,f5949]) ).
fof(f5949,plain,
( spl0_602
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
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(f5947,plain,
spl0_601,
inference(avatar_split_clause,[],[f1072,f5945]) ).
fof(f5945,plain,
( spl0_601
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
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(f5943,plain,
spl0_600,
inference(avatar_split_clause,[],[f1071,f5941]) ).
fof(f5941,plain,
( spl0_600
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
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(f5939,plain,
spl0_599,
inference(avatar_split_clause,[],[f1070,f5937]) ).
fof(f5937,plain,
( spl0_599
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
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(f5935,plain,
spl0_598,
inference(avatar_split_clause,[],[f1068,f5933]) ).
fof(f5933,plain,
( spl0_598
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
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(f5931,plain,
spl0_597,
inference(avatar_split_clause,[],[f1067,f5929]) ).
fof(f5929,plain,
( spl0_597
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
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(f5927,plain,
spl0_596,
inference(avatar_split_clause,[],[f1062,f5925]) ).
fof(f5925,plain,
( spl0_596
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
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(f5923,plain,
spl0_595,
inference(avatar_split_clause,[],[f1059,f5921]) ).
fof(f5921,plain,
( spl0_595
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
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(f5919,plain,
spl0_594,
inference(avatar_split_clause,[],[f1058,f5917]) ).
fof(f5917,plain,
( spl0_594
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
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(f5915,plain,
spl0_593,
inference(avatar_split_clause,[],[f1057,f5913]) ).
fof(f5913,plain,
( spl0_593
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
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(f5911,plain,
spl0_592,
inference(avatar_split_clause,[],[f1056,f5909]) ).
fof(f5909,plain,
( spl0_592
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
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(f5907,plain,
spl0_591,
inference(avatar_split_clause,[],[f1053,f5905]) ).
fof(f5905,plain,
( spl0_591
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
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(f5903,plain,
spl0_590,
inference(avatar_split_clause,[],[f1052,f5901]) ).
fof(f5901,plain,
( spl0_590
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
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(f5899,plain,
spl0_589,
inference(avatar_split_clause,[],[f1051,f5897]) ).
fof(f5897,plain,
( spl0_589
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
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(f5895,plain,
spl0_588,
inference(avatar_split_clause,[],[f1050,f5893]) ).
fof(f5893,plain,
( spl0_588
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
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(f5891,plain,
spl0_587,
inference(avatar_split_clause,[],[f1049,f5889]) ).
fof(f5889,plain,
( spl0_587
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
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(f5887,plain,
spl0_586,
inference(avatar_split_clause,[],[f1048,f5885]) ).
fof(f5885,plain,
( spl0_586
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
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(f5883,plain,
spl0_585,
inference(avatar_split_clause,[],[f1047,f5881]) ).
fof(f5881,plain,
( spl0_585
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
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(f5879,plain,
spl0_584,
inference(avatar_split_clause,[],[f1046,f5877]) ).
fof(f5877,plain,
( spl0_584
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
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(f5875,plain,
spl0_583,
inference(avatar_split_clause,[],[f1044,f5873]) ).
fof(f5873,plain,
( spl0_583
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
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(f5871,plain,
spl0_582,
inference(avatar_split_clause,[],[f1043,f5869]) ).
fof(f5869,plain,
( spl0_582
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
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(f5867,plain,
spl0_581,
inference(avatar_split_clause,[],[f1042,f5865]) ).
fof(f5865,plain,
( spl0_581
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
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(f5863,plain,
spl0_580,
inference(avatar_split_clause,[],[f1041,f5861]) ).
fof(f5861,plain,
( spl0_580
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
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(f5859,plain,
spl0_579,
inference(avatar_split_clause,[],[f1040,f5857]) ).
fof(f5857,plain,
( spl0_579
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
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(f5855,plain,
spl0_578,
inference(avatar_split_clause,[],[f1035,f5853]) ).
fof(f5853,plain,
( spl0_578
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
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(f5851,plain,
spl0_577,
inference(avatar_split_clause,[],[f1034,f5849]) ).
fof(f5849,plain,
( spl0_577
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
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(f5847,plain,
spl0_576,
inference(avatar_split_clause,[],[f1033,f5845]) ).
fof(f5845,plain,
( spl0_576
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
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(f5843,plain,
spl0_575,
inference(avatar_split_clause,[],[f1030,f5841]) ).
fof(f5841,plain,
( spl0_575
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
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(f5839,plain,
spl0_574,
inference(avatar_split_clause,[],[f1027,f5837]) ).
fof(f5837,plain,
( spl0_574
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
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(f5835,plain,
spl0_573,
inference(avatar_split_clause,[],[f1026,f5833]) ).
fof(f5833,plain,
( spl0_573
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
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(f5831,plain,
spl0_572,
inference(avatar_split_clause,[],[f1024,f5829]) ).
fof(f5829,plain,
( spl0_572
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
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(f5827,plain,
spl0_571,
inference(avatar_split_clause,[],[f1023,f5825]) ).
fof(f5825,plain,
( spl0_571
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
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(f5823,plain,
spl0_570,
inference(avatar_split_clause,[],[f1022,f5821]) ).
fof(f5821,plain,
( spl0_570
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
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(f5819,plain,
spl0_569,
inference(avatar_split_clause,[],[f1021,f5817]) ).
fof(f5817,plain,
( spl0_569
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
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(f5815,plain,
spl0_568,
inference(avatar_split_clause,[],[f1018,f5813]) ).
fof(f5813,plain,
( spl0_568
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
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(f5811,plain,
spl0_567,
inference(avatar_split_clause,[],[f1017,f5809]) ).
fof(f5809,plain,
( spl0_567
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
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(f5807,plain,
spl0_566,
inference(avatar_split_clause,[],[f989,f5805]) ).
fof(f5805,plain,
( spl0_566
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
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(f5803,plain,
spl0_565,
inference(avatar_split_clause,[],[f987,f5801]) ).
fof(f5801,plain,
( spl0_565
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
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(f5799,plain,
spl0_564,
inference(avatar_split_clause,[],[f984,f5797]) ).
fof(f5797,plain,
( spl0_564
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
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(f5795,plain,
spl0_563,
inference(avatar_split_clause,[],[f983,f5793]) ).
fof(f5793,plain,
( spl0_563
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
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(f5791,plain,
spl0_562,
inference(avatar_split_clause,[],[f982,f5789]) ).
fof(f5789,plain,
( spl0_562
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
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(f5787,plain,
spl0_561,
inference(avatar_split_clause,[],[f981,f5785]) ).
fof(f5785,plain,
( spl0_561
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
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(f5783,plain,
spl0_560,
inference(avatar_split_clause,[],[f980,f5781]) ).
fof(f5781,plain,
( spl0_560
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
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(f5779,plain,
spl0_559,
inference(avatar_split_clause,[],[f979,f5777]) ).
fof(f5777,plain,
( spl0_559
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
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(f5775,plain,
spl0_558,
inference(avatar_split_clause,[],[f977,f5773]) ).
fof(f5773,plain,
( spl0_558
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
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(f5771,plain,
spl0_557,
inference(avatar_split_clause,[],[f976,f5769]) ).
fof(f5769,plain,
( spl0_557
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
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(f5767,plain,
spl0_556,
inference(avatar_split_clause,[],[f974,f5765]) ).
fof(f5765,plain,
( spl0_556
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
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(f5763,plain,
spl0_555,
inference(avatar_split_clause,[],[f971,f5761]) ).
fof(f5761,plain,
( spl0_555
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
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(f5759,plain,
spl0_554,
inference(avatar_split_clause,[],[f970,f5757]) ).
fof(f5757,plain,
( spl0_554
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
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(f5755,plain,
spl0_553,
inference(avatar_split_clause,[],[f968,f5753]) ).
fof(f5753,plain,
( spl0_553
<=> ! [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_553])]) ).
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(f5751,plain,
spl0_552,
inference(avatar_split_clause,[],[f967,f5749]) ).
fof(f5749,plain,
( spl0_552
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
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(f5747,plain,
spl0_551,
inference(avatar_split_clause,[],[f966,f5745]) ).
fof(f5745,plain,
( spl0_551
<=> ! [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_551])]) ).
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(f5743,plain,
spl0_550,
inference(avatar_split_clause,[],[f965,f5741]) ).
fof(f5741,plain,
( spl0_550
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
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(f5739,plain,
spl0_549,
inference(avatar_split_clause,[],[f964,f5737]) ).
fof(f5737,plain,
( spl0_549
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
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(f5735,plain,
spl0_548,
inference(avatar_split_clause,[],[f963,f5733]) ).
fof(f5733,plain,
( spl0_548
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
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(f5731,plain,
spl0_547,
inference(avatar_split_clause,[],[f962,f5729]) ).
fof(f5729,plain,
( spl0_547
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
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(f5727,plain,
spl0_546,
inference(avatar_split_clause,[],[f961,f5725]) ).
fof(f5725,plain,
( spl0_546
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
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(f5723,plain,
spl0_545,
inference(avatar_split_clause,[],[f957,f5721]) ).
fof(f5721,plain,
( spl0_545
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
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(f5719,plain,
spl0_544,
inference(avatar_split_clause,[],[f956,f5717]) ).
fof(f5717,plain,
( spl0_544
<=> ! [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_544])]) ).
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(f5715,plain,
spl0_543,
inference(avatar_split_clause,[],[f955,f5713]) ).
fof(f5713,plain,
( spl0_543
<=> ! [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_543])]) ).
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(f5711,plain,
spl0_542,
inference(avatar_split_clause,[],[f954,f5709]) ).
fof(f5709,plain,
( spl0_542
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
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(f5707,plain,
spl0_541,
inference(avatar_split_clause,[],[f949,f5705]) ).
fof(f5705,plain,
( spl0_541
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
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(f5703,plain,
spl0_540,
inference(avatar_split_clause,[],[f947,f5701]) ).
fof(f5701,plain,
( spl0_540
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
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(f5699,plain,
spl0_539,
inference(avatar_split_clause,[],[f946,f5697]) ).
fof(f5697,plain,
( spl0_539
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
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(f5695,plain,
spl0_538,
inference(avatar_split_clause,[],[f945,f5693]) ).
fof(f5693,plain,
( spl0_538
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
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(f5691,plain,
spl0_537,
inference(avatar_split_clause,[],[f944,f5689]) ).
fof(f5689,plain,
( spl0_537
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
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(f5687,plain,
spl0_536,
inference(avatar_split_clause,[],[f942,f5685]) ).
fof(f5685,plain,
( spl0_536
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
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(f5683,plain,
spl0_535,
inference(avatar_split_clause,[],[f941,f5681]) ).
fof(f5681,plain,
( spl0_535
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
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(f5679,plain,
spl0_534,
inference(avatar_split_clause,[],[f940,f5677]) ).
fof(f5677,plain,
( spl0_534
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
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(f5675,plain,
spl0_533,
inference(avatar_split_clause,[],[f939,f5673]) ).
fof(f5673,plain,
( spl0_533
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
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(f5671,plain,
spl0_532,
inference(avatar_split_clause,[],[f938,f5669]) ).
fof(f5669,plain,
( spl0_532
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
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(f5667,plain,
spl0_531,
inference(avatar_split_clause,[],[f937,f5665]) ).
fof(f5665,plain,
( spl0_531
<=> ! [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_531])]) ).
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(f5663,plain,
spl0_530,
inference(avatar_split_clause,[],[f936,f5661]) ).
fof(f5661,plain,
( spl0_530
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
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(f5659,plain,
spl0_529,
inference(avatar_split_clause,[],[f935,f5657]) ).
fof(f5657,plain,
( spl0_529
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
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(f5655,plain,
spl0_528,
inference(avatar_split_clause,[],[f934,f5653]) ).
fof(f5653,plain,
( spl0_528
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
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(f5651,plain,
spl0_527,
inference(avatar_split_clause,[],[f933,f5649]) ).
fof(f5649,plain,
( spl0_527
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
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(f5647,plain,
spl0_526,
inference(avatar_split_clause,[],[f932,f5645]) ).
fof(f5645,plain,
( spl0_526
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
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(f5643,plain,
spl0_525,
inference(avatar_split_clause,[],[f931,f5641]) ).
fof(f5641,plain,
( spl0_525
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
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(f5639,plain,
spl0_524,
inference(avatar_split_clause,[],[f930,f5637]) ).
fof(f5637,plain,
( spl0_524
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
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(f5635,plain,
spl0_523,
inference(avatar_split_clause,[],[f929,f5633]) ).
fof(f5633,plain,
( spl0_523
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
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(f5631,plain,
spl0_522,
inference(avatar_split_clause,[],[f928,f5629]) ).
fof(f5629,plain,
( spl0_522
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
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(f5627,plain,
spl0_521,
inference(avatar_split_clause,[],[f927,f5625]) ).
fof(f5625,plain,
( spl0_521
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
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(f5623,plain,
spl0_520,
inference(avatar_split_clause,[],[f926,f5621]) ).
fof(f5621,plain,
( spl0_520
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
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(f5619,plain,
spl0_519,
inference(avatar_split_clause,[],[f925,f5617]) ).
fof(f5617,plain,
( spl0_519
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
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(f5615,plain,
spl0_518,
inference(avatar_split_clause,[],[f924,f5613]) ).
fof(f5613,plain,
( spl0_518
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
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(f5611,plain,
spl0_517,
inference(avatar_split_clause,[],[f923,f5609]) ).
fof(f5609,plain,
( spl0_517
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
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(f5607,plain,
spl0_516,
inference(avatar_split_clause,[],[f922,f5605]) ).
fof(f5605,plain,
( spl0_516
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
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(f5603,plain,
spl0_515,
inference(avatar_split_clause,[],[f921,f5601]) ).
fof(f5601,plain,
( spl0_515
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
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(f5599,plain,
spl0_514,
inference(avatar_split_clause,[],[f920,f5597]) ).
fof(f5597,plain,
( spl0_514
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
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(f5595,plain,
spl0_513,
inference(avatar_split_clause,[],[f919,f5593]) ).
fof(f5593,plain,
( spl0_513
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
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(f5591,plain,
spl0_512,
inference(avatar_split_clause,[],[f918,f5589]) ).
fof(f5589,plain,
( spl0_512
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
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(f5587,plain,
spl0_511,
inference(avatar_split_clause,[],[f917,f5585]) ).
fof(f5585,plain,
( spl0_511
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
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(f5583,plain,
spl0_510,
inference(avatar_split_clause,[],[f916,f5581]) ).
fof(f5581,plain,
( spl0_510
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
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(f5579,plain,
spl0_509,
inference(avatar_split_clause,[],[f915,f5577]) ).
fof(f5577,plain,
( spl0_509
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
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(f5575,plain,
spl0_508,
inference(avatar_split_clause,[],[f914,f5573]) ).
fof(f5573,plain,
( spl0_508
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
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(f5571,plain,
spl0_507,
inference(avatar_split_clause,[],[f913,f5569]) ).
fof(f5569,plain,
( spl0_507
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
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(f5567,plain,
spl0_506,
inference(avatar_split_clause,[],[f912,f5565]) ).
fof(f5565,plain,
( spl0_506
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
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(f5563,plain,
spl0_505,
inference(avatar_split_clause,[],[f911,f5561]) ).
fof(f5561,plain,
( spl0_505
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
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(f5559,plain,
spl0_504,
inference(avatar_split_clause,[],[f910,f5557]) ).
fof(f5557,plain,
( spl0_504
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
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(f5555,plain,
spl0_503,
inference(avatar_split_clause,[],[f909,f5553]) ).
fof(f5553,plain,
( spl0_503
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
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(f5551,plain,
spl0_502,
inference(avatar_split_clause,[],[f908,f5549]) ).
fof(f5549,plain,
( spl0_502
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
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(f5547,plain,
spl0_501,
inference(avatar_split_clause,[],[f905,f5545]) ).
fof(f5545,plain,
( spl0_501
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
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(f5543,plain,
spl0_500,
inference(avatar_split_clause,[],[f903,f5541]) ).
fof(f5541,plain,
( spl0_500
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
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(f5539,plain,
spl0_499,
inference(avatar_split_clause,[],[f902,f5537]) ).
fof(f5537,plain,
( spl0_499
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
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(f5535,plain,
spl0_498,
inference(avatar_split_clause,[],[f900,f5533]) ).
fof(f5533,plain,
( spl0_498
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
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(f5531,plain,
spl0_497,
inference(avatar_split_clause,[],[f897,f5529]) ).
fof(f5529,plain,
( spl0_497
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
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(f5527,plain,
spl0_496,
inference(avatar_split_clause,[],[f896,f5525]) ).
fof(f5525,plain,
( spl0_496
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
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(f5523,plain,
spl0_495,
inference(avatar_split_clause,[],[f895,f5521]) ).
fof(f5521,plain,
( spl0_495
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
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(f5519,plain,
spl0_494,
inference(avatar_split_clause,[],[f893,f5517]) ).
fof(f5517,plain,
( spl0_494
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
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(f5515,plain,
spl0_493,
inference(avatar_split_clause,[],[f892,f5513]) ).
fof(f5513,plain,
( spl0_493
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
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(f5511,plain,
spl0_492,
inference(avatar_split_clause,[],[f891,f5509]) ).
fof(f5509,plain,
( spl0_492
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
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(f5507,plain,
spl0_491,
inference(avatar_split_clause,[],[f888,f5505]) ).
fof(f5505,plain,
( spl0_491
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
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(f5503,plain,
spl0_490,
inference(avatar_split_clause,[],[f887,f5501]) ).
fof(f5501,plain,
( spl0_490
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
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(f5499,plain,
spl0_489,
inference(avatar_split_clause,[],[f886,f5497]) ).
fof(f5497,plain,
( spl0_489
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
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(f5495,plain,
spl0_488,
inference(avatar_split_clause,[],[f885,f5493]) ).
fof(f5493,plain,
( spl0_488
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
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(f5491,plain,
spl0_487,
inference(avatar_split_clause,[],[f883,f5489]) ).
fof(f5489,plain,
( spl0_487
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
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(f5487,plain,
spl0_486,
inference(avatar_split_clause,[],[f882,f5485]) ).
fof(f5485,plain,
( spl0_486
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
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(f5483,plain,
spl0_485,
inference(avatar_split_clause,[],[f881,f5481]) ).
fof(f5481,plain,
( spl0_485
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
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(f5479,plain,
spl0_484,
inference(avatar_split_clause,[],[f880,f5477]) ).
fof(f5477,plain,
( spl0_484
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
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(f5475,plain,
spl0_483,
inference(avatar_split_clause,[],[f879,f5473]) ).
fof(f5473,plain,
( spl0_483
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
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(f5471,plain,
spl0_482,
inference(avatar_split_clause,[],[f878,f5469]) ).
fof(f5469,plain,
( spl0_482
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
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(f5467,plain,
spl0_481,
inference(avatar_split_clause,[],[f877,f5465]) ).
fof(f5465,plain,
( spl0_481
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
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(f5463,plain,
spl0_480,
inference(avatar_split_clause,[],[f876,f5461]) ).
fof(f5461,plain,
( spl0_480
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
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(f5459,plain,
spl0_479,
inference(avatar_split_clause,[],[f875,f5457]) ).
fof(f5457,plain,
( spl0_479
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
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(f5455,plain,
spl0_478,
inference(avatar_split_clause,[],[f874,f5453]) ).
fof(f5453,plain,
( spl0_478
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
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(f5451,plain,
spl0_477,
inference(avatar_split_clause,[],[f873,f5449]) ).
fof(f5449,plain,
( spl0_477
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
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(f5447,plain,
spl0_476,
inference(avatar_split_clause,[],[f872,f5445]) ).
fof(f5445,plain,
( spl0_476
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
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(f5443,plain,
spl0_475,
inference(avatar_split_clause,[],[f871,f5441]) ).
fof(f5441,plain,
( spl0_475
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
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(f5439,plain,
spl0_474,
inference(avatar_split_clause,[],[f870,f5437]) ).
fof(f5437,plain,
( spl0_474
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
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(f5435,plain,
spl0_473,
inference(avatar_split_clause,[],[f869,f5433]) ).
fof(f5433,plain,
( spl0_473
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
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(f5431,plain,
spl0_472,
inference(avatar_split_clause,[],[f868,f5429]) ).
fof(f5429,plain,
( spl0_472
<=> ! [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_472])]) ).
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(f5427,plain,
spl0_471,
inference(avatar_split_clause,[],[f867,f5425]) ).
fof(f5425,plain,
( spl0_471
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
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(f5423,plain,
spl0_470,
inference(avatar_split_clause,[],[f865,f5421]) ).
fof(f5421,plain,
( spl0_470
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
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(f5419,plain,
spl0_469,
inference(avatar_split_clause,[],[f864,f5417]) ).
fof(f5417,plain,
( spl0_469
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
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(f5415,plain,
spl0_468,
inference(avatar_split_clause,[],[f863,f5413]) ).
fof(f5413,plain,
( spl0_468
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
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(f5411,plain,
spl0_467,
inference(avatar_split_clause,[],[f862,f5409]) ).
fof(f5409,plain,
( spl0_467
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
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(f5407,plain,
spl0_466,
inference(avatar_split_clause,[],[f861,f5405]) ).
fof(f5405,plain,
( spl0_466
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
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(f5403,plain,
spl0_465,
inference(avatar_split_clause,[],[f856,f5401]) ).
fof(f5401,plain,
( spl0_465
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
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(f5399,plain,
spl0_464,
inference(avatar_split_clause,[],[f855,f5397]) ).
fof(f5397,plain,
( spl0_464
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
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(f5395,plain,
spl0_463,
inference(avatar_split_clause,[],[f854,f5393]) ).
fof(f5393,plain,
( spl0_463
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
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(f5391,plain,
spl0_462,
inference(avatar_split_clause,[],[f853,f5389]) ).
fof(f5389,plain,
( spl0_462
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
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(f5387,plain,
spl0_461,
inference(avatar_split_clause,[],[f852,f5385]) ).
fof(f5385,plain,
( spl0_461
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
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(f5383,plain,
spl0_460,
inference(avatar_split_clause,[],[f851,f5381]) ).
fof(f5381,plain,
( spl0_460
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
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(f5379,plain,
spl0_459,
inference(avatar_split_clause,[],[f850,f5377]) ).
fof(f5377,plain,
( spl0_459
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
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(f5375,plain,
spl0_458,
inference(avatar_split_clause,[],[f849,f5373]) ).
fof(f5373,plain,
( spl0_458
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
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(f5371,plain,
spl0_457,
inference(avatar_split_clause,[],[f847,f5369]) ).
fof(f5369,plain,
( spl0_457
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
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(f5367,plain,
spl0_456,
inference(avatar_split_clause,[],[f846,f5365]) ).
fof(f5365,plain,
( spl0_456
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
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(f5363,plain,
spl0_455,
inference(avatar_split_clause,[],[f845,f5361]) ).
fof(f5361,plain,
( spl0_455
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
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(f5359,plain,
spl0_454,
inference(avatar_split_clause,[],[f844,f5357]) ).
fof(f5357,plain,
( spl0_454
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
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(f5355,plain,
spl0_453,
inference(avatar_split_clause,[],[f843,f5353]) ).
fof(f5353,plain,
( spl0_453
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
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(f5351,plain,
spl0_452,
inference(avatar_split_clause,[],[f842,f5349]) ).
fof(f5349,plain,
( spl0_452
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
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(f5347,plain,
spl0_451,
inference(avatar_split_clause,[],[f840,f5345]) ).
fof(f5345,plain,
( spl0_451
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
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(f5343,plain,
spl0_450,
inference(avatar_split_clause,[],[f839,f5341]) ).
fof(f5341,plain,
( spl0_450
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
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(f5339,plain,
spl0_449,
inference(avatar_split_clause,[],[f838,f5337]) ).
fof(f5337,plain,
( spl0_449
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
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(f5335,plain,
spl0_448,
inference(avatar_split_clause,[],[f837,f5333]) ).
fof(f5333,plain,
( spl0_448
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
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(f5331,plain,
spl0_447,
inference(avatar_split_clause,[],[f836,f5329]) ).
fof(f5329,plain,
( spl0_447
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
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(f5327,plain,
spl0_446,
inference(avatar_split_clause,[],[f835,f5325]) ).
fof(f5325,plain,
( spl0_446
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
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(f5323,plain,
spl0_445,
inference(avatar_split_clause,[],[f834,f5321]) ).
fof(f5321,plain,
( spl0_445
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
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(f5319,plain,
spl0_444,
inference(avatar_split_clause,[],[f833,f5317]) ).
fof(f5317,plain,
( spl0_444
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
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(f5315,plain,
spl0_443,
inference(avatar_split_clause,[],[f832,f5313]) ).
fof(f5313,plain,
( spl0_443
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
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(f5311,plain,
spl0_442,
inference(avatar_split_clause,[],[f831,f5309]) ).
fof(f5309,plain,
( spl0_442
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
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(f5307,plain,
spl0_441,
inference(avatar_split_clause,[],[f830,f5305]) ).
fof(f5305,plain,
( spl0_441
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
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(f5303,plain,
spl0_440,
inference(avatar_split_clause,[],[f829,f5301]) ).
fof(f5301,plain,
( spl0_440
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
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(f5299,plain,
spl0_439,
inference(avatar_split_clause,[],[f828,f5297]) ).
fof(f5297,plain,
( spl0_439
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
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(f5295,plain,
spl0_438,
inference(avatar_split_clause,[],[f827,f5293]) ).
fof(f5293,plain,
( spl0_438
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
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(f5291,plain,
spl0_437,
inference(avatar_split_clause,[],[f826,f5289]) ).
fof(f5289,plain,
( spl0_437
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
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(f5287,plain,
spl0_436,
inference(avatar_split_clause,[],[f825,f5285]) ).
fof(f5285,plain,
( spl0_436
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
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(f5283,plain,
spl0_435,
inference(avatar_split_clause,[],[f824,f5281]) ).
fof(f5281,plain,
( spl0_435
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
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(f5279,plain,
spl0_434,
inference(avatar_split_clause,[],[f823,f5277]) ).
fof(f5277,plain,
( spl0_434
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
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(f5275,plain,
spl0_433,
inference(avatar_split_clause,[],[f822,f5273]) ).
fof(f5273,plain,
( spl0_433
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
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(f5271,plain,
spl0_432,
inference(avatar_split_clause,[],[f821,f5269]) ).
fof(f5269,plain,
( spl0_432
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
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(f5267,plain,
spl0_431,
inference(avatar_split_clause,[],[f820,f5265]) ).
fof(f5265,plain,
( spl0_431
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
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(f5263,plain,
spl0_430,
inference(avatar_split_clause,[],[f819,f5261]) ).
fof(f5261,plain,
( spl0_430
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
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(f5259,plain,
spl0_429,
inference(avatar_split_clause,[],[f816,f5257]) ).
fof(f5257,plain,
( spl0_429
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
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(f5255,plain,
spl0_428,
inference(avatar_split_clause,[],[f814,f5253]) ).
fof(f5253,plain,
( spl0_428
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
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(f5251,plain,
spl0_427,
inference(avatar_split_clause,[],[f812,f5249]) ).
fof(f5249,plain,
( spl0_427
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
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(f5247,plain,
spl0_426,
inference(avatar_split_clause,[],[f809,f5245]) ).
fof(f5245,plain,
( spl0_426
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
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(f5243,plain,
spl0_425,
inference(avatar_split_clause,[],[f808,f5241]) ).
fof(f5241,plain,
( spl0_425
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
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(f5239,plain,
spl0_424,
inference(avatar_split_clause,[],[f807,f5237]) ).
fof(f5237,plain,
( spl0_424
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
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(f5235,plain,
spl0_423,
inference(avatar_split_clause,[],[f806,f5233]) ).
fof(f5233,plain,
( spl0_423
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
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(f5231,plain,
spl0_422,
inference(avatar_split_clause,[],[f804,f5229]) ).
fof(f5229,plain,
( spl0_422
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
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(f5227,plain,
spl0_421,
inference(avatar_split_clause,[],[f803,f5225]) ).
fof(f5225,plain,
( spl0_421
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
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(f5223,plain,
spl0_420,
inference(avatar_split_clause,[],[f802,f5221]) ).
fof(f5221,plain,
( spl0_420
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
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(f5219,plain,
spl0_419,
inference(avatar_split_clause,[],[f801,f5217]) ).
fof(f5217,plain,
( spl0_419
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
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(f5215,plain,
spl0_418,
inference(avatar_split_clause,[],[f800,f5213]) ).
fof(f5213,plain,
( spl0_418
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
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(f5211,plain,
spl0_417,
inference(avatar_split_clause,[],[f799,f5209]) ).
fof(f5209,plain,
( spl0_417
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
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(f5207,plain,
spl0_416,
inference(avatar_split_clause,[],[f798,f5205]) ).
fof(f5205,plain,
( spl0_416
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
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(f5203,plain,
spl0_415,
inference(avatar_split_clause,[],[f797,f5201]) ).
fof(f5201,plain,
( spl0_415
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
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(f5199,plain,
spl0_414,
inference(avatar_split_clause,[],[f796,f5197]) ).
fof(f5197,plain,
( spl0_414
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
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(f5195,plain,
spl0_413,
inference(avatar_split_clause,[],[f732,f5193]) ).
fof(f5193,plain,
( spl0_413
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
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(f5191,plain,
spl0_412,
inference(avatar_split_clause,[],[f729,f5189]) ).
fof(f5189,plain,
( spl0_412
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
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(f5187,plain,
spl0_411,
inference(avatar_split_clause,[],[f728,f5185]) ).
fof(f5185,plain,
( spl0_411
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
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(f5183,plain,
spl0_410,
inference(avatar_split_clause,[],[f727,f5181]) ).
fof(f5181,plain,
( spl0_410
<=> ! [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_410])]) ).
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(f5179,plain,
spl0_409,
inference(avatar_split_clause,[],[f726,f5177]) ).
fof(f5177,plain,
( spl0_409
<=> ! [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_409])]) ).
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(f5175,plain,
spl0_408,
inference(avatar_split_clause,[],[f725,f5173]) ).
fof(f5173,plain,
( spl0_408
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
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(f5171,plain,
spl0_407,
inference(avatar_split_clause,[],[f724,f5169]) ).
fof(f5169,plain,
( spl0_407
<=> ! [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_407])]) ).
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(f5167,plain,
spl0_406,
inference(avatar_split_clause,[],[f723,f5165]) ).
fof(f5165,plain,
( spl0_406
<=> ! [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_406])]) ).
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(f5163,plain,
spl0_405,
inference(avatar_split_clause,[],[f722,f5161]) ).
fof(f5161,plain,
( spl0_405
<=> ! [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_405])]) ).
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(f5159,plain,
spl0_404,
inference(avatar_split_clause,[],[f721,f5157]) ).
fof(f5157,plain,
( spl0_404
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
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(f5155,plain,
spl0_403,
inference(avatar_split_clause,[],[f720,f5153]) ).
fof(f5153,plain,
( spl0_403
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
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(f5151,plain,
spl0_402,
inference(avatar_split_clause,[],[f719,f5149]) ).
fof(f5149,plain,
( spl0_402
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
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(f5147,plain,
spl0_401,
inference(avatar_split_clause,[],[f718,f5145]) ).
fof(f5145,plain,
( spl0_401
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
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(f5143,plain,
spl0_400,
inference(avatar_split_clause,[],[f716,f5141]) ).
fof(f5141,plain,
( spl0_400
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
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(f5139,plain,
spl0_399,
inference(avatar_split_clause,[],[f715,f5137]) ).
fof(f5137,plain,
( spl0_399
<=> ! [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_399])]) ).
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(f5135,plain,
spl0_398,
inference(avatar_split_clause,[],[f714,f5133]) ).
fof(f5133,plain,
( spl0_398
<=> ! [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_398])]) ).
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(f5131,plain,
spl0_397,
inference(avatar_split_clause,[],[f713,f5129]) ).
fof(f5129,plain,
( spl0_397
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
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(f5127,plain,
spl0_396,
inference(avatar_split_clause,[],[f712,f5125]) ).
fof(f5125,plain,
( spl0_396
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
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(f5123,plain,
spl0_395,
inference(avatar_split_clause,[],[f711,f5121]) ).
fof(f5121,plain,
( spl0_395
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
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(f5119,plain,
spl0_394,
inference(avatar_split_clause,[],[f710,f5117]) ).
fof(f5117,plain,
( spl0_394
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
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(f5115,plain,
spl0_393,
inference(avatar_split_clause,[],[f709,f5113]) ).
fof(f5113,plain,
( spl0_393
<=> ! [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_393])]) ).
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(f5111,plain,
spl0_392,
inference(avatar_split_clause,[],[f706,f5109]) ).
fof(f5109,plain,
( spl0_392
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
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(f5107,plain,
spl0_391,
inference(avatar_split_clause,[],[f705,f5105]) ).
fof(f5105,plain,
( spl0_391
<=> ! [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_391])]) ).
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(f5103,plain,
spl0_390,
inference(avatar_split_clause,[],[f704,f5101]) ).
fof(f5101,plain,
( spl0_390
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
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(f5099,plain,
spl0_389,
inference(avatar_split_clause,[],[f703,f5097]) ).
fof(f5097,plain,
( spl0_389
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
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(f5095,plain,
spl0_388,
inference(avatar_split_clause,[],[f702,f5093]) ).
fof(f5093,plain,
( spl0_388
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
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(f5091,plain,
spl0_387,
inference(avatar_split_clause,[],[f701,f5089]) ).
fof(f5089,plain,
( spl0_387
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
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(f5087,plain,
spl0_386,
inference(avatar_split_clause,[],[f700,f5085]) ).
fof(f5085,plain,
( spl0_386
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
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(f5083,plain,
spl0_385,
inference(avatar_split_clause,[],[f698,f5081]) ).
fof(f5081,plain,
( spl0_385
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
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(f5079,plain,
spl0_384,
inference(avatar_split_clause,[],[f697,f5077]) ).
fof(f5077,plain,
( spl0_384
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
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(f5075,plain,
spl0_383,
inference(avatar_split_clause,[],[f696,f5073]) ).
fof(f5073,plain,
( spl0_383
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
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(f5071,plain,
spl0_382,
inference(avatar_split_clause,[],[f695,f5069]) ).
fof(f5069,plain,
( spl0_382
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
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(f5067,plain,
spl0_381,
inference(avatar_split_clause,[],[f694,f5065]) ).
fof(f5065,plain,
( spl0_381
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
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(f5063,plain,
spl0_380,
inference(avatar_split_clause,[],[f693,f5061]) ).
fof(f5061,plain,
( spl0_380
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
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(f5059,plain,
spl0_379,
inference(avatar_split_clause,[],[f692,f5057]) ).
fof(f5057,plain,
( spl0_379
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
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(f5055,plain,
spl0_378,
inference(avatar_split_clause,[],[f691,f5053]) ).
fof(f5053,plain,
( spl0_378
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
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(f5051,plain,
spl0_377,
inference(avatar_split_clause,[],[f688,f5049]) ).
fof(f5049,plain,
( spl0_377
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
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(f5047,plain,
spl0_376,
inference(avatar_split_clause,[],[f686,f5045]) ).
fof(f5045,plain,
( spl0_376
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
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(f5043,plain,
spl0_375,
inference(avatar_split_clause,[],[f685,f5041]) ).
fof(f5041,plain,
( spl0_375
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
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(f5039,plain,
spl0_374,
inference(avatar_split_clause,[],[f683,f5037]) ).
fof(f5037,plain,
( spl0_374
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
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(f5035,plain,
spl0_373,
inference(avatar_split_clause,[],[f680,f5033]) ).
fof(f5033,plain,
( spl0_373
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
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(f5031,plain,
spl0_372,
inference(avatar_split_clause,[],[f679,f5029]) ).
fof(f5029,plain,
( spl0_372
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
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(f5027,plain,
spl0_371,
inference(avatar_split_clause,[],[f678,f5025]) ).
fof(f5025,plain,
( spl0_371
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
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(f5023,plain,
spl0_370,
inference(avatar_split_clause,[],[f677,f5021]) ).
fof(f5021,plain,
( spl0_370
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
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(f5019,plain,
spl0_369,
inference(avatar_split_clause,[],[f676,f5017]) ).
fof(f5017,plain,
( spl0_369
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
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(f5015,plain,
spl0_368,
inference(avatar_split_clause,[],[f675,f5013]) ).
fof(f5013,plain,
( spl0_368
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
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(f5011,plain,
spl0_367,
inference(avatar_split_clause,[],[f674,f5009]) ).
fof(f5009,plain,
( spl0_367
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
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(f5007,plain,
spl0_366,
inference(avatar_split_clause,[],[f673,f5005]) ).
fof(f5005,plain,
( spl0_366
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
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(f5003,plain,
spl0_365,
inference(avatar_split_clause,[],[f672,f5001]) ).
fof(f5001,plain,
( spl0_365
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
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(f4999,plain,
spl0_364,
inference(avatar_split_clause,[],[f671,f4997]) ).
fof(f4997,plain,
( spl0_364
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
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(f4995,plain,
spl0_363,
inference(avatar_split_clause,[],[f670,f4993]) ).
fof(f4993,plain,
( spl0_363
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
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(f4991,plain,
spl0_362,
inference(avatar_split_clause,[],[f668,f4989]) ).
fof(f4989,plain,
( spl0_362
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
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(f4987,plain,
spl0_361,
inference(avatar_split_clause,[],[f666,f4985]) ).
fof(f4985,plain,
( spl0_361
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
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(f4983,plain,
spl0_360,
inference(avatar_split_clause,[],[f663,f4981]) ).
fof(f4981,plain,
( spl0_360
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
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(f4979,plain,
spl0_359,
inference(avatar_split_clause,[],[f661,f4977]) ).
fof(f4977,plain,
( spl0_359
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
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(f4975,plain,
spl0_358,
inference(avatar_split_clause,[],[f659,f4973]) ).
fof(f4973,plain,
( spl0_358
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
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(f4971,plain,
spl0_357,
inference(avatar_split_clause,[],[f656,f4969]) ).
fof(f4969,plain,
( spl0_357
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
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(f4967,plain,
spl0_356,
inference(avatar_split_clause,[],[f655,f4965]) ).
fof(f4965,plain,
( spl0_356
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
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(f4963,plain,
spl0_355,
inference(avatar_split_clause,[],[f654,f4961]) ).
fof(f4961,plain,
( spl0_355
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
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(f4959,plain,
spl0_354,
inference(avatar_split_clause,[],[f653,f4957]) ).
fof(f4957,plain,
( spl0_354
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
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(f4955,plain,
spl0_353,
inference(avatar_split_clause,[],[f651,f4953]) ).
fof(f4953,plain,
( spl0_353
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
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(f4951,plain,
spl0_352,
inference(avatar_split_clause,[],[f650,f4949]) ).
fof(f4949,plain,
( spl0_352
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
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(f4947,plain,
spl0_351,
inference(avatar_split_clause,[],[f649,f4945]) ).
fof(f4945,plain,
( spl0_351
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
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(f4943,plain,
spl0_350,
inference(avatar_split_clause,[],[f648,f4941]) ).
fof(f4941,plain,
( spl0_350
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
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(f4939,plain,
spl0_349,
inference(avatar_split_clause,[],[f647,f4937]) ).
fof(f4937,plain,
( spl0_349
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
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(f4935,plain,
spl0_348,
inference(avatar_split_clause,[],[f646,f4933]) ).
fof(f4933,plain,
( spl0_348
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
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(f4931,plain,
spl0_347,
inference(avatar_split_clause,[],[f645,f4929]) ).
fof(f4929,plain,
( spl0_347
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
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(f4927,plain,
spl0_346,
inference(avatar_split_clause,[],[f644,f4925]) ).
fof(f4925,plain,
( spl0_346
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
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(f4923,plain,
spl0_345,
inference(avatar_split_clause,[],[f643,f4921]) ).
fof(f4921,plain,
( spl0_345
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
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(f4919,plain,
spl0_344,
inference(avatar_split_clause,[],[f607,f4917]) ).
fof(f4917,plain,
( spl0_344
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
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(f4915,plain,
spl0_343,
inference(avatar_split_clause,[],[f606,f4913]) ).
fof(f4913,plain,
( spl0_343
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
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(f4911,plain,
spl0_342,
inference(avatar_split_clause,[],[f605,f4909]) ).
fof(f4909,plain,
( spl0_342
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
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(f4907,plain,
spl0_341,
inference(avatar_split_clause,[],[f604,f4905]) ).
fof(f4905,plain,
( spl0_341
<=> ! [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_341])]) ).
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(f4903,plain,
spl0_340,
inference(avatar_split_clause,[],[f603,f4901]) ).
fof(f4901,plain,
( spl0_340
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
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(f4899,plain,
spl0_339,
inference(avatar_split_clause,[],[f601,f4897]) ).
fof(f4897,plain,
( spl0_339
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
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(f4895,plain,
spl0_338,
inference(avatar_split_clause,[],[f600,f4893]) ).
fof(f4893,plain,
( spl0_338
<=> ! [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_338])]) ).
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(f4891,plain,
spl0_337,
inference(avatar_split_clause,[],[f599,f4889]) ).
fof(f4889,plain,
( spl0_337
<=> ! [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_337])]) ).
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(f4887,plain,
spl0_336,
inference(avatar_split_clause,[],[f598,f4885]) ).
fof(f4885,plain,
( spl0_336
<=> ! [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_336])]) ).
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(f4883,plain,
spl0_335,
inference(avatar_split_clause,[],[f597,f4881]) ).
fof(f4881,plain,
( spl0_335
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
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(f4879,plain,
spl0_334,
inference(avatar_split_clause,[],[f596,f4877]) ).
fof(f4877,plain,
( spl0_334
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
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(f4875,plain,
spl0_333,
inference(avatar_split_clause,[],[f595,f4873]) ).
fof(f4873,plain,
( spl0_333
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
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(f4871,plain,
spl0_332,
inference(avatar_split_clause,[],[f592,f4869]) ).
fof(f4869,plain,
( spl0_332
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
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(f4867,plain,
spl0_331,
inference(avatar_split_clause,[],[f591,f4865]) ).
fof(f4865,plain,
( spl0_331
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
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(f4863,plain,
spl0_330,
inference(avatar_split_clause,[],[f586,f4861]) ).
fof(f4861,plain,
( spl0_330
<=> ! [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_330])]) ).
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(f4859,plain,
spl0_329,
inference(avatar_split_clause,[],[f585,f4857]) ).
fof(f4857,plain,
( spl0_329
<=> ! [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_329])]) ).
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(f4855,plain,
spl0_328,
inference(avatar_split_clause,[],[f582,f4853]) ).
fof(f4853,plain,
( spl0_328
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
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(f4851,plain,
spl0_327,
inference(avatar_split_clause,[],[f581,f4849]) ).
fof(f4849,plain,
( spl0_327
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
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(f4847,plain,
spl0_326,
inference(avatar_split_clause,[],[f579,f4845]) ).
fof(f4845,plain,
( spl0_326
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
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(f4843,plain,
spl0_325,
inference(avatar_split_clause,[],[f578,f4841]) ).
fof(f4841,plain,
( spl0_325
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
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(f4839,plain,
spl0_324,
inference(avatar_split_clause,[],[f577,f4837]) ).
fof(f4837,plain,
( spl0_324
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
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(f4835,plain,
spl0_323,
inference(avatar_split_clause,[],[f576,f4833]) ).
fof(f4833,plain,
( spl0_323
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
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(f4831,plain,
spl0_322,
inference(avatar_split_clause,[],[f575,f4829]) ).
fof(f4829,plain,
( spl0_322
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
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(f4827,plain,
spl0_321,
inference(avatar_split_clause,[],[f574,f4825]) ).
fof(f4825,plain,
( spl0_321
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
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(f4823,plain,
spl0_320,
inference(avatar_split_clause,[],[f570,f4821]) ).
fof(f4821,plain,
( spl0_320
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
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(f4819,plain,
spl0_319,
inference(avatar_split_clause,[],[f568,f4817]) ).
fof(f4817,plain,
( spl0_319
<=> ! [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_319])]) ).
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(f4815,plain,
spl0_318,
inference(avatar_split_clause,[],[f565,f4813]) ).
fof(f4813,plain,
( spl0_318
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
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(f4811,plain,
spl0_317,
inference(avatar_split_clause,[],[f562,f4809]) ).
fof(f4809,plain,
( spl0_317
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
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(f4807,plain,
spl0_316,
inference(avatar_split_clause,[],[f561,f4805]) ).
fof(f4805,plain,
( spl0_316
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
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(f4803,plain,
spl0_315,
inference(avatar_split_clause,[],[f559,f4801]) ).
fof(f4801,plain,
( spl0_315
<=> ! [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_315])]) ).
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(f4799,plain,
spl0_314,
inference(avatar_split_clause,[],[f558,f4797]) ).
fof(f4797,plain,
( spl0_314
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
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(f4795,plain,
spl0_313,
inference(avatar_split_clause,[],[f557,f4793]) ).
fof(f4793,plain,
( spl0_313
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
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(f4791,plain,
spl0_312,
inference(avatar_split_clause,[],[f554,f4789]) ).
fof(f4789,plain,
( spl0_312
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
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(f4787,plain,
spl0_311,
inference(avatar_split_clause,[],[f553,f4785]) ).
fof(f4785,plain,
( spl0_311
<=> ! [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_311])]) ).
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(f4783,plain,
spl0_310,
inference(avatar_split_clause,[],[f551,f4781]) ).
fof(f4781,plain,
( spl0_310
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
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(f4779,plain,
spl0_309,
inference(avatar_split_clause,[],[f545,f4777]) ).
fof(f4777,plain,
( spl0_309
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
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(f4775,plain,
spl0_308,
inference(avatar_split_clause,[],[f544,f4773]) ).
fof(f4773,plain,
( spl0_308
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
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(f4771,plain,
spl0_307,
inference(avatar_split_clause,[],[f542,f4769]) ).
fof(f4769,plain,
( spl0_307
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
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(f4767,plain,
spl0_306,
inference(avatar_split_clause,[],[f541,f4765]) ).
fof(f4765,plain,
( spl0_306
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
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(f4763,plain,
spl0_305,
inference(avatar_split_clause,[],[f534,f4761]) ).
fof(f4761,plain,
( spl0_305
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
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(f4759,plain,
spl0_304,
inference(avatar_split_clause,[],[f533,f4757]) ).
fof(f4757,plain,
( spl0_304
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
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(f4755,plain,
spl0_303,
inference(avatar_split_clause,[],[f531,f4753]) ).
fof(f4753,plain,
( spl0_303
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
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(f4751,plain,
spl0_302,
inference(avatar_split_clause,[],[f530,f4749]) ).
fof(f4749,plain,
( spl0_302
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
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(f4747,plain,
spl0_301,
inference(avatar_split_clause,[],[f529,f4745]) ).
fof(f4745,plain,
( spl0_301
<=> ! [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_301])]) ).
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(f4743,plain,
spl0_300,
inference(avatar_split_clause,[],[f527,f4741]) ).
fof(f4741,plain,
( spl0_300
<=> ! [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_300])]) ).
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(f4739,plain,
spl0_299,
inference(avatar_split_clause,[],[f526,f4737]) ).
fof(f4737,plain,
( spl0_299
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
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(f4735,plain,
spl0_298,
inference(avatar_split_clause,[],[f525,f4733]) ).
fof(f4733,plain,
( spl0_298
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
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(f4731,plain,
spl0_297,
inference(avatar_split_clause,[],[f524,f4729]) ).
fof(f4729,plain,
( spl0_297
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
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(f4727,plain,
spl0_296,
inference(avatar_split_clause,[],[f523,f4725]) ).
fof(f4725,plain,
( spl0_296
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
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(f4723,plain,
spl0_295,
inference(avatar_split_clause,[],[f522,f4721]) ).
fof(f4721,plain,
( spl0_295
<=> ! [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_295])]) ).
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(f4719,plain,
spl0_294,
inference(avatar_split_clause,[],[f521,f4717]) ).
fof(f4717,plain,
( spl0_294
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
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(f4715,plain,
spl0_293,
inference(avatar_split_clause,[],[f520,f4713]) ).
fof(f4713,plain,
( spl0_293
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
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(f4711,plain,
spl0_292,
inference(avatar_split_clause,[],[f519,f4709]) ).
fof(f4709,plain,
( spl0_292
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
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(f4707,plain,
spl0_291,
inference(avatar_split_clause,[],[f518,f4705]) ).
fof(f4705,plain,
( spl0_291
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
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(f4703,plain,
spl0_290,
inference(avatar_split_clause,[],[f515,f4701]) ).
fof(f4701,plain,
( spl0_290
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
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(f4699,plain,
spl0_289,
inference(avatar_split_clause,[],[f513,f4697]) ).
fof(f4697,plain,
( spl0_289
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
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(f4695,plain,
spl0_288,
inference(avatar_split_clause,[],[f511,f4693]) ).
fof(f4693,plain,
( spl0_288
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
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(f4691,plain,
spl0_287,
inference(avatar_split_clause,[],[f508,f4689]) ).
fof(f4689,plain,
( spl0_287
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
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(f4687,plain,
spl0_286,
inference(avatar_split_clause,[],[f507,f4685]) ).
fof(f4685,plain,
( spl0_286
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
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(f4683,plain,
spl0_285,
inference(avatar_split_clause,[],[f506,f4681]) ).
fof(f4681,plain,
( spl0_285
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
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(f4679,plain,
spl0_284,
inference(avatar_split_clause,[],[f503,f4677]) ).
fof(f4677,plain,
( spl0_284
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
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(f4675,plain,
spl0_283,
inference(avatar_split_clause,[],[f500,f4673]) ).
fof(f4673,plain,
( spl0_283
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
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(f4671,plain,
spl0_282,
inference(avatar_split_clause,[],[f499,f4669]) ).
fof(f4669,plain,
( spl0_282
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
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(f4667,plain,
spl0_281,
inference(avatar_split_clause,[],[f497,f4665]) ).
fof(f4665,plain,
( spl0_281
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
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(f4663,plain,
spl0_280,
inference(avatar_split_clause,[],[f496,f4661]) ).
fof(f4661,plain,
( spl0_280
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
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(f4659,plain,
spl0_279,
inference(avatar_split_clause,[],[f495,f4657]) ).
fof(f4657,plain,
( spl0_279
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
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(f4655,plain,
spl0_278,
inference(avatar_split_clause,[],[f494,f4653]) ).
fof(f4653,plain,
( spl0_278
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
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(f4651,plain,
spl0_277,
inference(avatar_split_clause,[],[f493,f4649]) ).
fof(f4649,plain,
( spl0_277
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
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(f4647,plain,
spl0_276,
inference(avatar_split_clause,[],[f491,f4645]) ).
fof(f4645,plain,
( spl0_276
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
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(f4643,plain,
spl0_275,
inference(avatar_split_clause,[],[f488,f4641]) ).
fof(f4641,plain,
( spl0_275
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
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(f4639,plain,
spl0_274,
inference(avatar_split_clause,[],[f487,f4637]) ).
fof(f4637,plain,
( spl0_274
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
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(f4635,plain,
spl0_273,
inference(avatar_split_clause,[],[f483,f4633]) ).
fof(f4633,plain,
( spl0_273
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
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(f4631,plain,
spl0_272,
inference(avatar_split_clause,[],[f481,f4629]) ).
fof(f4629,plain,
( spl0_272
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
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(f4627,plain,
spl0_271,
inference(avatar_split_clause,[],[f473,f4625]) ).
fof(f4625,plain,
( spl0_271
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
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(f4623,plain,
spl0_270,
inference(avatar_split_clause,[],[f472,f4621]) ).
fof(f4621,plain,
( spl0_270
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
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(f4619,plain,
spl0_269,
inference(avatar_split_clause,[],[f471,f4617]) ).
fof(f4617,plain,
( spl0_269
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
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(f4615,plain,
spl0_268,
inference(avatar_split_clause,[],[f470,f4613]) ).
fof(f4613,plain,
( spl0_268
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
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(f4611,plain,
spl0_267,
inference(avatar_split_clause,[],[f469,f4609]) ).
fof(f4609,plain,
( spl0_267
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
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(f4607,plain,
spl0_266,
inference(avatar_split_clause,[],[f468,f4605]) ).
fof(f4605,plain,
( spl0_266
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
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(f4603,plain,
spl0_265,
inference(avatar_split_clause,[],[f467,f4601]) ).
fof(f4601,plain,
( spl0_265
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f467,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4599,plain,
spl0_264,
inference(avatar_split_clause,[],[f466,f4597]) ).
fof(f4597,plain,
( spl0_264
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
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(f4595,plain,
spl0_263,
inference(avatar_split_clause,[],[f465,f4593]) ).
fof(f4593,plain,
( spl0_263
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
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(f4591,plain,
spl0_262,
inference(avatar_split_clause,[],[f464,f4589]) ).
fof(f4589,plain,
( spl0_262
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
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(f4587,plain,
spl0_261,
inference(avatar_split_clause,[],[f463,f4585]) ).
fof(f4585,plain,
( spl0_261
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
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(f4583,plain,
spl0_260,
inference(avatar_split_clause,[],[f462,f4581]) ).
fof(f4581,plain,
( spl0_260
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
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(f4579,plain,
spl0_259,
inference(avatar_split_clause,[],[f461,f4577]) ).
fof(f4577,plain,
( spl0_259
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
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(f4575,plain,
spl0_258,
inference(avatar_split_clause,[],[f460,f4573]) ).
fof(f4573,plain,
( spl0_258
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
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(f4571,plain,
spl0_257,
inference(avatar_split_clause,[],[f459,f4569]) ).
fof(f4569,plain,
( spl0_257
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
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(f4567,plain,
spl0_256,
inference(avatar_split_clause,[],[f458,f4565]) ).
fof(f4565,plain,
( spl0_256
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
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(f4563,plain,
spl0_255,
inference(avatar_split_clause,[],[f457,f4561]) ).
fof(f4561,plain,
( spl0_255
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
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(f4559,plain,
spl0_254,
inference(avatar_split_clause,[],[f454,f4557]) ).
fof(f4557,plain,
( spl0_254
<=> ! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f454,axiom,
! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4555,plain,
spl0_253,
inference(avatar_split_clause,[],[f453,f4553]) ).
fof(f4553,plain,
( spl0_253
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f453,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4551,plain,
spl0_252,
inference(avatar_split_clause,[],[f452,f4549]) ).
fof(f4549,plain,
( spl0_252
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f452,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4547,plain,
spl0_251,
inference(avatar_split_clause,[],[f451,f4545]) ).
fof(f4545,plain,
( spl0_251
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
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(f4543,plain,
spl0_250,
inference(avatar_split_clause,[],[f450,f4541]) ).
fof(f4541,plain,
( spl0_250
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
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(f4539,plain,
spl0_249,
inference(avatar_split_clause,[],[f449,f4537]) ).
fof(f4537,plain,
( spl0_249
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f449,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4535,plain,
spl0_248,
inference(avatar_split_clause,[],[f446,f4533]) ).
fof(f4533,plain,
( spl0_248
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
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(f4531,plain,
spl0_247,
inference(avatar_split_clause,[],[f445,f4529]) ).
fof(f4529,plain,
( spl0_247
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
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(f4527,plain,
spl0_246,
inference(avatar_split_clause,[],[f441,f4525]) ).
fof(f4525,plain,
( spl0_246
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
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(f4523,plain,
spl0_245,
inference(avatar_split_clause,[],[f440,f4521]) ).
fof(f4521,plain,
( spl0_245
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
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(f4519,plain,
spl0_244,
inference(avatar_split_clause,[],[f439,f4517]) ).
fof(f4517,plain,
( spl0_244
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
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(f4515,plain,
spl0_243,
inference(avatar_split_clause,[],[f436,f4513]) ).
fof(f4513,plain,
( spl0_243
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
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(f4511,plain,
spl0_242,
inference(avatar_split_clause,[],[f434,f4509]) ).
fof(f4509,plain,
( spl0_242
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
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(f4507,plain,
spl0_241,
inference(avatar_split_clause,[],[f433,f4505]) ).
fof(f4505,plain,
( spl0_241
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
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(f4503,plain,
spl0_240,
inference(avatar_split_clause,[],[f432,f4501]) ).
fof(f4501,plain,
( spl0_240
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
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(f4499,plain,
spl0_239,
inference(avatar_split_clause,[],[f431,f4497]) ).
fof(f4497,plain,
( spl0_239
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
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(f4495,plain,
spl0_238,
inference(avatar_split_clause,[],[f430,f4493]) ).
fof(f4493,plain,
( spl0_238
<=> ! [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_238])]) ).
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(f4491,plain,
spl0_237,
inference(avatar_split_clause,[],[f426,f4489]) ).
fof(f4489,plain,
( spl0_237
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
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(f4487,plain,
spl0_236,
inference(avatar_split_clause,[],[f425,f4485]) ).
fof(f4485,plain,
( spl0_236
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
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(f4483,plain,
spl0_235,
inference(avatar_split_clause,[],[f424,f4481]) ).
fof(f4481,plain,
( spl0_235
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
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(f4479,plain,
spl0_234,
inference(avatar_split_clause,[],[f421,f4477]) ).
fof(f4477,plain,
( spl0_234
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
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(f4475,plain,
spl0_233,
inference(avatar_split_clause,[],[f419,f4473]) ).
fof(f4473,plain,
( spl0_233
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
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(f4471,plain,
spl0_232,
inference(avatar_split_clause,[],[f417,f4469]) ).
fof(f4469,plain,
( spl0_232
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
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(f4467,plain,
spl0_231,
inference(avatar_split_clause,[],[f416,f4465]) ).
fof(f4465,plain,
( spl0_231
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
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(f4463,plain,
spl0_230,
inference(avatar_split_clause,[],[f415,f4461]) ).
fof(f4461,plain,
( spl0_230
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
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(f4459,plain,
spl0_229,
inference(avatar_split_clause,[],[f414,f4457]) ).
fof(f4457,plain,
( spl0_229
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
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(f4455,plain,
spl0_228,
inference(avatar_split_clause,[],[f413,f4453]) ).
fof(f4453,plain,
( spl0_228
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
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(f4451,plain,
spl0_227,
inference(avatar_split_clause,[],[f411,f4449]) ).
fof(f4449,plain,
( spl0_227
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
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(f4447,plain,
spl0_226,
inference(avatar_split_clause,[],[f410,f4445]) ).
fof(f4445,plain,
( spl0_226
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
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(f4443,plain,
spl0_225,
inference(avatar_split_clause,[],[f407,f4441]) ).
fof(f4441,plain,
( spl0_225
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
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(f4439,plain,
spl0_224,
inference(avatar_split_clause,[],[f405,f4437]) ).
fof(f4437,plain,
( spl0_224
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
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(f4435,plain,
spl0_223,
inference(avatar_split_clause,[],[f404,f4433]) ).
fof(f4433,plain,
( spl0_223
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
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(f4431,plain,
spl0_222,
inference(avatar_split_clause,[],[f403,f4429]) ).
fof(f4429,plain,
( spl0_222
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
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(f4427,plain,
spl0_221,
inference(avatar_split_clause,[],[f402,f4425]) ).
fof(f4425,plain,
( spl0_221
<=> ! [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_221])]) ).
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(f4423,plain,
spl0_220,
inference(avatar_split_clause,[],[f401,f4421]) ).
fof(f4421,plain,
( spl0_220
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
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(f4419,plain,
spl0_219,
inference(avatar_split_clause,[],[f400,f4417]) ).
fof(f4417,plain,
( spl0_219
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
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(f4415,plain,
spl0_218,
inference(avatar_split_clause,[],[f399,f4413]) ).
fof(f4413,plain,
( spl0_218
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
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(f4411,plain,
spl0_217,
inference(avatar_split_clause,[],[f398,f4409]) ).
fof(f4409,plain,
( spl0_217
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
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(f4407,plain,
spl0_216,
inference(avatar_split_clause,[],[f397,f4405]) ).
fof(f4405,plain,
( spl0_216
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
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(f4403,plain,
spl0_215,
inference(avatar_split_clause,[],[f394,f4401]) ).
fof(f4401,plain,
( spl0_215
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
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(f4399,plain,
spl0_214,
inference(avatar_split_clause,[],[f393,f4397]) ).
fof(f4397,plain,
( spl0_214
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
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(f4395,plain,
spl0_213,
inference(avatar_split_clause,[],[f392,f4393]) ).
fof(f4393,plain,
( spl0_213
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
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(f4391,plain,
spl0_212,
inference(avatar_split_clause,[],[f391,f4389]) ).
fof(f4389,plain,
( spl0_212
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
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(f4387,plain,
spl0_211,
inference(avatar_split_clause,[],[f390,f4385]) ).
fof(f4385,plain,
( spl0_211
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
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(f4383,plain,
spl0_210,
inference(avatar_split_clause,[],[f389,f4381]) ).
fof(f4381,plain,
( spl0_210
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
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(f4379,plain,
spl0_209,
inference(avatar_split_clause,[],[f387,f4377]) ).
fof(f4377,plain,
( spl0_209
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
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(f4375,plain,
spl0_208,
inference(avatar_split_clause,[],[f385,f4373]) ).
fof(f4373,plain,
( spl0_208
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
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(f4371,plain,
spl0_207,
inference(avatar_split_clause,[],[f384,f4369]) ).
fof(f4369,plain,
( spl0_207
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
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(f4367,plain,
spl0_206,
inference(avatar_split_clause,[],[f383,f4365]) ).
fof(f4365,plain,
( spl0_206
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
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(f4363,plain,
spl0_205,
inference(avatar_split_clause,[],[f382,f4361]) ).
fof(f4361,plain,
( spl0_205
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
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(f4359,plain,
spl0_204,
inference(avatar_split_clause,[],[f379,f4357]) ).
fof(f4357,plain,
( spl0_204
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
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(f4355,plain,
spl0_203,
inference(avatar_split_clause,[],[f377,f4353]) ).
fof(f4353,plain,
( spl0_203
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
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(f4351,plain,
spl0_202,
inference(avatar_split_clause,[],[f376,f4349]) ).
fof(f4349,plain,
( spl0_202
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
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(f4347,plain,
spl0_201,
inference(avatar_split_clause,[],[f375,f4345]) ).
fof(f4345,plain,
( spl0_201
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
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(f4343,plain,
spl0_200,
inference(avatar_split_clause,[],[f374,f4341]) ).
fof(f4341,plain,
( spl0_200
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
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(f4339,plain,
spl0_199,
inference(avatar_split_clause,[],[f373,f4337]) ).
fof(f4337,plain,
( spl0_199
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
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(f4335,plain,
spl0_198,
inference(avatar_split_clause,[],[f372,f4333]) ).
fof(f4333,plain,
( spl0_198
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
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(f4331,plain,
spl0_197,
inference(avatar_split_clause,[],[f371,f4329]) ).
fof(f4329,plain,
( spl0_197
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
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(f4327,plain,
spl0_196,
inference(avatar_split_clause,[],[f370,f4325]) ).
fof(f4325,plain,
( spl0_196
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
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(f4323,plain,
spl0_195,
inference(avatar_split_clause,[],[f368,f4321]) ).
fof(f4321,plain,
( spl0_195
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
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(f4319,plain,
spl0_194,
inference(avatar_split_clause,[],[f366,f4317]) ).
fof(f4317,plain,
( spl0_194
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
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(f4315,plain,
spl0_193,
inference(avatar_split_clause,[],[f365,f4313]) ).
fof(f4313,plain,
( spl0_193
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
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(f4311,plain,
spl0_192,
inference(avatar_split_clause,[],[f364,f4309]) ).
fof(f4309,plain,
( spl0_192
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
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(f4307,plain,
spl0_191,
inference(avatar_split_clause,[],[f363,f4305]) ).
fof(f4305,plain,
( spl0_191
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
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(f4303,plain,
spl0_190,
inference(avatar_split_clause,[],[f360,f4301]) ).
fof(f4301,plain,
( spl0_190
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
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(f4299,plain,
spl0_189,
inference(avatar_split_clause,[],[f358,f4297]) ).
fof(f4297,plain,
( spl0_189
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
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(f4295,plain,
spl0_188,
inference(avatar_split_clause,[],[f357,f4293]) ).
fof(f4293,plain,
( spl0_188
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
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(f4291,plain,
spl0_187,
inference(avatar_split_clause,[],[f356,f4289]) ).
fof(f4289,plain,
( spl0_187
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
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(f4287,plain,
spl0_186,
inference(avatar_split_clause,[],[f355,f4285]) ).
fof(f4285,plain,
( spl0_186
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
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(f4283,plain,
spl0_185,
inference(avatar_split_clause,[],[f354,f4281]) ).
fof(f4281,plain,
( spl0_185
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
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(f4279,plain,
spl0_184,
inference(avatar_split_clause,[],[f353,f4277]) ).
fof(f4277,plain,
( spl0_184
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
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(f4275,plain,
spl0_183,
inference(avatar_split_clause,[],[f352,f4273]) ).
fof(f4273,plain,
( spl0_183
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
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(f4271,plain,
spl0_182,
inference(avatar_split_clause,[],[f350,f4269]) ).
fof(f4269,plain,
( spl0_182
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
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(f4267,plain,
spl0_181,
inference(avatar_split_clause,[],[f348,f4265]) ).
fof(f4265,plain,
( spl0_181
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
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(f4263,plain,
spl0_180,
inference(avatar_split_clause,[],[f347,f4261]) ).
fof(f4261,plain,
( spl0_180
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
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(f4259,plain,
spl0_179,
inference(avatar_split_clause,[],[f346,f4257]) ).
fof(f4257,plain,
( spl0_179
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
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(f4255,plain,
spl0_178,
inference(avatar_split_clause,[],[f345,f4253]) ).
fof(f4253,plain,
( spl0_178
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
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(f4251,plain,
spl0_177,
inference(avatar_split_clause,[],[f344,f4249]) ).
fof(f4249,plain,
( spl0_177
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
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(f4247,plain,
spl0_176,
inference(avatar_split_clause,[],[f343,f4245]) ).
fof(f4245,plain,
( spl0_176
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
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(f4243,plain,
spl0_175,
inference(avatar_split_clause,[],[f340,f4241]) ).
fof(f4241,plain,
( spl0_175
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
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(f4239,plain,
spl0_174,
inference(avatar_split_clause,[],[f338,f4237]) ).
fof(f4237,plain,
( spl0_174
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
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(f4235,plain,
spl0_173,
inference(avatar_split_clause,[],[f337,f4233]) ).
fof(f4233,plain,
( spl0_173
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
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(f4231,plain,
spl0_172,
inference(avatar_split_clause,[],[f336,f4229]) ).
fof(f4229,plain,
( spl0_172
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
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(f4227,plain,
spl0_171,
inference(avatar_split_clause,[],[f335,f4225]) ).
fof(f4225,plain,
( spl0_171
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
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(f4223,plain,
spl0_170,
inference(avatar_split_clause,[],[f334,f4221]) ).
fof(f4221,plain,
( spl0_170
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
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(f4219,plain,
spl0_169,
inference(avatar_split_clause,[],[f333,f4217]) ).
fof(f4217,plain,
( spl0_169
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
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(f4215,plain,
spl0_168,
inference(avatar_split_clause,[],[f332,f4213]) ).
fof(f4213,plain,
( spl0_168
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
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(f4211,plain,
spl0_167,
inference(avatar_split_clause,[],[f330,f4209]) ).
fof(f4209,plain,
( spl0_167
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
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(f4207,plain,
spl0_166,
inference(avatar_split_clause,[],[f328,f4205]) ).
fof(f4205,plain,
( spl0_166
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
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(f4203,plain,
spl0_165,
inference(avatar_split_clause,[],[f327,f4201]) ).
fof(f4201,plain,
( spl0_165
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
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(f4199,plain,
spl0_164,
inference(avatar_split_clause,[],[f326,f4197]) ).
fof(f4197,plain,
( spl0_164
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
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(f4195,plain,
spl0_163,
inference(avatar_split_clause,[],[f323,f4193]) ).
fof(f4193,plain,
( spl0_163
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
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(f4191,plain,
spl0_162,
inference(avatar_split_clause,[],[f321,f4189]) ).
fof(f4189,plain,
( spl0_162
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
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(f4187,plain,
spl0_161,
inference(avatar_split_clause,[],[f320,f4185]) ).
fof(f4185,plain,
( spl0_161
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
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(f4183,plain,
spl0_160,
inference(avatar_split_clause,[],[f319,f4181]) ).
fof(f4181,plain,
( spl0_160
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
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(f4179,plain,
spl0_159,
inference(avatar_split_clause,[],[f318,f4177]) ).
fof(f4177,plain,
( spl0_159
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
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(f4175,plain,
spl0_158,
inference(avatar_split_clause,[],[f314,f4173]) ).
fof(f4173,plain,
( spl0_158
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
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(f4171,plain,
spl0_157,
inference(avatar_split_clause,[],[f307,f4169]) ).
fof(f4169,plain,
( spl0_157
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
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(f4167,plain,
spl0_156,
inference(avatar_split_clause,[],[f299,f4165]) ).
fof(f4165,plain,
( spl0_156
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
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(f4163,plain,
spl0_155,
inference(avatar_split_clause,[],[f298,f4161]) ).
fof(f4161,plain,
( spl0_155
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
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(f4159,plain,
spl0_154,
inference(avatar_split_clause,[],[f293,f4157]) ).
fof(f4157,plain,
( spl0_154
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
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(f4155,plain,
spl0_153,
inference(avatar_split_clause,[],[f291,f4153]) ).
fof(f4153,plain,
( spl0_153
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
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(f4151,plain,
spl0_152,
inference(avatar_split_clause,[],[f289,f4149]) ).
fof(f4149,plain,
( spl0_152
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
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(f4147,plain,
spl0_151,
inference(avatar_split_clause,[],[f288,f4145]) ).
fof(f4145,plain,
( spl0_151
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
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(f4143,plain,
spl0_150,
inference(avatar_split_clause,[],[f285,f4141]) ).
fof(f4141,plain,
( spl0_150
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
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(f4139,plain,
spl0_149,
inference(avatar_split_clause,[],[f283,f4137]) ).
fof(f4137,plain,
( spl0_149
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
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(f4135,plain,
spl0_148,
inference(avatar_split_clause,[],[f282,f4133]) ).
fof(f4133,plain,
( spl0_148
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
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(f4131,plain,
spl0_147,
inference(avatar_split_clause,[],[f281,f4129]) ).
fof(f4129,plain,
( spl0_147
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
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(f4127,plain,
spl0_146,
inference(avatar_split_clause,[],[f280,f4125]) ).
fof(f4125,plain,
( spl0_146
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
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(f4123,plain,
spl0_145,
inference(avatar_split_clause,[],[f279,f4121]) ).
fof(f4121,plain,
( spl0_145
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
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(f4119,plain,
spl0_144,
inference(avatar_split_clause,[],[f278,f4117]) ).
fof(f4117,plain,
( spl0_144
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
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(f4115,plain,
spl0_143,
inference(avatar_split_clause,[],[f277,f4113]) ).
fof(f4113,plain,
( spl0_143
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
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(f4111,plain,
spl0_142,
inference(avatar_split_clause,[],[f276,f4109]) ).
fof(f4109,plain,
( spl0_142
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
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(f4107,plain,
spl0_141,
inference(avatar_split_clause,[],[f275,f4105]) ).
fof(f4105,plain,
( spl0_141
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
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(f4103,plain,
spl0_140,
inference(avatar_split_clause,[],[f274,f4101]) ).
fof(f4101,plain,
( spl0_140
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
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(f4099,plain,
spl0_139,
inference(avatar_split_clause,[],[f272,f4097]) ).
fof(f4097,plain,
( spl0_139
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
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(f4095,plain,
spl0_138,
inference(avatar_split_clause,[],[f271,f4093]) ).
fof(f4093,plain,
( spl0_138
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
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(f4091,plain,
spl0_137,
inference(avatar_split_clause,[],[f270,f4089]) ).
fof(f4089,plain,
( spl0_137
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
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(f4087,plain,
spl0_136,
inference(avatar_split_clause,[],[f269,f4085]) ).
fof(f4085,plain,
( spl0_136
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
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(f4083,plain,
spl0_135,
inference(avatar_split_clause,[],[f268,f4081]) ).
fof(f4081,plain,
( spl0_135
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
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(f4079,plain,
spl0_134,
inference(avatar_split_clause,[],[f267,f4077]) ).
fof(f4077,plain,
( spl0_134
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
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(f4075,plain,
spl0_133,
inference(avatar_split_clause,[],[f266,f4073]) ).
fof(f4073,plain,
( spl0_133
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
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(f4071,plain,
spl0_132,
inference(avatar_split_clause,[],[f264,f4069]) ).
fof(f4069,plain,
( spl0_132
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
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(f4067,plain,
spl0_131,
inference(avatar_split_clause,[],[f263,f4065]) ).
fof(f4065,plain,
( spl0_131
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
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(f4063,plain,
spl0_130,
inference(avatar_split_clause,[],[f260,f4061]) ).
fof(f4061,plain,
( spl0_130
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
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(f4059,plain,
spl0_129,
inference(avatar_split_clause,[],[f259,f4057]) ).
fof(f4057,plain,
( spl0_129
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
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(f4055,plain,
spl0_128,
inference(avatar_split_clause,[],[f258,f4053]) ).
fof(f4053,plain,
( spl0_128
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
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(f4051,plain,
spl0_127,
inference(avatar_split_clause,[],[f257,f4049]) ).
fof(f4049,plain,
( spl0_127
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f257,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f4047,plain,
spl0_126,
inference(avatar_split_clause,[],[f256,f4045]) ).
fof(f4045,plain,
( spl0_126
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f256,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f4043,plain,
spl0_125,
inference(avatar_split_clause,[],[f255,f4041]) ).
fof(f4041,plain,
( spl0_125
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
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(f4039,plain,
spl0_124,
inference(avatar_split_clause,[],[f254,f4037]) ).
fof(f4037,plain,
( spl0_124
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
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(f4035,plain,
spl0_123,
inference(avatar_split_clause,[],[f253,f4033]) ).
fof(f4033,plain,
( spl0_123
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
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(f4031,plain,
spl0_122,
inference(avatar_split_clause,[],[f98,f4029]) ).
fof(f98,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f4027,plain,
spl0_121,
inference(avatar_split_clause,[],[f66,f4025]) ).
fof(f66,axiom,
! [X21] : ~ c_less(X21,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f4023,plain,
spl0_120,
inference(avatar_split_clause,[],[f64,f4021]) ).
fof(f64,axiom,
! [X21] : c_lessequals(c_0,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f4019,plain,
spl0_119,
inference(avatar_split_clause,[],[f40,f4017]) ).
fof(f4017,plain,
( spl0_119
<=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
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(f4015,plain,
spl0_118,
inference(avatar_split_clause,[],[f39,f4013]) ).
fof(f4013,plain,
( spl0_118
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
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(f4011,plain,
spl0_117,
inference(avatar_split_clause,[],[f23,f4009]) ).
fof(f4009,plain,
( spl0_117
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
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(f4007,plain,
spl0_116,
inference(avatar_split_clause,[],[f2974,f4005]) ).
fof(f2974,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_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f4003,plain,
~ spl0_115,
inference(avatar_split_clause,[],[f2903,f4000]) ).
fof(f4000,plain,
( spl0_115
<=> c_Public_Okeymode_OSignature = c_Public_Okeymode_OEncryption ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f2903,axiom,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Okeymode_Odistinct__1_0) ).
fof(f3998,plain,
~ spl0_114,
inference(avatar_split_clause,[],[f2733,f3995]) ).
fof(f3995,plain,
( spl0_114
<=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
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(f3993,plain,
~ spl0_113,
inference(avatar_split_clause,[],[f2629,f3990]) ).
fof(f3990,plain,
( spl0_113
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f2629,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3988,plain,
~ spl0_112,
inference(avatar_split_clause,[],[f2310,f3985]) ).
fof(f3985,plain,
( spl0_112
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2310,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3983,plain,
spl0_111,
inference(avatar_split_clause,[],[f2303,f3980]) ).
fof(f3980,plain,
( spl0_111
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3978,plain,
spl0_110,
inference(avatar_split_clause,[],[f2290,f3975]) ).
fof(f3975,plain,
( spl0_110
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3973,plain,
~ spl0_109,
inference(avatar_split_clause,[],[f2159,f3970]) ).
fof(f3970,plain,
( spl0_109
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
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(f3968,plain,
spl0_108,
inference(avatar_split_clause,[],[f1706,f3966]) ).
fof(f3966,plain,
( spl0_108
<=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
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(f3964,plain,
spl0_107,
inference(avatar_split_clause,[],[f1551,f3962]) ).
fof(f3962,plain,
( spl0_107
<=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
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(f3960,plain,
~ spl0_106,
inference(avatar_split_clause,[],[f1370,f3957]) ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3955,plain,
~ spl0_105,
inference(avatar_split_clause,[],[f1251,f3952]) ).
fof(f3952,plain,
( spl0_105
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1251,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2_0) ).
fof(f3950,plain,
spl0_104,
inference(avatar_split_clause,[],[f249,f3948]) ).
fof(f3948,plain,
( spl0_104
<=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f249,axiom,
! [X37] : class_Orderings_Oorder(tc_set(X37)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3946,plain,
spl0_103,
inference(avatar_split_clause,[],[f248,f3944]) ).
fof(f3944,plain,
( spl0_103
<=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f248,axiom,
! [X37] : class_Orderings_Oord(tc_set(X37)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3942,plain,
spl0_102,
inference(avatar_split_clause,[],[f126,f3939]) ).
fof(f3939,plain,
( spl0_102
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
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(f3937,plain,
spl0_101,
inference(avatar_split_clause,[],[f124,f3934]) ).
fof(f3934,plain,
( spl0_101
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
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(f3932,plain,
spl0_100,
inference(avatar_split_clause,[],[f123,f3930]) ).
fof(f3930,plain,
( spl0_100
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
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(f3928,plain,
spl0_99,
inference(avatar_split_clause,[],[f244,f3925]) ).
fof(f3925,plain,
( spl0_99
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f244,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3923,plain,
spl0_98,
inference(avatar_split_clause,[],[f243,f3920]) ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3918,plain,
spl0_97,
inference(avatar_split_clause,[],[f242,f3915]) ).
fof(f3915,plain,
( spl0_97
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f242,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3913,plain,
spl0_96,
inference(avatar_split_clause,[],[f241,f3910]) ).
fof(f241,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3908,plain,
spl0_95,
inference(avatar_split_clause,[],[f239,f3905]) ).
fof(f3905,plain,
( spl0_95
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f239,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3903,plain,
spl0_94,
inference(avatar_split_clause,[],[f238,f3900]) ).
fof(f238,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3898,plain,
spl0_93,
inference(avatar_split_clause,[],[f236,f3895]) ).
fof(f3895,plain,
( spl0_93
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3893,plain,
spl0_92,
inference(avatar_split_clause,[],[f235,f3890]) ).
fof(f3890,plain,
( spl0_92
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f235,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3888,plain,
spl0_91,
inference(avatar_split_clause,[],[f234,f3885]) ).
fof(f3885,plain,
( spl0_91
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f234,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3883,plain,
spl0_90,
inference(avatar_split_clause,[],[f233,f3880]) ).
fof(f3880,plain,
( spl0_90
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f233,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3878,plain,
spl0_89,
inference(avatar_split_clause,[],[f232,f3875]) ).
fof(f232,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3873,plain,
spl0_88,
inference(avatar_split_clause,[],[f231,f3870]) ).
fof(f3870,plain,
( spl0_88
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f231,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3868,plain,
spl0_87,
inference(avatar_split_clause,[],[f230,f3865]) ).
fof(f3865,plain,
( spl0_87
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f230,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3863,plain,
spl0_86,
inference(avatar_split_clause,[],[f229,f3860]) ).
fof(f3860,plain,
( spl0_86
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f229,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3858,plain,
spl0_85,
inference(avatar_split_clause,[],[f228,f3855]) ).
fof(f3855,plain,
( spl0_85
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3853,plain,
spl0_84,
inference(avatar_split_clause,[],[f227,f3850]) ).
fof(f3850,plain,
( spl0_84
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3848,plain,
spl0_83,
inference(avatar_split_clause,[],[f226,f3845]) ).
fof(f3845,plain,
( spl0_83
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f226,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3843,plain,
spl0_82,
inference(avatar_split_clause,[],[f225,f3840]) ).
fof(f3840,plain,
( spl0_82
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f225,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3838,plain,
spl0_81,
inference(avatar_split_clause,[],[f224,f3835]) ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3833,plain,
spl0_80,
inference(avatar_split_clause,[],[f223,f3830]) ).
fof(f3830,plain,
( spl0_80
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f223,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3828,plain,
spl0_79,
inference(avatar_split_clause,[],[f222,f3825]) ).
fof(f3825,plain,
( spl0_79
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f222,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3823,plain,
spl0_78,
inference(avatar_split_clause,[],[f221,f3820]) ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3818,plain,
spl0_77,
inference(avatar_split_clause,[],[f220,f3815]) ).
fof(f3815,plain,
( spl0_77
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f220,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3813,plain,
spl0_76,
inference(avatar_split_clause,[],[f219,f3810]) ).
fof(f3810,plain,
( spl0_76
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f219,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3808,plain,
spl0_75,
inference(avatar_split_clause,[],[f218,f3805]) ).
fof(f3805,plain,
( spl0_75
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f218,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3803,plain,
spl0_74,
inference(avatar_split_clause,[],[f217,f3800]) ).
fof(f3800,plain,
( spl0_74
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f217,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3798,plain,
spl0_73,
inference(avatar_split_clause,[],[f216,f3795]) ).
fof(f3795,plain,
( spl0_73
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f216,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3793,plain,
spl0_72,
inference(avatar_split_clause,[],[f215,f3790]) ).
fof(f3790,plain,
( spl0_72
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f215,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3788,plain,
spl0_71,
inference(avatar_split_clause,[],[f214,f3785]) ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3783,plain,
spl0_70,
inference(avatar_split_clause,[],[f213,f3780]) ).
fof(f3780,plain,
( spl0_70
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f213,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3778,plain,
spl0_69,
inference(avatar_split_clause,[],[f212,f3775]) ).
fof(f3775,plain,
( spl0_69
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f212,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3773,plain,
spl0_68,
inference(avatar_split_clause,[],[f211,f3770]) ).
fof(f3770,plain,
( spl0_68
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3768,plain,
spl0_67,
inference(avatar_split_clause,[],[f210,f3765]) ).
fof(f3765,plain,
( spl0_67
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3763,plain,
spl0_66,
inference(avatar_split_clause,[],[f209,f3760]) ).
fof(f3760,plain,
( spl0_66
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f209,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3758,plain,
spl0_65,
inference(avatar_split_clause,[],[f208,f3755]) ).
fof(f3755,plain,
( spl0_65
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f208,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3753,plain,
spl0_64,
inference(avatar_split_clause,[],[f203,f3750]) ).
fof(f3750,plain,
( spl0_64
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3748,plain,
spl0_63,
inference(avatar_split_clause,[],[f198,f3745]) ).
fof(f3745,plain,
( spl0_63
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f198,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3743,plain,
spl0_62,
inference(avatar_split_clause,[],[f195,f3740]) ).
fof(f3740,plain,
( spl0_62
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f195,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3738,plain,
spl0_61,
inference(avatar_split_clause,[],[f194,f3735]) ).
fof(f3735,plain,
( spl0_61
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f194,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3733,plain,
spl0_60,
inference(avatar_split_clause,[],[f189,f3730]) ).
fof(f189,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3728,plain,
spl0_59,
inference(avatar_split_clause,[],[f186,f3725]) ).
fof(f186,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3723,plain,
spl0_58,
inference(avatar_split_clause,[],[f184,f3720]) ).
fof(f3720,plain,
( spl0_58
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f184,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3718,plain,
spl0_57,
inference(avatar_split_clause,[],[f183,f3715]) ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3713,plain,
spl0_56,
inference(avatar_split_clause,[],[f182,f3710]) ).
fof(f3710,plain,
( spl0_56
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f182,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3708,plain,
spl0_55,
inference(avatar_split_clause,[],[f181,f3705]) ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3703,plain,
spl0_54,
inference(avatar_split_clause,[],[f180,f3700]) ).
fof(f3700,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
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(f3698,plain,
spl0_53,
inference(avatar_split_clause,[],[f178,f3695]) ).
fof(f3695,plain,
( spl0_53
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f178,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3693,plain,
spl0_52,
inference(avatar_split_clause,[],[f177,f3690]) ).
fof(f3690,plain,
( spl0_52
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f177,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3688,plain,
spl0_51,
inference(avatar_split_clause,[],[f176,f3685]) ).
fof(f3685,plain,
( spl0_51
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f176,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3683,plain,
spl0_50,
inference(avatar_split_clause,[],[f175,f3680]) ).
fof(f175,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3678,plain,
spl0_49,
inference(avatar_split_clause,[],[f174,f3675]) ).
fof(f3675,plain,
( spl0_49
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f174,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3673,plain,
spl0_48,
inference(avatar_split_clause,[],[f173,f3670]) ).
fof(f3670,plain,
( spl0_48
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f173,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3668,plain,
spl0_47,
inference(avatar_split_clause,[],[f172,f3665]) ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3663,plain,
spl0_46,
inference(avatar_split_clause,[],[f171,f3660]) ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3658,plain,
spl0_45,
inference(avatar_split_clause,[],[f170,f3655]) ).
fof(f3655,plain,
( spl0_45
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
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(f3653,plain,
spl0_44,
inference(avatar_split_clause,[],[f169,f3650]) ).
fof(f3650,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
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(f3648,plain,
spl0_43,
inference(avatar_split_clause,[],[f168,f3645]) ).
fof(f3645,plain,
( spl0_43
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
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(f3643,plain,
spl0_42,
inference(avatar_split_clause,[],[f167,f3640]) ).
fof(f3640,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
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(f3638,plain,
spl0_41,
inference(avatar_split_clause,[],[f166,f3635]) ).
fof(f3635,plain,
( spl0_41
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
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(f3633,plain,
spl0_40,
inference(avatar_split_clause,[],[f165,f3630]) ).
fof(f3630,plain,
( spl0_40
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
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(f3628,plain,
spl0_39,
inference(avatar_split_clause,[],[f164,f3625]) ).
fof(f3625,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f164,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3623,plain,
spl0_38,
inference(avatar_split_clause,[],[f162,f3620]) ).
fof(f3620,plain,
( spl0_38
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
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(f3618,plain,
spl0_37,
inference(avatar_split_clause,[],[f161,f3615]) ).
fof(f3615,plain,
( spl0_37
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
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(f3613,plain,
spl0_36,
inference(avatar_split_clause,[],[f160,f3610]) ).
fof(f3610,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
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(f3608,plain,
spl0_35,
inference(avatar_split_clause,[],[f159,f3605]) ).
fof(f3605,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3603,plain,
spl0_34,
inference(avatar_split_clause,[],[f158,f3600]) ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3598,plain,
spl0_33,
inference(avatar_split_clause,[],[f157,f3595]) ).
fof(f3595,plain,
( spl0_33
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f157,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3593,plain,
spl0_32,
inference(avatar_split_clause,[],[f156,f3590]) ).
fof(f156,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3588,plain,
spl0_31,
inference(avatar_split_clause,[],[f155,f3585]) ).
fof(f155,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3583,plain,
spl0_30,
inference(avatar_split_clause,[],[f154,f3580]) ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3578,plain,
spl0_29,
inference(avatar_split_clause,[],[f153,f3575]) ).
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(f3573,plain,
spl0_28,
inference(avatar_split_clause,[],[f151,f3570]) ).
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(f3568,plain,
spl0_27,
inference(avatar_split_clause,[],[f150,f3565]) ).
fof(f3565,plain,
( spl0_27
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f150,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3563,plain,
spl0_26,
inference(avatar_split_clause,[],[f149,f3560]) ).
fof(f3560,plain,
( spl0_26
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
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(f3558,plain,
spl0_25,
inference(avatar_split_clause,[],[f148,f3555]) ).
fof(f3555,plain,
( spl0_25
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
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(f3553,plain,
spl0_24,
inference(avatar_split_clause,[],[f147,f3550]) ).
fof(f3550,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f147,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3548,plain,
spl0_23,
inference(avatar_split_clause,[],[f146,f3545]) ).
fof(f3545,plain,
( spl0_23
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f146,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3543,plain,
spl0_22,
inference(avatar_split_clause,[],[f145,f3540]) ).
fof(f145,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3538,plain,
spl0_21,
inference(avatar_split_clause,[],[f144,f3535]) ).
fof(f3535,plain,
( spl0_21
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
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(f3533,plain,
spl0_20,
inference(avatar_split_clause,[],[f143,f3530]) ).
fof(f3530,plain,
( spl0_20
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f143,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3528,plain,
spl0_19,
inference(avatar_split_clause,[],[f142,f3525]) ).
fof(f3525,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
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(f3523,plain,
spl0_18,
inference(avatar_split_clause,[],[f140,f3520]) ).
fof(f3520,plain,
( spl0_18
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f140,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3518,plain,
spl0_17,
inference(avatar_split_clause,[],[f139,f3515]) ).
fof(f3515,plain,
( spl0_17
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
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(f3513,plain,
spl0_16,
inference(avatar_split_clause,[],[f138,f3510]) ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3508,plain,
spl0_15,
inference(avatar_split_clause,[],[f137,f3505]) ).
fof(f3505,plain,
( spl0_15
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f137,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3503,plain,
spl0_14,
inference(avatar_split_clause,[],[f136,f3500]) ).
fof(f3500,plain,
( spl0_14
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f136,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3498,plain,
spl0_13,
inference(avatar_split_clause,[],[f135,f3495]) ).
fof(f3495,plain,
( spl0_13
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
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(f3493,plain,
spl0_12,
inference(avatar_split_clause,[],[f134,f3490]) ).
fof(f3490,plain,
( spl0_12
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f134,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3488,plain,
spl0_11,
inference(avatar_split_clause,[],[f133,f3485]) ).
fof(f133,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3483,plain,
spl0_10,
inference(avatar_split_clause,[],[f132,f3480]) ).
fof(f3480,plain,
( spl0_10
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f132,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3478,plain,
spl0_9,
inference(avatar_split_clause,[],[f131,f3475]) ).
fof(f3475,plain,
( spl0_9
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f131,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3473,plain,
spl0_8,
inference(avatar_split_clause,[],[f130,f3470]) ).
fof(f3470,plain,
( spl0_8
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f130,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3468,plain,
~ spl0_7,
inference(avatar_split_clause,[],[f2976,f3465]) ).
fof(f2976,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
fof(f3463,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f2971,f3460]) ).
fof(f2971,axiom,
~ c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(v_evs3),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3458,plain,
spl0_5,
inference(avatar_split_clause,[],[f2970,f3455]) ).
fof(f2970,axiom,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3453,plain,
spl0_4,
inference(avatar_split_clause,[],[f2977,f3450]) ).
fof(f2977,axiom,
c_in(v_Aa,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
fof(f3448,plain,
spl0_3,
inference(avatar_split_clause,[],[f2972,f3445]) ).
fof(f2972,axiom,
c_in(v_KAB,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3443,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f2968,f3440]) ).
fof(f2968,axiom,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3438,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2967,f3435]) ).
fof(f2967,axiom,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWV347-1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 30 04:37:41 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.31 % (6714)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.43 % (6718)WARNING: value z3 for option sas not known
% 0.16/0.43 % (6717)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.43 % (6719)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.43 % (6722)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.43 % (6720)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)
% 0.16/0.43 % (6716)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.43 % (6721)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)
% 0.16/0.43 % (6718)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)
% 2.64/0.78 TRYING [1]
% 6.07/1.30 TRYING [2]
% 9.57/1.76 TRYING [1]
% 9.95/1.82 TRYING [1]
% 10.14/1.86 % (6720)First to succeed.
% 11.17/1.99 % (6720)Refutation found. Thanks to Tanya!
% 11.17/1.99 % SZS status Unsatisfiable for theBenchmark
% 11.17/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 11.29/2.07 % (6720)------------------------------
% 11.29/2.07 % (6720)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 11.29/2.07 % (6720)Termination reason: Refutation
% 11.29/2.07
% 11.29/2.07 % (6720)Memory used [KB]: 21615
% 11.29/2.07 % (6720)Time elapsed: 1.555 s
% 11.29/2.07 % (6720)Instructions burned: 2788 (million)
% 11.29/2.07 % (6720)------------------------------
% 11.29/2.07 % (6720)------------------------------
% 11.29/2.07 % (6714)Success in time 1.735 s
%------------------------------------------------------------------------------