TSTP Solution File: SWV362-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV362-1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 May 21 06:18:12 EDT 2024
% Result : Unsatisfiable 7.33s 1.49s
% Output : Refutation 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4902
% Syntax : Number of formulae : 8920 (3079 unt; 0 def)
% Number of atoms : 20080 (3768 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 19398 (8238 ~;8502 |; 0 &)
% (2658 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 2729 (2727 usr;2659 prp; 0-3 aty)
% Number of functors : 280 ( 280 usr; 64 con; 0-18 aty)
% Number of variables : 12959 (12959 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34733,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,f3933,f3937,f3942,f3947,f3951,f3955,f3960,f3965,f3969,f3973,f3978,f3983,f3988,f3993,f3998,f4003,f4008,f4012,f4016,f4020,f4024,f4028,f4032,f4036,f4040,f4044,f4048,f4052,f4056,f4060,f4064,f4068,f4072,f4076,f4080,f4084,f4088,f4092,f4096,f4100,f4104,f4108,f4112,f4116,f4120,f4124,f4128,f4132,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4212,f4216,f4220,f4224,f4228,f4232,f4236,f4240,f4244,f4248,f4252,f4256,f4260,f4264,f4268,f4272,f4276,f4280,f4284,f4288,f4292,f4296,f4300,f4304,f4308,f4312,f4316,f4320,f4324,f4328,f4332,f4336,f4340,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4372,f4376,f4380,f4384,f4388,f4392,f4396,f4400,f4404,f4408,f4412,f4416,f4420,f4424,f4428,f4432,f4436,f4440,f4444,f4448,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4524,f4528,f4532,f4536,f4540,f4544,f4548,f4552,f4556,f4560,f4564,f4568,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4600,f4604,f4608,f4612,f4616,f4620,f4624,f4628,f4632,f4636,f4640,f4644,f4648,f4652,f4656,f4660,f4664,f4668,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4700,f4704,f4708,f4712,f4716,f4720,f4724,f4728,f4732,f4736,f4740,f4744,f4748,f4752,f4756,f4760,f4764,f4768,f4772,f4776,f4780,f4784,f4788,f4792,f4796,f4800,f4804,f4808,f4812,f4816,f4820,f4824,f4828,f4832,f4836,f4840,f4844,f4848,f4852,f4856,f4860,f4864,f4868,f4872,f4876,f4880,f4884,f4888,f4892,f4896,f4900,f4904,f4908,f4912,f4916,f4920,f4924,f4928,f4932,f4936,f4940,f4944,f4948,f4952,f4956,f4960,f4964,f4968,f4972,f4976,f4980,f4984,f4988,f4992,f4996,f5000,f5004,f5008,f5012,f5016,f5020,f5024,f5028,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5092,f5096,f5100,f5104,f5108,f5112,f5116,f5120,f5124,f5128,f5132,f5136,f5140,f5144,f5148,f5152,f5156,f5160,f5164,f5168,f5172,f5176,f5180,f5184,f5188,f5192,f5196,f5200,f5204,f5208,f5212,f5216,f5220,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5252,f5256,f5260,f5264,f5268,f5272,f5276,f5280,f5284,f5288,f5292,f5296,f5300,f5304,f5308,f5312,f5316,f5320,f5324,f5328,f5332,f5336,f5340,f5344,f5348,f5352,f5356,f5360,f5364,f5368,f5372,f5376,f5380,f5384,f5388,f5392,f5396,f5400,f5404,f5408,f5412,f5416,f5420,f5424,f5428,f5432,f5436,f5440,f5444,f5448,f5452,f5456,f5460,f5464,f5468,f5472,f5476,f5480,f5484,f5488,f5492,f5496,f5500,f5504,f5508,f5512,f5516,f5520,f5524,f5528,f5532,f5536,f5540,f5544,f5548,f5552,f5556,f5560,f5564,f5568,f5572,f5576,f5580,f5584,f5588,f5592,f5596,f5600,f5604,f5608,f5612,f5616,f5620,f5624,f5628,f5632,f5636,f5640,f5644,f5648,f5652,f5656,f5660,f5664,f5668,f5672,f5676,f5680,f5684,f5688,f5692,f5696,f5700,f5704,f5708,f5712,f5716,f5720,f5724,f5728,f5732,f5736,f5740,f5744,f5748,f5752,f5756,f5760,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5792,f5796,f5800,f5804,f5808,f5812,f5816,f5820,f5824,f5828,f5832,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5872,f5876,f5880,f5884,f5888,f5892,f5896,f5900,f5904,f5908,f5912,f5916,f5920,f5924,f5928,f5932,f5936,f5940,f5944,f5948,f5952,f5956,f5960,f5964,f5968,f5972,f5976,f5980,f5984,f5988,f5992,f5996,f6000,f6004,f6008,f6012,f6016,f6020,f6024,f6028,f6032,f6036,f6040,f6044,f6048,f6052,f6056,f6060,f6064,f6068,f6072,f6076,f6080,f6084,f6088,f6092,f6096,f6100,f6104,f6108,f6112,f6116,f6120,f6124,f6128,f6132,f6136,f6141,f6146,f6151,f6155,f6159,f6163,f6168,f6172,f6177,f6181,f6185,f6189,f6194,f6199,f6204,f6209,f6214,f6219,f6224,f6228,f6233,f7000,f7005,f7009,f7013,f7017,f7021,f7025,f7029,f7033,f7037,f7041,f7045,f7050,f7055,f7060,f7064,f7068,f7072,f7077,f7081,f7085,f7089,f7093,f7097,f7101,f7105,f7110,f7115,f7120,f7125,f7130,f7135,f7140,f7145,f7150,f7155,f7160,f7165,f7170,f7175,f7180,f7185,f7189,f7193,f7197,f7201,f7205,f7209,f7214,f7219,f7224,f7228,f7232,f7236,f7240,f7244,f7248,f7253,f7258,f7262,f7267,f7272,f7276,f7280,f7284,f7288,f7292,f7296,f7300,f7304,f7309,f7314,f7318,f7323,f7328,f7332,f7337,f7341,f7346,f7357,f7362,f7368,f7374,f7379,f7383,f7387,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7419,f7424,f7428,f7432,f7436,f7440,f7444,f7448,f7452,f7456,f7460,f7464,f7468,f7472,f7476,f7480,f7484,f7488,f7492,f7496,f7500,f7504,f7508,f7512,f7516,f7520,f7524,f7528,f7532,f7536,f7540,f7544,f7548,f7552,f7556,f7560,f7564,f7568,f7573,f7577,f7581,f7585,f7589,f7593,f7597,f7601,f7605,f7609,f7613,f7617,f7621,f7625,f7629,f7633,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7673,f7677,f7681,f7685,f7689,f7693,f7697,f7701,f7705,f7709,f7714,f7718,f7723,f7727,f7732,f7736,f7750,f7754,f7758,f7762,f7766,f7770,f7774,f7778,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f7834,f7838,f7842,f7846,f7850,f7854,f7858,f7862,f7866,f7870,f7874,f7878,f7882,f7886,f7890,f7894,f7898,f7902,f7906,f7910,f7914,f7918,f7922,f7926,f7930,f7934,f7938,f7942,f7946,f7950,f7954,f7958,f7962,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8014,f8018,f8022,f8026,f8031,f8035,f8040,f8044,f8048,f8052,f8072,f8107,f8121,f8131,f8137,f8145,f8151,f8155,f8159,f8163,f8167,f8171,f8175,f8179,f8184,f8188,f8192,f8196,f8200,f8204,f8209,f8213,f8217,f8221,f8225,f8229,f8233,f8237,f8241,f8245,f8249,f8253,f8257,f8261,f8265,f8274,f8278,f8282,f8286,f8290,f8294,f8298,f8302,f8306,f8310,f8314,f8318,f8322,f8326,f8330,f8334,f8338,f8342,f8346,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8382,f8386,f8390,f8394,f8399,f8403,f8407,f8411,f8415,f8419,f8423,f8427,f8431,f8435,f8439,f8444,f8448,f8452,f8456,f8461,f8465,f8469,f8473,f8477,f8481,f8486,f8490,f8494,f8498,f8502,f8506,f8510,f8514,f8518,f8522,f8526,f8531,f8535,f8539,f8543,f8547,f8551,f8555,f8559,f8563,f8676,f8701,f8706,f8710,f8714,f8718,f8722,f8726,f8730,f8737,f8741,f8745,f8749,f8753,f8757,f8761,f8765,f8769,f8773,f8777,f8781,f8785,f8789,f8793,f8797,f8801,f8805,f8809,f8813,f8817,f8824,f8828,f8832,f8836,f8840,f8844,f8848,f8852,f8856,f8860,f8864,f8868,f8872,f8876,f8880,f8884,f8888,f8892,f8896,f8900,f8904,f8909,f8913,f8917,f8921,f8925,f8929,f8933,f8937,f8941,f8945,f8950,f8954,f8958,f8962,f8966,f8970,f8974,f8978,f8982,f8986,f8990,f8994,f8998,f9002,f9006,f9010,f9014,f9018,f9022,f9026,f9030,f9035,f9039,f9043,f9047,f9051,f9055,f9059,f9063,f9067,f9071,f9075,f9079,f9083,f9087,f9091,f9095,f9099,f9103,f9107,f9111,f9127,f9165,f9225,f9246,f9293,f9330,f9357,f9361,f9365,f9369,f9373,f9377,f9381,f9385,f9389,f9393,f9397,f9401,f9405,f9409,f9413,f9417,f9421,f9425,f9430,f9434,f9438,f9442,f9446,f9450,f9454,f9458,f9462,f9466,f9470,f9474,f9478,f9482,f9486,f9491,f9495,f9499,f9503,f9507,f9511,f9515,f9519,f9523,f9527,f9531,f9535,f9539,f9543,f9547,f9551,f9555,f9559,f9563,f9567,f9571,f9575,f9579,f9583,f9587,f9591,f9595,f9599,f9604,f9608,f9612,f9616,f9620,f9624,f9628,f9632,f9636,f9640,f9644,f9648,f9652,f9656,f9660,f9664,f9668,f9672,f9676,f9680,f9684,f9688,f9692,f9696,f9700,f9704,f9708,f9713,f9717,f9721,f9726,f9734,f9738,f9742,f9746,f9750,f9754,f9758,f9762,f9794,f9830,f9875,f9909,f9950,f9966,f9978,f10006,f10023,f10027,f10031,f10035,f10039,f10043,f10047,f10051,f10056,f10060,f10064,f10068,f10072,f10076,f10080,f10084,f10088,f10092,f10096,f10100,f10104,f10108,f10112,f10116,f10120,f10124,f10128,f10132,f10136,f10140,f10144,f10148,f10152,f10156,f10160,f10164,f10168,f10172,f10176,f10180,f10184,f10188,f10192,f10196,f10200,f10204,f10208,f10212,f10216,f10220,f10224,f10228,f10232,f10236,f10240,f10244,f10248,f10252,f10256,f10260,f10264,f10268,f10272,f10276,f10280,f10284,f10288,f10292,f10296,f10300,f10304,f10308,f10312,f10316,f10320,f10325,f10333,f10337,f10341,f10345,f10349,f10353,f10357,f10361,f10395,f10400,f10445,f10632,f10779,f10783,f10787,f10791,f10795,f10799,f10803,f10807,f10811,f10815,f10819,f10823,f10827,f10831,f10835,f10839,f10843,f10847,f10851,f10855,f10859,f10863,f10867,f10875,f10879,f10883,f10887,f10891,f10895,f10899,f10903,f10908,f10913,f10917,f10921,f10925,f10929,f10933,f10937,f10941,f10945,f10949,f10953,f10958,f10962,f10966,f10970,f10974,f10978,f10982,f10986,f10990,f10994,f10998,f11002,f11006,f11010,f11014,f11018,f11022,f11026,f11030,f11034,f11038,f11042,f11046,f11050,f11054,f11058,f11062,f11066,f11070,f11074,f11078,f11082,f11086,f11090,f11094,f11098,f11102,f11106,f11110,f11114,f11118,f11125,f11129,f11133,f11137,f11141,f11145,f11149,f11153,f11157,f11161,f11165,f11169,f11173,f11177,f11181,f11185,f11189,f11193,f11197,f11201,f11209,f11213,f11217,f11221,f11225,f11229,f11233,f11237,f11241,f11245,f11250,f11254,f11258,f11262,f11266,f11270,f11274,f11278,f11282,f11286,f11290,f11294,f11298,f11302,f11306,f11310,f11314,f11318,f11322,f11326,f11330,f11334,f11338,f11342,f11346,f11350,f11354,f11358,f11444,f11649,f11862,f11949,f12270,f12407,f12411,f12415,f12419,f12423,f12427,f12431,f12435,f12439,f12443,f12447,f12451,f12455,f12459,f12463,f12467,f12471,f12475,f12479,f12483,f12487,f12491,f12495,f12499,f12503,f12507,f12511,f12515,f12519,f12525,f12529,f12533,f12537,f12541,f12545,f12549,f12553,f12557,f12561,f12569,f12573,f12577,f12581,f12585,f12589,f12593,f12597,f12601,f12605,f12614,f12618,f12622,f12626,f12630,f12634,f12638,f12642,f12646,f12650,f12655,f12659,f12663,f12667,f12671,f12675,f12679,f12683,f12687,f12691,f12695,f12704,f12708,f12712,f12716,f12720,f12724,f12728,f12732,f12736,f12740,f12745,f12749,f12753,f12757,f12761,f12765,f12769,f12773,f12777,f12781,f12796,f12800,f12804,f12808,f12812,f12816,f12820,f12824,f12828,f12832,f12842,f12846,f12850,f12854,f12858,f12862,f12867,f12874,f12878,f12887,f12891,f12896,f12904,f12908,f12913,f12945,f12949,f12957,f12961,f12965,f12969,f12973,f13131,f13570,f13982,f14149,f14295,f14299,f14303,f14307,f14311,f14315,f14319,f14323,f14327,f14331,f14338,f14342,f14346,f14350,f14354,f14358,f14362,f14366,f14370,f14374,f14378,f14382,f14386,f14390,f14394,f14398,f14402,f14406,f14410,f14414,f14418,f14422,f14426,f14430,f14434,f14438,f14442,f14446,f14450,f14454,f14458,f14462,f14466,f14470,f14474,f14478,f14482,f14486,f14490,f14494,f14498,f14502,f14506,f14510,f14514,f14518,f14522,f14526,f14530,f14534,f14538,f14542,f14546,f14550,f14555,f14559,f14563,f14567,f14571,f14575,f14579,f14583,f14587,f14591,f14595,f14599,f14603,f14607,f14611,f14615,f14619,f14623,f14628,f14637,f14641,f14646,f14650,f15473,f15600,f15706,f15710,f15714,f15718,f15722,f15726,f15730,f15734,f15738,f15743,f15747,f15751,f15755,f15759,f15763,f15767,f15771,f15775,f15779,f15783,f15788,f15792,f15796,f15800,f15804,f15808,f15812,f15816,f15820,f15824,f15828,f15832,f15836,f15840,f15844,f15848,f15852,f15856,f15860,f15864,f15868,f15881,f15885,f15889,f15893,f15897,f15901,f15905,f15909,f15913,f15917,f15921,f15925,f15929,f15933,f15937,f15941,f15945,f15949,f15953,f15958,f15962,f15986,f15991,f16009,f16014,f16034,f16038,f16042,f16046,f16050,f16054,f16058,f16062,f16066,f16070,f16074,f16078,f16085,f16243,f16571,f16748,f16993,f17060,f17064,f17068,f17072,f17076,f17080,f17084,f17088,f17092,f17096,f17100,f17104,f17108,f17112,f17169,f17173,f17177,f17181,f17185,f17189,f17193,f17198,f17202,f17206,f17210,f17214,f17218,f17222,f17226,f17230,f17234,f17238,f17242,f17246,f17250,f17269,f17273,f17277,f17281,f17285,f17289,f17293,f17297,f17301,f17305,f17309,f17313,f17317,f17321,f17325,f17329,f17333,f17337,f17341,f17345,f17349,f17353,f17357,f17361,f17365,f17369,f17373,f17377,f17381,f17385,f17390,f17418,f17422,f17427,f17485,f17490,f17585,f17590,f17689,f17694,f17698,f17735,f17740,f17758,f17763,f17771,f17776,f17784,f17792,f17796,f17802,f17808,f17812,f17816,f17822,f17828,f17832,f17836,f17840,f17844,f17850,f17883,f17887,f17901,f17906,f18072,f18229,f18532,f19028,f19191,f19195,f19199,f19203,f19207,f19211,f19215,f19219,f19223,f19227,f19231,f19235,f19239,f19243,f19247,f19251,f19255,f19259,f19263,f19267,f19271,f19275,f19279,f19283,f19296,f19300,f19304,f19308,f19312,f19316,f19320,f19324,f19328,f19332,f19345,f19349,f19353,f19357,f19361,f19365,f19369,f19373,f19377,f19381,f19394,f19398,f19402,f19406,f19410,f19414,f19418,f19422,f19426,f19430,f19435,f19439,f19443,f19447,f19453,f19479,f19485,f19570,f19575,f19611,f19615,f19619,f19624,f19629,f19634,f19639,f19645,f19649,f19654,f19658,f19662,f19666,f19671,f19693,f19697,f19709,f19713,f19718,f19723,f19728,f19734,f19739,f19745,f19749,f19754,f19767,f19771,f19776,f19785,f19789,f19793,f19797,f19801,f19805,f19899,f20423,f20559,f20865,f20869,f20873,f20877,f20881,f20885,f20889,f20895,f20901,f20905,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,f21046,f21050,f21054,f21058,f21064,f21398,f21402,f21640,f22148,f22340,f22392,f22396,f22400,f22404,f22408,f22413,f22417,f22422,f22427,f22431,f22435,f22439,f22443,f22447,f22451,f22455,f22459,f22463,f22467,f22471,f22475,f22479,f22537,f22579,f22849,f22987,f22991,f22995,f22999,f23003,f23007,f23011,f23015,f23019,f23023,f23027,f23031,f23035,f23039,f23043,f23047,f23051,f23055,f23059,f23063,f23067,f23071,f23076,f23081,f23087,f23091,f23112,f23117,f23130,f23134,f23138,f23143,f23164,f23169,f23173,f23194,f23198,f23202,f23207,f23576,f23580,f23704,f23708,f23712,f23716,f23720,f23724,f23752,f23756,f23760,f23764,f23768,f23772,f23776,f23780,f23784,f23788,f23792,f23796,f23800,f23804,f23808,f23812,f23816,f23820,f23824,f23828,f23832,f23836,f23840,f23844,f23848,f23852,f23856,f23860,f23864,f23868,f23872,f23876,f23901,f23905,f23909,f23913,f23917,f23921,f23925,f23929,f23933,f23937,f23960,f23964,f23968,f23972,f23976,f23980,f23984,f23988,f23992,f23996,f24000,f24004,f24008,f24012,f24016,f24023,f24043,f24050,f24073,f24077,f24081,f24085,f24089,f24095,f24160,f24164,f24168,f24172,f24176,f24180,f24184,f24188,f24192,f24197,f24224,f24230,f24560,f24670,f24773,f25079,f25267,f25271,f25275,f25287,f25291,f25295,f25299,f25303,f25307,f25311,f25315,f25319,f25323,f25328,f25332,f25336,f25340,f25344,f25348,f25352,f25356,f25360,f25364,f25373,f25377,f25381,f25385,f25389,f25393,f25397,f25401,f26112,f26116,f26120,f26132,f26136,f26140,f26144,f26148,f26152,f26156,f26160,f26164,f26168,f26176,f26180,f26184,f26188,f26192,f26196,f26200,f26204,f26208,f26212,f26217,f26247,f26277,f26282,f26332,f26336,f26340,f26345,f26745,f26981,f27131,f27135,f27139,f27143,f27147,f27151,f27155,f27160,f27170,f27174,f27178,f27182,f27186,f27190,f27194,f27198,f27202,f27208,f27215,f27219,f27301,f27305,f27309,f27313,f27318,f27328,f27332,f27411,f27415,f27853,f27857,f27903,f27907,f27911,f27915,f27919,f27923,f27933,f27937,f28128,f28132,f28136,f28140,f28144,f28148,f28152,f28156,f28160,f28164,f28168,f28172,f28176,f28180,f28184,f28188,f28259,f28556,f28560,f28564,f28568,f28572,f28577,f28732,f28736,f28740,f28744,f28748,f28752,f28756,f28760,f28764,f28768,f28772,f28776,f28780,f28784,f28788,f28792,f28796,f28800,f28804,f28808,f28812,f28816,f28820,f28824,f28828,f28832,f28836,f28840,f28846,f28854,f28860,f28864,f28872,f28878,f28894,f28900,f28949,f28955,f29010,f29015,f29195,f29754,f29758,f29763,f29775,f29779,f29783,f29787,f29791,f29796,f29876,f29880,f29884,f29888,f29892,f29896,f29900,f29904,f30192,f30196,f30200,f30204,f30307,f30311,f30315,f30319,f30323,f30327,f30331,f30344,f30364,f30496,f30500,f30504,f30508,f30646,f30650,f30654,f30665,f30670,f30675,f30680,f30703,f30707,f30711,f30715,f30762,f30766,f30770,f30774,f30778,f30786,f30790,f30794,f30941,f30974,f30988,f30992,f31020,f31024,f31028,f31032,f31036,f31041,f31052,f31057,f31137,f31141,f31145,f31149,f31153,f31173,f31177,f31181,f31187,f31205,f31218,f31253,f31260,f31299,f31303,f31309,f31339,f31378,f31382,f31403,f31409,f31426,f31430,f31434,f31438,f31478,f31482,f31486,f31490,f31624,f31631,f31675,f31679,f31683,f31696,f31740,f31744,f31748,f31752,f31756,f31760,f31815,f31819,f31823,f31882,f31903,f31919,f31942,f31946,f31969,f31992,f32015,f32028,f32049,f32053,f32083,f32111,f32115,f32128,f32161,f32170,f32175,f32179,f32218,f32222,f32226,f32230,f32234,f32239,f32244,f32249,f32257,f32261,f32265,f32269,f32273,f32277,f32281,f32285,f32289,f32298,f32303,f32361,f32365,f32624,f32707,f32735,f32797,f32801,f32813,f32817,f32821,f32828,f32832,f32836,f32840,f32849,f32854,f32859,f32863,f32867,f32872,f32876,f32880,f32884,f32888,f32892,f32896,f32912,f32919,f32930,f32938,f32956,f32960,f32970,f32974,f32981,f32986,f32990,f32994,f32998,f33002,f33006,f33010,f33014,f33018,f33024,f33028,f33033,f33037,f33041,f33045,f33049,f33053,f33057,f33061,f33065,f33070,f33074,f33078,f33082,f33086,f33090,f33094,f33098,f33102,f33106,f33111,f33115,f33119,f33123,f33127,f33170,f33175,f33179,f33183,f33184,f33209,f33213,f33303,f33308,f33607,f33814,f34080,f34322,f34349,f34376,f34388,f34397,f34409,f34414,f34418,f34422,f34426,f34430,f34434,f34438,f34442,f34446,f34450,f34456,f34460,f34464,f34468,f34472,f34476,f34480,f34484,f34488,f34492,f34496,f34501,f34505,f34509,f34514,f34519,f34523,f34527,f34531,f34535,f34539,f34543,f34562,f34568,f34587,f34592,f34596,f34600,f34604,f34608,f34620,f34638,f34642,f34646,f34651,f34655,f34659,f34663,f34667,f34696,f34700,f34705,f34709,f34714,f34718,f34726,f34731,f34732]) ).
fof(f34732,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_2610 ),
inference(avatar_split_clause,[],[f34621,f34453,f3455,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(f3455,plain,
( spl0_5
<=> c_in(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f34453,plain,
( spl0_2610
<=> v_A = v_Aa ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2610])]) ).
fof(f34621,plain,
( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_5
| ~ spl0_2610 ),
inference(superposition,[],[f3457,f34455]) ).
fof(f34455,plain,
( v_A = v_Aa
| ~ spl0_2610 ),
inference(avatar_component_clause,[],[f34453]) ).
fof(f3457,plain,
( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f3455]) ).
fof(f34731,plain,
( spl0_2658
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_1326 ),
inference(avatar_split_clause,[],[f10775,f10393,f8902,f3730,f34728]) ).
fof(f34728,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(f3730,plain,
( spl0_60
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f8902,plain,
( spl0_1076
<=> ! [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_1076])]) ).
fof(f10393,plain,
( spl0_1326
<=> ! [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_1326])]) ).
fof(f10775,plain,
( c_uminus(c_1,tc_IntDef_Oint) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_1326 ),
inference(forward_demodulation,[],[f10774,f9266]) ).
fof(f9266,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1076 ),
inference(resolution,[],[f8903,f3732]) ).
fof(f3732,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f3730]) ).
fof(f8903,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
| ~ spl0_1076 ),
inference(avatar_component_clause,[],[f8902]) ).
fof(f10774,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_60
| ~ spl0_1326 ),
inference(resolution,[],[f10394,f3732]) ).
fof(f10394,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_1326 ),
inference(avatar_component_clause,[],[f10393]) ).
fof(f34726,plain,
( spl0_2657
| ~ spl0_875
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10761,f10343,f7880,f34724]) ).
fof(f34724,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(f7880,plain,
( spl0_875
<=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f10343,plain,
( spl0_1321
<=> ! [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_1321])]) ).
fof(f10761,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_875
| ~ spl0_1321 ),
inference(superposition,[],[f7881,f10344]) ).
fof(f10344,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_1321 ),
inference(avatar_component_clause,[],[f10343]) ).
fof(f7881,plain,
( ! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat)
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f7880]) ).
fof(f34718,plain,
( spl0_107
| spl0_2656
| ~ spl0_1075
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10758,f10343,f8898,f34716,f3962]) ).
fof(f3962,plain,
( spl0_107
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f34716,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(f8898,plain,
( spl0_1075
<=> ! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f10758,plain,
( ! [X0] :
( c_0 != c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg)
| c_0 = c_1 )
| ~ spl0_1075
| ~ spl0_1321 ),
inference(superposition,[],[f8899,f10344]) ).
fof(f8899,plain,
( ! [X21,X15] :
( c_0 != c_plus(X15,X21,tc_nat)
| c_0 = X21 )
| ~ spl0_1075 ),
inference(avatar_component_clause,[],[f8898]) ).
fof(f34714,plain,
( spl0_2655
| ~ spl0_801
| ~ spl0_836
| ~ spl0_914
| ~ spl0_1079
| ~ spl0_1318 ),
inference(avatar_split_clause,[],[f10736,f10331,f8915,f8037,f7711,f7570,f34711]) ).
fof(f34711,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(f7570,plain,
( spl0_801
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f7711,plain,
( spl0_836
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f8037,plain,
( spl0_914
<=> 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_914])]) ).
fof(f8915,plain,
( spl0_1079
<=> ! [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_1079])]) ).
fof(f10331,plain,
( spl0_1318
<=> ! [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_1318])]) ).
fof(f10736,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_801
| ~ spl0_836
| ~ spl0_914
| ~ spl0_1079
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f10735,f7572]) ).
fof(f7572,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_801 ),
inference(avatar_component_clause,[],[f7570]) ).
fof(f10735,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_836
| ~ spl0_914
| ~ spl0_1079
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f10734,f8916]) ).
fof(f8916,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_1079 ),
inference(avatar_component_clause,[],[f8915]) ).
fof(f10734,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_836
| ~ spl0_914
| ~ spl0_1318 ),
inference(forward_demodulation,[],[f10729,f8039]) ).
fof(f8039,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f8037]) ).
fof(f10729,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_836
| ~ spl0_1318 ),
inference(superposition,[],[f10332,f7713]) ).
fof(f7713,plain,
( c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_836 ),
inference(avatar_component_clause,[],[f7711]) ).
fof(f10332,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_1318 ),
inference(avatar_component_clause,[],[f10331]) ).
fof(f34709,plain,
( spl0_2654
| ~ spl0_79
| ~ spl0_1299 ),
inference(avatar_split_clause,[],[f10687,f10250,f3825,f34707]) ).
fof(f34707,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(f3825,plain,
( spl0_79
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f10250,plain,
( spl0_1299
<=> ! [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_1299])]) ).
fof(f10687,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_nat) = c_SetInterval_OatLeastAtMost(X0,X0,tc_nat)
| ~ spl0_79
| ~ spl0_1299 ),
inference(resolution,[],[f10251,f3827]) ).
fof(f3827,plain,
( class_Orderings_Oorder(tc_nat)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f3825]) ).
fof(f10251,plain,
( ! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) )
| ~ spl0_1299 ),
inference(avatar_component_clause,[],[f10250]) ).
fof(f34705,plain,
( spl0_2653
| ~ spl0_31
| ~ spl0_1299 ),
inference(avatar_split_clause,[],[f10686,f10250,f3585,f34703]) ).
fof(f34703,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(f3585,plain,
( spl0_31
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f10686,plain,
( ! [X0] : c_insert(X0,c_emptyset,tc_IntDef_Oint) = c_SetInterval_OatLeastAtMost(X0,X0,tc_IntDef_Oint)
| ~ spl0_31
| ~ spl0_1299 ),
inference(resolution,[],[f10251,f3587]) ).
fof(f3587,plain,
( class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f3585]) ).
fof(f34700,plain,
( spl0_2652
| ~ spl0_738
| ~ spl0_1295 ),
inference(avatar_split_clause,[],[f10663,f10234,f7298,f34698]) ).
fof(f34698,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(f7298,plain,
( spl0_738
<=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f10234,plain,
( spl0_1295
<=> ! [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_1295])]) ).
fof(f10663,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_UNIV = c_OrderedGroup_Opprt(c_UNIV,tc_set(X0)) )
| ~ spl0_738
| ~ spl0_1295 ),
inference(resolution,[],[f10235,f7299]) ).
fof(f7299,plain,
( ! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1))
| ~ spl0_738 ),
inference(avatar_component_clause,[],[f7298]) ).
fof(f10235,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 )
| ~ spl0_1295 ),
inference(avatar_component_clause,[],[f10234]) ).
fof(f34696,plain,
( spl0_2651
| ~ spl0_812
| ~ spl0_1295 ),
inference(avatar_split_clause,[],[f10656,f10234,f7615,f34694]) ).
fof(f34694,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(f7615,plain,
( spl0_812
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f10656,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_1 = c_OrderedGroup_Opprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_812
| ~ spl0_1295 ),
inference(resolution,[],[f10235,f7616]) ).
fof(f7616,plain,
( ! [X1] :
( c_lessequals(c_0,c_1,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_812 ),
inference(avatar_component_clause,[],[f7615]) ).
fof(f34667,plain,
( spl0_2650
| ~ spl0_48
| ~ spl0_691
| ~ spl0_1295 ),
inference(avatar_split_clause,[],[f10654,f10234,f7087,f3670,f34665]) ).
fof(f34665,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(f3670,plain,
( spl0_48
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f7087,plain,
( spl0_691
<=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f10654,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_691
| ~ spl0_1295 ),
inference(resolution,[],[f10235,f7088]) ).
fof(f7088,plain,
( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_691 ),
inference(avatar_component_clause,[],[f7087]) ).
fof(f34663,plain,
( spl0_2649
| ~ spl0_979
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f10647,f10230,f8372,f34661]) ).
fof(f34661,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(f8372,plain,
( spl0_979
<=> ! [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_979])]) ).
fof(f10230,plain,
( spl0_1294
<=> ! [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_1294])]) ).
fof(f10647,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_OrderedGroup_Onprt(X1,X0),X0) )
| ~ spl0_979
| ~ spl0_1294 ),
inference(duplicate_literal_removal,[],[f10646]) ).
fof(f10646,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_979
| ~ spl0_1294 ),
inference(resolution,[],[f10231,f8373]) ).
fof(f8373,plain,
( ! [X18,X1] :
( c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_979 ),
inference(avatar_component_clause,[],[f8372]) ).
fof(f10231,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) )
| ~ spl0_1294 ),
inference(avatar_component_clause,[],[f10230]) ).
fof(f34659,plain,
( spl0_2648
| ~ spl0_674
| ~ spl0_1294 ),
inference(avatar_split_clause,[],[f10641,f10230,f7015,f34657]) ).
fof(f34657,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(f7015,plain,
( spl0_674
<=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f10641,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Opprt(c_emptyset,tc_set(X0)) )
| ~ spl0_674
| ~ spl0_1294 ),
inference(resolution,[],[f10231,f7016]) ).
fof(f7016,plain,
( ! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1))
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f7015]) ).
fof(f34655,plain,
( spl0_2647
| ~ spl0_674
| ~ spl0_1293 ),
inference(avatar_split_clause,[],[f10616,f10226,f7015,f34653]) ).
fof(f34653,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(f10226,plain,
( spl0_1293
<=> ! [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_1293])]) ).
fof(f10616,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_emptyset = c_OrderedGroup_Onprt(c_emptyset,tc_set(X0)) )
| ~ spl0_674
| ~ spl0_1293 ),
inference(resolution,[],[f10227,f7016]) ).
fof(f10227,plain,
( ! [X3,X1] :
( ~ c_lessequals(X3,c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 )
| ~ spl0_1293 ),
inference(avatar_component_clause,[],[f10226]) ).
fof(f34651,plain,
( spl0_2646
| ~ spl0_980
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10607,f10222,f8376,f34649]) ).
fof(f34649,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(f8376,plain,
( spl0_980
<=> ! [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_980])]) ).
fof(f10222,plain,
( spl0_1292
<=> ! [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_1292])]) ).
fof(f10607,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_OrderedGroup_Opprt(X1,X0),X0) )
| ~ spl0_980
| ~ spl0_1292 ),
inference(duplicate_literal_removal,[],[f10601]) ).
fof(f10601,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_980
| ~ spl0_1292 ),
inference(resolution,[],[f10223,f8377]) ).
fof(f8377,plain,
( ! [X18,X1] :
( c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_980 ),
inference(avatar_component_clause,[],[f8376]) ).
fof(f10223,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_0,X0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) )
| ~ spl0_1292 ),
inference(avatar_component_clause,[],[f10222]) ).
fof(f34646,plain,
( spl0_2645
| ~ spl0_738
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10604,f10222,f7298,f34644]) ).
fof(f34644,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(f10604,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_set(X0))
| c_0 = c_OrderedGroup_Onprt(c_UNIV,tc_set(X0)) )
| ~ spl0_738
| ~ spl0_1292 ),
inference(resolution,[],[f10223,f7299]) ).
fof(f34642,plain,
( spl0_2644
| ~ spl0_812
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10597,f10222,f7615,f34640]) ).
fof(f34640,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(f10597,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_812
| ~ spl0_1292 ),
inference(resolution,[],[f10223,f7616]) ).
fof(f34638,plain,
( spl0_2640
| spl0_2643
| ~ spl0_895
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f10588,f10218,f7960,f34636,f34611]) ).
fof(f34611,plain,
( spl0_2640
<=> ! [X1] : ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2640])]) ).
fof(f34636,plain,
( spl0_2643
<=> ! [X0] :
( c_0 != X0
| c_emptyset = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2643])]) ).
fof(f7960,plain,
( spl0_895
<=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f10218,plain,
( spl0_1291
<=> ! [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_1291])]) ).
fof(f10588,plain,
( ! [X0,X1] :
( c_0 != X0
| c_emptyset = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_895
| ~ spl0_1291 ),
inference(superposition,[],[f10219,f7961]) ).
fof(f7961,plain,
( ! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3
| ~ spl0_895 ),
inference(avatar_component_clause,[],[f7960]) ).
fof(f10219,plain,
( ! [X18,X1,X27] :
( c_0 != c_minus(X18,X27,X1)
| X18 = X27
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_1291 ),
inference(avatar_component_clause,[],[f10218]) ).
fof(f34620,plain,
( spl0_2640
| spl0_2641
| ~ spl0_2642
| ~ spl0_893
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f10586,f10218,f7952,f34617,f34614,f34611]) ).
fof(f34614,plain,
( spl0_2641
<=> ! [X0] : c_UNIV = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2641])]) ).
fof(f34617,plain,
( spl0_2642
<=> c_0 = c_emptyset ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2642])]) ).
fof(f7952,plain,
( spl0_893
<=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f10586,plain,
( ! [X0,X1] :
( c_0 != c_emptyset
| c_UNIV = X0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X1)) )
| ~ spl0_893
| ~ spl0_1291 ),
inference(superposition,[],[f10219,f7953]) ).
fof(f7953,plain,
( ! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1))
| ~ spl0_893 ),
inference(avatar_component_clause,[],[f7952]) ).
fof(f34608,plain,
( spl0_2639
| ~ spl0_738
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10579,f10210,f7298,f34606]) ).
fof(f34606,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(f10210,plain,
( spl0_1289
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f10579,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_set(X0))
| c_UNIV = c_HOL_Oabs(c_UNIV,tc_set(X0)) )
| ~ spl0_738
| ~ spl0_1289 ),
inference(resolution,[],[f10211,f7299]) ).
fof(f10211,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X3,X1) = X3 )
| ~ spl0_1289 ),
inference(avatar_component_clause,[],[f10210]) ).
fof(f34604,plain,
( spl0_2638
| ~ spl0_812
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10572,f10210,f7615,f34602]) ).
fof(f34602,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(f10572,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_812
| ~ spl0_1289 ),
inference(resolution,[],[f10211,f7616]) ).
fof(f34600,plain,
( spl0_2637
| ~ spl0_51
| ~ spl0_1288 ),
inference(avatar_split_clause,[],[f10565,f10206,f3685,f34598]) ).
fof(f34598,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(f3685,plain,
( spl0_51
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f10206,plain,
( spl0_1288
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f10565,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_51
| ~ spl0_1288 ),
inference(resolution,[],[f10207,f3687]) ).
fof(f3687,plain,
( class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f3685]) ).
fof(f10207,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) )
| ~ spl0_1288 ),
inference(avatar_component_clause,[],[f10206]) ).
fof(f34596,plain,
( spl0_2636
| ~ spl0_51
| ~ spl0_1286 ),
inference(avatar_split_clause,[],[f10559,f10198,f3685,f34594]) ).
fof(f34594,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(f10198,plain,
( spl0_1286
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f10559,plain,
( ! [X0] : c_HOL_Oabs(X0,tc_IntDef_Oint) = c_HOL_Oabs(c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_51
| ~ spl0_1286 ),
inference(resolution,[],[f10199,f3687]) ).
fof(f10199,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_1286 ),
inference(avatar_component_clause,[],[f10198]) ).
fof(f34592,plain,
( spl0_2635
| ~ spl0_801
| ~ spl0_836
| ~ spl0_914
| ~ spl0_1079
| ~ spl0_1284 ),
inference(avatar_split_clause,[],[f10556,f10190,f8915,f8037,f7711,f7570,f34589]) ).
fof(f34589,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(f10190,plain,
( spl0_1284
<=> ! [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_1284])]) ).
fof(f10556,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_801
| ~ spl0_836
| ~ spl0_914
| ~ spl0_1079
| ~ spl0_1284 ),
inference(forward_demodulation,[],[f10555,f7572]) ).
fof(f10555,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_836
| ~ spl0_914
| ~ spl0_1079
| ~ spl0_1284 ),
inference(forward_demodulation,[],[f10554,f8916]) ).
fof(f10554,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_836
| ~ spl0_914
| ~ spl0_1284 ),
inference(forward_demodulation,[],[f10549,f8039]) ).
fof(f10549,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_836
| ~ spl0_1284 ),
inference(superposition,[],[f10191,f7713]) ).
fof(f10191,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_1284 ),
inference(avatar_component_clause,[],[f10190]) ).
fof(f34587,plain,
( spl0_2634
| ~ spl0_30
| ~ spl0_1255 ),
inference(avatar_split_clause,[],[f10409,f10074,f3580,f34585]) ).
fof(f34585,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(f3580,plain,
( spl0_30
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f10074,plain,
( spl0_1255
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f10409,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_30
| ~ spl0_1255 ),
inference(resolution,[],[f10075,f3582]) ).
fof(f3582,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f3580]) ).
fof(f10075,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_1255 ),
inference(avatar_component_clause,[],[f10074]) ).
fof(f34568,plain,
( ~ spl0_58
| spl0_2633
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_1248 ),
inference(avatar_split_clause,[],[f10391,f10045,f8902,f3730,f34565,f3720]) ).
fof(f3720,plain,
( spl0_58
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f34565,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(f10045,plain,
( spl0_1248
<=> ! [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_1248])]) ).
fof(f10391,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_60
| ~ spl0_1076
| ~ spl0_1248 ),
inference(forward_demodulation,[],[f10390,f9266]) ).
fof(f10390,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_60
| ~ spl0_1248 ),
inference(resolution,[],[f10046,f3732]) ).
fof(f10046,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_1248 ),
inference(avatar_component_clause,[],[f10045]) ).
fof(f34562,plain,
( ~ spl0_2632
| ~ spl0_649
| ~ spl0_1317 ),
inference(avatar_split_clause,[],[f10327,f10323,f6138,f34559]) ).
fof(f34559,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(f6138,plain,
( spl0_649
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f10323,plain,
( spl0_1317
<=> ! [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_1317])]) ).
fof(f10327,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_1317 ),
inference(superposition,[],[f10324,f6140]) ).
fof(f6140,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f6138]) ).
fof(f10324,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_1317 ),
inference(avatar_component_clause,[],[f10323]) ).
fof(f34543,plain,
( spl0_2631
| ~ spl0_1092
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f9997,f9686,f8968,f34541]) ).
fof(f34541,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(f8968,plain,
( spl0_1092
<=> ! [X13,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f9686,plain,
( spl0_1216
<=> ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f9997,plain,
( ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oparts(X0) )
| ~ spl0_1092
| ~ spl0_1216 ),
inference(superposition,[],[f8969,f9687]) ).
fof(f9687,plain,
( ! [X88] : c_Message_Oparts(c_Message_Osynth(X88)) = c_union(c_Message_Oparts(X88),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1216 ),
inference(avatar_component_clause,[],[f9686]) ).
fof(f8969,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_union(X12,X13,X1)
| c_emptyset = X12 )
| ~ spl0_1092 ),
inference(avatar_component_clause,[],[f8968]) ).
fof(f34539,plain,
( spl0_2630
| ~ spl0_1093
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f9996,f9686,f8972,f34537]) ).
fof(f34537,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(f8972,plain,
( spl0_1093
<=> ! [X13,X12,X1] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f9996,plain,
( ! [X0] :
( c_emptyset != c_Message_Oparts(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) )
| ~ spl0_1093
| ~ spl0_1216 ),
inference(superposition,[],[f8973,f9687]) ).
fof(f8973,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_union(X12,X13,X1)
| c_emptyset = X13 )
| ~ spl0_1093 ),
inference(avatar_component_clause,[],[f8972]) ).
fof(f34535,plain,
( spl0_2629
| ~ spl0_1092
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f9991,f9682,f8968,f34533]) ).
fof(f34533,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(f9682,plain,
( spl0_1215
<=> ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f9991,plain,
( ! [X0] :
( c_emptyset != c_Message_Oanalz(c_Message_Osynth(X0))
| c_emptyset = c_Message_Oanalz(X0) )
| ~ spl0_1092
| ~ spl0_1215 ),
inference(superposition,[],[f8969,f9683]) ).
fof(f9683,plain,
( ! [X88] : c_Message_Oanalz(c_Message_Osynth(X88)) = c_union(c_Message_Oanalz(X88),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1215 ),
inference(avatar_component_clause,[],[f9682]) ).
fof(f34531,plain,
( spl0_2628
| ~ spl0_1093
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f9990,f9682,f8972,f34529]) ).
fof(f34529,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(f9990,plain,
( ! [X0] :
( c_emptyset != c_Message_Oanalz(c_Message_Osynth(X0))
| c_emptyset = c_Message_Osynth(X0) )
| ~ spl0_1093
| ~ spl0_1215 ),
inference(superposition,[],[f8973,f9683]) ).
fof(f34527,plain,
( spl0_2627
| ~ spl0_877
| ~ spl0_1192 ),
inference(avatar_split_clause,[],[f9952,f9589,f7888,f34525]) ).
fof(f34525,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(f7888,plain,
( spl0_877
<=> ! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f9589,plain,
( spl0_1192
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f9952,plain,
( ! [X0] :
( c_0 = X0
| c_0 = c_Nat_Opower(c_0,X0,tc_nat) )
| ~ spl0_877
| ~ spl0_1192 ),
inference(resolution,[],[f9590,f7889]) ).
fof(f7889,plain,
( ! [X21] :
( c_less(c_0,X21,tc_nat)
| c_0 = X21 )
| ~ spl0_877 ),
inference(avatar_component_clause,[],[f7888]) ).
fof(f9590,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat)
| c_0 = X21 )
| ~ spl0_1192 ),
inference(avatar_component_clause,[],[f9589]) ).
fof(f34523,plain,
( spl0_2626
| ~ spl0_872
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f9923,f9545,f7868,f34521]) ).
fof(f34521,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(f7868,plain,
( spl0_872
<=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f9545,plain,
( spl0_1181
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f9923,plain,
( ! [X0,X1] : c_0 = c_minus(c_minus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_872
| ~ spl0_1181 ),
inference(resolution,[],[f9546,f7869]) ).
fof(f7869,plain,
( ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_872 ),
inference(avatar_component_clause,[],[f7868]) ).
fof(f9546,plain,
( ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) )
| ~ spl0_1181 ),
inference(avatar_component_clause,[],[f9545]) ).
fof(f34519,plain,
( spl0_2625
| ~ spl0_852
| ~ spl0_1181 ),
inference(avatar_split_clause,[],[f9922,f9545,f7788,f34517]) ).
fof(f34517,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(f7788,plain,
( spl0_852
<=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f9922,plain,
( ! [X0,X1] : c_0 = c_minus(c_div(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_852
| ~ spl0_1181 ),
inference(resolution,[],[f9546,f7789]) ).
fof(f7789,plain,
( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_852 ),
inference(avatar_component_clause,[],[f7788]) ).
fof(f34514,plain,
( spl0_2624
| ~ spl0_845
| ~ spl0_1167 ),
inference(avatar_split_clause,[],[f9879,f9489,f7760,f34512]) ).
fof(f34512,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(f7760,plain,
( spl0_845
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f9489,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(f9879,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_845
| ~ spl0_1167 ),
inference(resolution,[],[f9490,f7761]) ).
fof(f7761,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_845 ),
inference(avatar_component_clause,[],[f7760]) ).
fof(f9490,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_1167 ),
inference(avatar_component_clause,[],[f9489]) ).
fof(f34509,plain,
( spl0_2623
| ~ spl0_844
| ~ spl0_1167 ),
inference(avatar_split_clause,[],[f9878,f9489,f7756,f34507]) ).
fof(f34507,plain,
( spl0_2623
<=> ! [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_2623])]) ).
fof(f7756,plain,
( spl0_844
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f9878,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_844
| ~ spl0_1167 ),
inference(resolution,[],[f9490,f7757]) ).
fof(f7757,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_844 ),
inference(avatar_component_clause,[],[f7756]) ).
fof(f34505,plain,
( spl0_2622
| ~ spl0_863
| ~ spl0_1165 ),
inference(avatar_split_clause,[],[f9869,f9480,f7832,f34503]) ).
fof(f34503,plain,
( spl0_2622
<=> ! [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_2622])]) ).
fof(f7832,plain,
( spl0_863
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f9480,plain,
( spl0_1165
<=> ! [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_1165])]) ).
fof(f9869,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_863
| ~ spl0_1165 ),
inference(resolution,[],[f9481,f7833]) ).
fof(f7833,plain,
( ! [X15] :
( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
| c_0 = X15 )
| ~ spl0_863 ),
inference(avatar_component_clause,[],[f7832]) ).
fof(f9481,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_1165 ),
inference(avatar_component_clause,[],[f9480]) ).
fof(f34501,plain,
( spl0_2621
| ~ spl0_752
| ~ spl0_2598 ),
inference(avatar_split_clause,[],[f34398,f34395,f7371,f34498]) ).
fof(f34498,plain,
( spl0_2621
<=> v_B = v_Ba ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2621])]) ).
fof(f7371,plain,
( spl0_752
<=> 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_752])]) ).
fof(f34395,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(f34398,plain,
( v_B = v_Ba
| ~ spl0_752
| ~ spl0_2598 ),
inference(resolution,[],[f34396,f7373]) ).
fof(f7373,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_752 ),
inference(avatar_component_clause,[],[f7371]) ).
fof(f34396,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,[],[f34395]) ).
fof(f34496,plain,
( spl0_2620
| ~ spl0_666
| ~ spl0_1163 ),
inference(avatar_split_clause,[],[f9864,f9472,f6216,f34494]) ).
fof(f34494,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(f6216,plain,
( spl0_666
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f9472,plain,
( spl0_1163
<=> ! [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_1163])]) ).
fof(f9864,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| c_less(X0,c_1,tc_IntDef_Oint) )
| ~ spl0_666
| ~ spl0_1163 ),
inference(superposition,[],[f9473,f6218]) ).
fof(f6218,plain,
( c_1 = c_IntDef_Onat(c_1)
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f6216]) ).
fof(f9473,plain,
( ! [X48,X11] :
( ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
| c_less(X11,X48,tc_IntDef_Oint) )
| ~ spl0_1163 ),
inference(avatar_component_clause,[],[f9472]) ).
fof(f34492,plain,
( spl0_2619
| ~ spl0_690
| ~ spl0_1161 ),
inference(avatar_split_clause,[],[f9847,f9464,f7083,f34490]) ).
fof(f34490,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(f7083,plain,
( spl0_690
<=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f9464,plain,
( spl0_1161
<=> ! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f9847,plain,
( ! [X0,X1] :
( ~ c_less(X0,c_IntDef_Onat(X1),tc_nat)
| c_less(c_0,X1,tc_IntDef_Oint) )
| ~ spl0_690
| ~ spl0_1161 ),
inference(superposition,[],[f9465,f7084]) ).
fof(f7084,plain,
( ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3
| ~ spl0_690 ),
inference(avatar_component_clause,[],[f7083]) ).
fof(f9465,plain,
( ! [X48,X11] :
( ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat)
| c_less(c_0,X48,tc_IntDef_Oint) )
| ~ spl0_1161 ),
inference(avatar_component_clause,[],[f9464]) ).
fof(f34488,plain,
( spl0_2618
| ~ spl0_649
| ~ spl0_1160 ),
inference(avatar_split_clause,[],[f9844,f9460,f6138,f34486]) ).
fof(f34486,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(f9460,plain,
( spl0_1160
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f9844,plain,
( ! [X0] :
( c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_less(X0,c_1,tc_nat) )
| ~ spl0_649
| ~ spl0_1160 ),
inference(superposition,[],[f9461,f6140]) ).
fof(f9461,plain,
( ! [X21,X15] :
( c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ c_less(X15,X21,tc_nat) )
| ~ spl0_1160 ),
inference(avatar_component_clause,[],[f9460]) ).
fof(f34484,plain,
( spl0_2617
| ~ spl0_649
| ~ spl0_1159 ),
inference(avatar_split_clause,[],[f9838,f9456,f6138,f34482]) ).
fof(f34482,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(f9456,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(f9838,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_less(X0,c_1,tc_nat) )
| ~ spl0_649
| ~ spl0_1159 ),
inference(superposition,[],[f9457,f6140]) ).
fof(f9457,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,[],[f9456]) ).
fof(f34480,plain,
( spl0_2616
| ~ spl0_650
| ~ spl0_1158 ),
inference(avatar_split_clause,[],[f9835,f9452,f6143,f34478]) ).
fof(f34478,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(f6143,plain,
( spl0_650
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f9452,plain,
( spl0_1158
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f9835,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_650
| ~ spl0_1158 ),
inference(superposition,[],[f9453,f6145]) ).
fof(f6145,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_650 ),
inference(avatar_component_clause,[],[f6143]) ).
fof(f9453,plain,
( ! [X21,X15] :
( c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1158 ),
inference(avatar_component_clause,[],[f9452]) ).
fof(f34476,plain,
( spl0_2615
| ~ spl0_649
| ~ spl0_1158 ),
inference(avatar_split_clause,[],[f9834,f9452,f6138,f34474]) ).
fof(f34474,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(f9834,plain,
( ! [X0] :
( c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_649
| ~ spl0_1158 ),
inference(superposition,[],[f9453,f6140]) ).
fof(f34472,plain,
( spl0_2614
| ~ spl0_649
| ~ spl0_1158 ),
inference(avatar_split_clause,[],[f9832,f9452,f6138,f34470]) ).
fof(f34470,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(f9832,plain,
( ! [X0] :
( c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_649
| ~ spl0_1158 ),
inference(superposition,[],[f9453,f6140]) ).
fof(f34468,plain,
( spl0_2613
| ~ spl0_650
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9825,f9448,f6143,f34466]) ).
fof(f34466,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(f9448,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_650
| ~ spl0_1157 ),
inference(superposition,[],[f9449,f6145]) ).
fof(f9449,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,[],[f9448]) ).
fof(f34464,plain,
( spl0_2612
| ~ spl0_649
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9824,f9448,f6138,f34462]) ).
fof(f34462,plain,
( spl0_2612
<=> ! [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_2612])]) ).
fof(f9824,plain,
( ! [X0] :
( ~ c_lessequals(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_lessequals(X0,c_1,tc_nat) )
| ~ spl0_649
| ~ spl0_1157 ),
inference(superposition,[],[f9449,f6140]) ).
fof(f34460,plain,
( spl0_2611
| ~ spl0_649
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9822,f9448,f6138,f34458]) ).
fof(f34458,plain,
( spl0_2611
<=> ! [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_2611])]) ).
fof(f9822,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_649
| ~ spl0_1157 ),
inference(superposition,[],[f9449,f6140]) ).
fof(f34456,plain,
( spl0_2610
| ~ spl0_752
| ~ spl0_2597 ),
inference(avatar_split_clause,[],[f34389,f34386,f7371,f34453]) ).
fof(f34386,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(f34389,plain,
( v_A = v_Aa
| ~ spl0_752
| ~ spl0_2597 ),
inference(resolution,[],[f34387,f7373]) ).
fof(f34387,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,[],[f34386]) ).
fof(f34450,plain,
( spl0_107
| spl0_2609
| ~ spl0_649
| ~ spl0_1153 ),
inference(avatar_split_clause,[],[f9813,f9432,f6138,f34448,f3962]) ).
fof(f34448,plain,
( spl0_2609
<=> ! [X0] : c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2609])]) ).
fof(f9432,plain,
( spl0_1153
<=> ! [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_1153])]) ).
fof(f9813,plain,
( ! [X0] :
( c_uminus(c_1,tc_IntDef_Oint) != c_IntDef_Oint(X0)
| c_0 = c_1 )
| ~ spl0_649
| ~ spl0_1153 ),
inference(superposition,[],[f9433,f6140]) ).
fof(f9433,plain,
( ! [X21,X15] :
( c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15)
| c_0 = X21 )
| ~ spl0_1153 ),
inference(avatar_component_clause,[],[f9432]) ).
fof(f34446,plain,
( spl0_2608
| ~ spl0_877
| ~ spl0_1148 ),
inference(avatar_split_clause,[],[f9795,f9411,f7888,f34444]) ).
fof(f34444,plain,
( spl0_2608
<=> ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2608])]) ).
fof(f9411,plain,
( spl0_1148
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f9795,plain,
( ! [X0] :
( c_1 = c_div(X0,X0,tc_nat)
| c_0 = X0 )
| ~ spl0_877
| ~ spl0_1148 ),
inference(resolution,[],[f9412,f7889]) ).
fof(f9412,plain,
( ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) )
| ~ spl0_1148 ),
inference(avatar_component_clause,[],[f9411]) ).
fof(f34442,plain,
( spl0_2607
| ~ spl0_939
| ~ spl0_1137 ),
inference(avatar_split_clause,[],[f9770,f9367,f8211,f34440]) ).
fof(f34440,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(f8211,plain,
( spl0_939
<=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f9367,plain,
( spl0_1137
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f9770,plain,
( ! [X0,X1] :
( c_0 = c_Nat_Osize(X0,tc_Datatype_Ooption(X1))
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_939
| ~ spl0_1137 ),
inference(superposition,[],[f8212,f9368]) ).
fof(f9368,plain,
( ! [X0,X1] :
( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_1137 ),
inference(avatar_component_clause,[],[f9367]) ).
fof(f8212,plain,
( ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1))
| ~ spl0_939 ),
inference(avatar_component_clause,[],[f8211]) ).
fof(f34438,plain,
( spl0_2606
| ~ spl0_1000
| ~ spl0_1136 ),
inference(avatar_split_clause,[],[f9767,f9363,f8458,f34436]) ).
fof(f34436,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(f8458,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(f9363,plain,
( spl0_1136
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f9767,plain,
( ! [X0] :
( ~ c_in(X0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| c_0 = X0 )
| ~ spl0_1000
| ~ spl0_1136 ),
inference(superposition,[],[f9364,f8460]) ).
fof(f8460,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_1000 ),
inference(avatar_component_clause,[],[f8458]) ).
fof(f9364,plain,
( ! [X18,X1,X27] :
( ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1)
| X18 = X27 )
| ~ spl0_1136 ),
inference(avatar_component_clause,[],[f9363]) ).
fof(f34434,plain,
( spl0_2605
| ~ spl0_690
| ~ spl0_1127 ),
inference(avatar_split_clause,[],[f9350,f9109,f7083,f34432]) ).
fof(f34432,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(f9109,plain,
( spl0_1127
<=> ! [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_1127])]) ).
fof(f9350,plain,
( ! [X0] :
( ~ c_less(c_1,X0,tc_nat)
| c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_690
| ~ spl0_1127 ),
inference(superposition,[],[f9110,f7084]) ).
fof(f9110,plain,
( ! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) )
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f9109]) ).
fof(f34430,plain,
( spl0_2604
| ~ spl0_690
| ~ spl0_1126 ),
inference(avatar_split_clause,[],[f9344,f9105,f7083,f34428]) ).
fof(f34428,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(f9105,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(f9344,plain,
( ! [X0] :
( c_less(c_1,X0,tc_nat)
| ~ c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_690
| ~ spl0_1126 ),
inference(superposition,[],[f9106,f7084]) ).
fof(f9106,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,[],[f9105]) ).
fof(f34426,plain,
( spl0_2603
| ~ spl0_915
| ~ spl0_1122 ),
inference(avatar_split_clause,[],[f9336,f9089,f8042,f34424]) ).
fof(f34424,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(f8042,plain,
( spl0_915
<=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f9089,plain,
( spl0_1122
<=> ! [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_1122])]) ).
fof(f9336,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_915
| ~ spl0_1122 ),
inference(superposition,[],[f9090,f8043]) ).
fof(f8043,plain,
( ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin)
| ~ spl0_915 ),
inference(avatar_component_clause,[],[f8042]) ).
fof(f9090,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_1122 ),
inference(avatar_component_clause,[],[f9089]) ).
fof(f34422,plain,
( spl0_2602
| ~ spl0_1061
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f9228,f8846,f8842,f34420]) ).
fof(f34420,plain,
( spl0_2602
<=> ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2602])]) ).
fof(f8842,plain,
( spl0_1061
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f8846,plain,
( spl0_1062
<=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f9228,plain,
( ! [X2,X0,X1] :
( c_0 != X0
| c_List_Olist_ONil = c_List_Oreplicate(X0,X1,X2) )
| ~ spl0_1061
| ~ spl0_1062 ),
inference(superposition,[],[f8843,f8847]) ).
fof(f8847,plain,
( ! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f8846]) ).
fof(f8843,plain,
( ! [X1,X23] :
( c_0 != c_Nat_Osize(X23,tc_List_Olist(X1))
| c_List_Olist_ONil = X23 )
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f8842]) ).
fof(f34418,plain,
( spl0_2601
| ~ spl0_858
| ~ spl0_1038 ),
inference(avatar_split_clause,[],[f9147,f8747,f7812,f34416]) ).
fof(f34416,plain,
( spl0_2601
<=> ! [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_2601])]) ).
fof(f7812,plain,
( spl0_858
<=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f8747,plain,
( spl0_1038
<=> ! [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_1038])]) ).
fof(f9147,plain,
( ! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_1,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(X0) )
| ~ spl0_858
| ~ spl0_1038 ),
inference(superposition,[],[f8748,f7813]) ).
fof(f7813,plain,
( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_858 ),
inference(avatar_component_clause,[],[f7812]) ).
fof(f8748,plain,
( ! [X48] :
( ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| c_0 = X48 )
| ~ spl0_1038 ),
inference(avatar_component_clause,[],[f8747]) ).
fof(f34414,plain,
( spl0_2600
| ~ spl0_752
| ~ spl0_2596 ),
inference(avatar_split_clause,[],[f34377,f34374,f7371,f34411]) ).
fof(f34411,plain,
( spl0_2600
<=> v_NAa = v_NA ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2600])]) ).
fof(f34374,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(f34377,plain,
( v_NAa = v_NA
| ~ spl0_752
| ~ spl0_2596 ),
inference(resolution,[],[f34375,f7373]) ).
fof(f34375,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,[],[f34374]) ).
fof(f34409,plain,
( spl0_2599
| ~ spl0_833
| ~ spl0_1004 ),
inference(avatar_split_clause,[],[f8683,f8475,f7699,f34407]) ).
fof(f34407,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(f7699,plain,
( spl0_833
<=> ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f8475,plain,
( spl0_1004
<=> ! [X92,X91] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f8683,plain,
( ! [X0,X1] :
( c_Public_OshrK(X0) != c_Message_OinvKey(X1)
| c_Public_OshrK(X0) = X1 )
| ~ spl0_833
| ~ spl0_1004 ),
inference(superposition,[],[f8476,f7700]) ).
fof(f7700,plain,
( ! [X12] : c_Public_OshrK(X12) = c_Message_OinvKey(c_Public_OshrK(X12))
| ~ spl0_833 ),
inference(avatar_component_clause,[],[f7699]) ).
fof(f8476,plain,
( ! [X91,X92] :
( c_Message_OinvKey(X91) != c_Message_OinvKey(X92)
| X91 = X92 )
| ~ spl0_1004 ),
inference(avatar_component_clause,[],[f8475]) ).
fof(f34397,plain,
( spl0_2598
| spl0_8
| ~ spl0_6
| ~ spl0_753
| ~ spl0_2466 ),
inference(avatar_split_clause,[],[f31799,f31754,f7376,f3460,f3470,f34395]) ).
fof(f3470,plain,
( spl0_8
<=> 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_8])]) ).
fof(f3460,plain,
( spl0_6
<=> c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f7376,plain,
( spl0_753
<=> 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_753])]) ).
fof(f31754,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(f31799,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_753
| ~ spl0_2466 ),
inference(resolution,[],[f31755,f7378]) ).
fof(f7378,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_753 ),
inference(avatar_component_clause,[],[f7376]) ).
fof(f31755,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,[],[f31754]) ).
fof(f34388,plain,
( spl0_2597
| spl0_8
| ~ spl0_6
| ~ spl0_753
| ~ spl0_2465 ),
inference(avatar_split_clause,[],[f31786,f31750,f7376,f3460,f3470,f34386]) ).
fof(f31750,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(f31786,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_753
| ~ spl0_2465 ),
inference(resolution,[],[f31751,f7378]) ).
fof(f31751,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,[],[f31750]) ).
fof(f34376,plain,
( spl0_2596
| spl0_8
| ~ spl0_6
| ~ spl0_753
| ~ spl0_2464 ),
inference(avatar_split_clause,[],[f31773,f31746,f7376,f3460,f3470,f34374]) ).
fof(f31746,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(f31773,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_753
| ~ spl0_2464 ),
inference(resolution,[],[f31747,f7378]) ).
fof(f31747,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,[],[f31746]) ).
fof(f34349,plain,
( spl0_2595
| ~ spl0_753
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f22055,f20980,f7376,f34347]) ).
fof(f34347,plain,
( spl0_2595
<=> ! [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_2595])]) ).
fof(f20980,plain,
( spl0_2014
<=> ! [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_2014])]) ).
fof(f22055,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_753
| ~ spl0_2014 ),
inference(resolution,[],[f20981,f7378]) ).
fof(f20981,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_2014 ),
inference(avatar_component_clause,[],[f20980]) ).
fof(f34322,plain,
( spl0_2594
| ~ spl0_752
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f22056,f20980,f7371,f34320]) ).
fof(f34320,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_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_2594])]) ).
fof(f22056,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_752
| ~ spl0_2014 ),
inference(resolution,[],[f20981,f7373]) ).
fof(f34080,plain,
( ~ spl0_2593
| ~ spl0_2568
| ~ spl0_2578 ),
inference(avatar_split_clause,[],[f33831,f33108,f33068,f34077]) ).
fof(f34077,plain,
( spl0_2593
<=> c_emptyset = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2593])]) ).
fof(f33068,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(f33108,plain,
( spl0_2578
<=> c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)) = c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(v_B),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2578])]) ).
fof(f33831,plain,
( c_emptyset != c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))
| ~ spl0_2568
| ~ spl0_2578 ),
inference(superposition,[],[f33069,f33110]) ).
fof(f33110,plain,
( c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)) = c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(v_B),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg))
| ~ spl0_2578 ),
inference(avatar_component_clause,[],[f33108]) ).
fof(f33069,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_2568 ),
inference(avatar_component_clause,[],[f33068]) ).
fof(f33814,plain,
( spl0_2592
| ~ spl0_2378
| ~ spl0_2561 ),
inference(avatar_split_clause,[],[f33641,f33039,f29902,f33812]) ).
fof(f33812,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(f29902,plain,
( spl0_2378
<=> ! [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_2378])]) ).
fof(f33039,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(f33641,plain,
( ! [X0] : c_in(v_Aa,c_union(c_Event_Obad,X0,tc_Message_Oagent),tc_Message_Oagent)
| ~ spl0_2378
| ~ spl0_2561 ),
inference(resolution,[],[f33040,f29903]) ).
fof(f29903,plain,
( ! [X0] :
( ~ c_lessequals(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_2378 ),
inference(avatar_component_clause,[],[f29902]) ).
fof(f33040,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| ~ spl0_2561 ),
inference(avatar_component_clause,[],[f33039]) ).
fof(f33607,plain,
( spl0_2591
| ~ spl0_1474
| ~ spl0_2552 ),
inference(avatar_split_clause,[],[f33581,f33000,f11442,f33604]) ).
fof(f33604,plain,
( spl0_2591
<=> c_UNIV = c_IntDef_ONats ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2591])]) ).
fof(f11442,plain,
( spl0_1474
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f33000,plain,
( spl0_2552
<=> ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2552])]) ).
fof(f33581,plain,
( c_UNIV = c_IntDef_ONats
| ~ spl0_1474
| ~ spl0_2552 ),
inference(resolution,[],[f33001,f11443]) ).
fof(f11443,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1474 ),
inference(avatar_component_clause,[],[f11442]) ).
fof(f33001,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 )
| ~ spl0_2552 ),
inference(avatar_component_clause,[],[f33000]) ).
fof(f33308,plain,
( spl0_2590
| ~ spl0_17
| ~ spl0_1250
| ~ spl0_1917
| ~ spl0_2527 ),
inference(avatar_split_clause,[],[f32855,f32851,f19326,f10054,f3515,f33305]) ).
fof(f33305,plain,
( spl0_2590
<=> 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_2590])]) ).
fof(f3515,plain,
( spl0_17
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f10054,plain,
( spl0_1250
<=> ! [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_1250])]) ).
fof(f19326,plain,
( spl0_1917
<=> ! [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_1917])]) ).
fof(f32851,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(f32855,plain,
( c_IntDef_Oneg(c_minus(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_17
| ~ spl0_1250
| ~ spl0_1917
| ~ spl0_2527 ),
inference(forward_demodulation,[],[f32853,f20150]) ).
fof(f20150,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_17
| ~ spl0_1250
| ~ spl0_1917 ),
inference(forward_demodulation,[],[f20149,f10055]) ).
fof(f10055,plain,
( ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint)
| ~ spl0_1250 ),
inference(avatar_component_clause,[],[f10054]) ).
fof(f20149,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_17
| ~ spl0_1917 ),
inference(resolution,[],[f19327,f3517]) ).
fof(f3517,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f3515]) ).
fof(f19327,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_1917 ),
inference(avatar_component_clause,[],[f19326]) ).
fof(f32853,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,[],[f32851]) ).
fof(f33303,plain,
( spl0_2589
| ~ spl0_1570
| ~ spl0_2514 ),
inference(avatar_split_clause,[],[f32976,f32704,f12798,f33300]) ).
fof(f33300,plain,
( spl0_2589
<=> c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)) = c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(v_Ba),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2589])]) ).
fof(f12798,plain,
( spl0_1570
<=> ! [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_1570])]) ).
fof(f32704,plain,
( spl0_2514
<=> 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_2514])]) ).
fof(f32976,plain,
( c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)) = c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(v_Ba),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg))
| ~ spl0_1570
| ~ spl0_2514 ),
inference(resolution,[],[f32706,f12799]) ).
fof(f12799,plain,
( ! [X88,X86] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) )
| ~ spl0_1570 ),
inference(avatar_component_clause,[],[f12798]) ).
fof(f32706,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_2514 ),
inference(avatar_component_clause,[],[f32704]) ).
fof(f33213,plain,
( spl0_2588
| ~ spl0_658
| ~ spl0_2228 ),
inference(avatar_split_clause,[],[f26436,f26118,f6179,f33211]) ).
fof(f33211,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(f6179,plain,
( spl0_658
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f26118,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(f26436,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3)
| ~ spl0_658
| ~ spl0_2228 ),
inference(resolution,[],[f26119,f6180]) ).
fof(f6180,plain,
( ! [X1,X4] : ~ c_in(X4,c_emptyset,X1)
| ~ spl0_658 ),
inference(avatar_component_clause,[],[f6179]) ).
fof(f26119,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,[],[f26118]) ).
fof(f33209,plain,
( spl0_2587
| ~ spl0_60
| ~ spl0_948
| ~ spl0_1076
| ~ spl0_1991 ),
inference(avatar_split_clause,[],[f21394,f20883,f8902,f8247,f3730,f33207]) ).
fof(f33207,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(f8247,plain,
( spl0_948
<=> ! [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_948])]) ).
fof(f20883,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(f21394,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_60
| ~ spl0_948
| ~ spl0_1076
| ~ spl0_1991 ),
inference(forward_demodulation,[],[f21391,f9266]) ).
fof(f21391,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_948
| ~ spl0_1991 ),
inference(trivial_inequality_removal,[],[f21388]) ).
fof(f21388,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_948
| ~ spl0_1991 ),
inference(superposition,[],[f20884,f8248]) ).
fof(f8248,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_948 ),
inference(avatar_component_clause,[],[f8247]) ).
fof(f20884,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_1991 ),
inference(avatar_component_clause,[],[f20883]) ).
fof(f33184,plain,
( ~ spl0_31
| ~ spl0_58
| ~ spl0_2582 ),
inference(avatar_split_clause,[],[f33171,f33125,f3720,f3585]) ).
fof(f33125,plain,
( spl0_2582
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2582])]) ).
fof(f33171,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_2582 ),
inference(resolution,[],[f33126,f3722]) ).
fof(f3722,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f3720]) ).
fof(f33126,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_2582 ),
inference(avatar_component_clause,[],[f33125]) ).
fof(f33183,plain,
( spl0_2586
| ~ spl0_876
| ~ spl0_1963 ),
inference(avatar_split_clause,[],[f20697,f19695,f7884,f33181]) ).
fof(f33181,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(f7884,plain,
( spl0_876
<=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f19695,plain,
( spl0_1963
<=> ! [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_1963])]) ).
fof(f20697,plain,
( ! [X0,X1] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OMPair(X0,X1),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_876
| ~ spl0_1963 ),
inference(superposition,[],[f7885,f19696]) ).
fof(f19696,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_1963 ),
inference(avatar_component_clause,[],[f19695]) ).
fof(f7885,plain,
( ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat)
| ~ spl0_876 ),
inference(avatar_component_clause,[],[f7884]) ).
fof(f33179,plain,
( spl0_2585
| ~ spl0_791
| ~ spl0_1759 ),
inference(avatar_split_clause,[],[f15993,f15989,f7530,f33177]) ).
fof(f33177,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(f7530,plain,
( spl0_791
<=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f15989,plain,
( spl0_1759
<=> ! [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_1759])]) ).
fof(f15993,plain,
( ! [X0] : c_0 = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X0,c_0,tc_nat),tc_nat)
| ~ spl0_791
| ~ spl0_1759 ),
inference(superposition,[],[f15990,f7531]) ).
fof(f7531,plain,
( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
| ~ spl0_791 ),
inference(avatar_component_clause,[],[f7530]) ).
fof(f15990,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_1759 ),
inference(avatar_component_clause,[],[f15989]) ).
fof(f33175,plain,
( spl0_2584
| ~ spl0_122
| ~ spl0_1620 ),
inference(avatar_split_clause,[],[f14822,f14348,f4030,f33173]) ).
fof(f33173,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(f4030,plain,
( spl0_122
<=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f14348,plain,
( spl0_1620
<=> ! [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_1620])]) ).
fof(f14822,plain,
( ! [X0] :
( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) )
| ~ spl0_122
| ~ spl0_1620 ),
inference(resolution,[],[f14349,f4031]) ).
fof(f4031,plain,
( ! [X21] : ~ c_less(X21,X21,tc_nat)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f4030]) ).
fof(f14349,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_1620 ),
inference(avatar_component_clause,[],[f14348]) ).
fof(f33170,plain,
( spl0_2582
| spl0_2583
| ~ spl0_802
| ~ spl0_1619 ),
inference(avatar_split_clause,[],[f14807,f14344,f7575,f33168,f33125]) ).
fof(f33168,plain,
( spl0_2583
<=> ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2583])]) ).
fof(f7575,plain,
( spl0_802
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f14344,plain,
( spl0_1619
<=> ! [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_1619])]) ).
fof(f14807,plain,
( ! [X0,X1] :
( ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_802
| ~ spl0_1619 ),
inference(resolution,[],[f14345,f7576]) ).
fof(f7576,plain,
( ! [X0,X1] :
( ~ c_less(X0,X0,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f7575]) ).
fof(f14345,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_1619 ),
inference(avatar_component_clause,[],[f14344]) ).
fof(f33127,plain,
( spl0_2582
| spl0_2509
| ~ spl0_754
| ~ spl0_1616 ),
inference(avatar_split_clause,[],[f14777,f14329,f7381,f32296,f33125]) ).
fof(f32296,plain,
( spl0_2509
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).
fof(f7381,plain,
( spl0_754
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f14329,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(f14777,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_754
| ~ spl0_1616 ),
inference(resolution,[],[f14330,f7382]) ).
fof(f7382,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_754 ),
inference(avatar_component_clause,[],[f7381]) ).
fof(f14330,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_1616 ),
inference(avatar_component_clause,[],[f14329]) ).
fof(f33123,plain,
( spl0_2581
| ~ spl0_774
| ~ spl0_1608 ),
inference(avatar_split_clause,[],[f14681,f14297,f7462,f33121]) ).
fof(f33121,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(f7462,plain,
( spl0_774
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f14297,plain,
( spl0_1608
<=> ! [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_1608])]) ).
fof(f14681,plain,
( ! [X0] : c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0
| ~ spl0_774
| ~ spl0_1608 ),
inference(trivial_inequality_removal,[],[f14666]) ).
fof(f14666,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,X0),tc_IntDef_Oint) = X0 )
| ~ spl0_774
| ~ spl0_1608 ),
inference(superposition,[],[f14298,f7463]) ).
fof(f7463,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint)
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f7462]) ).
fof(f14298,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_1608 ),
inference(avatar_component_clause,[],[f14297]) ).
fof(f33119,plain,
( spl0_2580
| ~ spl0_773
| ~ spl0_1608 ),
inference(avatar_split_clause,[],[f14680,f14297,f7458,f33117]) ).
fof(f33117,plain,
( spl0_2580
<=> ! [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_2580])]) ).
fof(f7458,plain,
( spl0_773
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f14680,plain,
( ! [X0] : c_times(c_1,c_Main_Ozmod__eq__0D__dest__1(c_1,X0),tc_IntDef_Oint) = X0
| ~ spl0_773
| ~ spl0_1608 ),
inference(trivial_inequality_removal,[],[f14668]) ).
fof(f14668,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_773
| ~ spl0_1608 ),
inference(superposition,[],[f14298,f7459]) ).
fof(f7459,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint)
| ~ spl0_773 ),
inference(avatar_component_clause,[],[f7458]) ).
fof(f33115,plain,
( spl0_2579
| ~ spl0_775
| ~ spl0_1608 ),
inference(avatar_split_clause,[],[f14678,f14297,f7466,f33113]) ).
fof(f33113,plain,
( spl0_2579
<=> ! [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_2579])]) ).
fof(f7466,plain,
( spl0_775
<=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f14678,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Ozmod__eq__0D__dest__1(X0,c_0),tc_IntDef_Oint)
| ~ spl0_775
| ~ spl0_1608 ),
inference(trivial_inequality_removal,[],[f14670]) ).
fof(f14670,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_775
| ~ spl0_1608 ),
inference(superposition,[],[f14298,f7467]) ).
fof(f7467,plain,
( ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint)
| ~ spl0_775 ),
inference(avatar_component_clause,[],[f7466]) ).
fof(f33111,plain,
( spl0_2578
| ~ spl0_1570
| ~ spl0_2513 ),
inference(avatar_split_clause,[],[f32823,f32621,f12798,f33108]) ).
fof(f32621,plain,
( spl0_2513
<=> 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_2513])]) ).
fof(f32823,plain,
( c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)) = c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(v_B),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg))
| ~ spl0_1570
| ~ spl0_2513 ),
inference(resolution,[],[f32623,f12799]) ).
fof(f32623,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_2513 ),
inference(avatar_component_clause,[],[f32621]) ).
fof(f33106,plain,
( spl0_2577
| ~ spl0_762
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f14664,f14293,f7413,f33104]) ).
fof(f33104,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(f7413,plain,
( spl0_762
<=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f14293,plain,
( spl0_1607
<=> ! [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_1607])]) ).
fof(f14664,plain,
( ! [X0] : c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0
| ~ spl0_762
| ~ spl0_1607 ),
inference(trivial_inequality_removal,[],[f14652]) ).
fof(f14652,plain,
( ! [X0] :
( c_0 != c_0
| c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,X0),tc_nat) = X0 )
| ~ spl0_762
| ~ spl0_1607 ),
inference(superposition,[],[f14294,f7414]) ).
fof(f7414,plain,
( ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat)
| ~ spl0_762 ),
inference(avatar_component_clause,[],[f7413]) ).
fof(f14294,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_1607 ),
inference(avatar_component_clause,[],[f14293]) ).
fof(f33102,plain,
( spl0_2576
| ~ spl0_839
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f14663,f14293,f7725,f33100]) ).
fof(f33100,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(f7725,plain,
( spl0_839
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f14663,plain,
( ! [X0] : c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0
| ~ spl0_839
| ~ spl0_1607 ),
inference(trivial_inequality_removal,[],[f14653]) ).
fof(f14653,plain,
( ! [X0] :
( c_0 != c_0
| c_times(c_1,c_Main_Omod__eq__0D__dest__1(c_1,X0),tc_nat) = X0 )
| ~ spl0_839
| ~ spl0_1607 ),
inference(superposition,[],[f14294,f7726]) ).
fof(f7726,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat)
| ~ spl0_839 ),
inference(avatar_component_clause,[],[f7725]) ).
fof(f33098,plain,
( spl0_2575
| ~ spl0_761
| ~ spl0_1607 ),
inference(avatar_split_clause,[],[f14662,f14293,f7409,f33096]) ).
fof(f33096,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(f7409,plain,
( spl0_761
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f14662,plain,
( ! [X0] : c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat)
| ~ spl0_761
| ~ spl0_1607 ),
inference(trivial_inequality_removal,[],[f14654]) ).
fof(f14654,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = c_times(X0,c_Main_Omod__eq__0D__dest__1(X0,c_0),tc_nat) )
| ~ spl0_761
| ~ spl0_1607 ),
inference(superposition,[],[f14294,f7410]) ).
fof(f7410,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat)
| ~ spl0_761 ),
inference(avatar_component_clause,[],[f7409]) ).
fof(f33094,plain,
( spl0_2574
| ~ spl0_815
| ~ spl0_1587 ),
inference(avatar_split_clause,[],[f14211,f12876,f7627,f33092]) ).
fof(f33092,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(f7627,plain,
( spl0_815
<=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f12876,plain,
( spl0_1587
<=> ! [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_1587])]) ).
fof(f14211,plain,
( ! [X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_815
| ~ spl0_1587 ),
inference(superposition,[],[f12877,f7628]) ).
fof(f7628,plain,
( ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1)
| ~ spl0_815 ),
inference(avatar_component_clause,[],[f7627]) ).
fof(f12877,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_1587 ),
inference(avatar_component_clause,[],[f12876]) ).
fof(f33090,plain,
( spl0_2573
| ~ spl0_815
| ~ spl0_1586 ),
inference(avatar_split_clause,[],[f14203,f12872,f7627,f33088]) ).
fof(f33088,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(f12872,plain,
( spl0_1586
<=> ! [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_1586])]) ).
fof(f14203,plain,
( ! [X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_UNIV,X0),X0,X0)
| ~ spl0_815
| ~ spl0_1586 ),
inference(superposition,[],[f12873,f7628]) ).
fof(f12873,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_1586 ),
inference(avatar_component_clause,[],[f12872]) ).
fof(f33086,plain,
( spl0_2572
| ~ spl0_820
| ~ spl0_1575 ),
inference(avatar_split_clause,[],[f14155,f12818,f7647,f33084]) ).
fof(f33084,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(f7647,plain,
( spl0_820
<=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f12818,plain,
( spl0_1575
<=> ! [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_1575])]) ).
fof(f14155,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1575 ),
inference(superposition,[],[f7648,f12819]) ).
fof(f12819,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_1575 ),
inference(avatar_component_clause,[],[f12818]) ).
fof(f7648,plain,
( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
| ~ spl0_820 ),
inference(avatar_component_clause,[],[f7647]) ).
fof(f33082,plain,
( spl0_2571
| ~ spl0_820
| ~ spl0_1574 ),
inference(avatar_split_clause,[],[f14134,f12814,f7647,f33080]) ).
fof(f33080,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(f12814,plain,
( spl0_1574
<=> ! [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_1574])]) ).
fof(f14134,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1574 ),
inference(superposition,[],[f7648,f12815]) ).
fof(f12815,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_1574 ),
inference(avatar_component_clause,[],[f12814]) ).
fof(f33078,plain,
( spl0_2570
| ~ spl0_820
| ~ spl0_1573 ),
inference(avatar_split_clause,[],[f14118,f12810,f7647,f33076]) ).
fof(f33076,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(f12810,plain,
( spl0_1573
<=> ! [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_1573])]) ).
fof(f14118,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1573 ),
inference(superposition,[],[f7648,f12811]) ).
fof(f12811,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_1573 ),
inference(avatar_component_clause,[],[f12810]) ).
fof(f33074,plain,
( spl0_2569
| ~ spl0_820
| ~ spl0_1572 ),
inference(avatar_split_clause,[],[f14101,f12806,f7647,f33072]) ).
fof(f33072,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(f12806,plain,
( spl0_1572
<=> ! [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_1572])]) ).
fof(f14101,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1572 ),
inference(superposition,[],[f7648,f12807]) ).
fof(f12807,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_1572 ),
inference(avatar_component_clause,[],[f12806]) ).
fof(f33070,plain,
( spl0_2568
| ~ spl0_820
| ~ spl0_1571 ),
inference(avatar_split_clause,[],[f14084,f12802,f7647,f33068]) ).
fof(f12802,plain,
( spl0_1571
<=> ! [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_1571])]) ).
fof(f14084,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1571 ),
inference(superposition,[],[f7648,f12803]) ).
fof(f12803,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_1571 ),
inference(avatar_component_clause,[],[f12802]) ).
fof(f33065,plain,
( spl0_2567
| ~ spl0_820
| ~ spl0_1567 ),
inference(avatar_split_clause,[],[f14029,f12775,f7647,f33063]) ).
fof(f33063,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(f12775,plain,
( spl0_1567
<=> ! [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_1567])]) ).
fof(f14029,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1567 ),
inference(superposition,[],[f7648,f12776]) ).
fof(f12776,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_1567 ),
inference(avatar_component_clause,[],[f12775]) ).
fof(f33061,plain,
( spl0_2566
| ~ spl0_820
| ~ spl0_1566 ),
inference(avatar_split_clause,[],[f14009,f12771,f7647,f33059]) ).
fof(f33059,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(f12771,plain,
( spl0_1566
<=> ! [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_1566])]) ).
fof(f14009,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1566 ),
inference(superposition,[],[f7648,f12772]) ).
fof(f12772,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_1566 ),
inference(avatar_component_clause,[],[f12771]) ).
fof(f33057,plain,
( spl0_2565
| ~ spl0_820
| ~ spl0_1565 ),
inference(avatar_split_clause,[],[f13989,f12767,f7647,f33055]) ).
fof(f33055,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(f12767,plain,
( spl0_1565
<=> ! [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_1565])]) ).
fof(f13989,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1565 ),
inference(superposition,[],[f7648,f12768]) ).
fof(f12768,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_1565 ),
inference(avatar_component_clause,[],[f12767]) ).
fof(f33053,plain,
( spl0_2564
| ~ spl0_820
| ~ spl0_1564 ),
inference(avatar_split_clause,[],[f13965,f12763,f7647,f33051]) ).
fof(f33051,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(f12763,plain,
( spl0_1564
<=> ! [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_1564])]) ).
fof(f13965,plain,
( ! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X0),X1,tc_Message_Omsg))
| ~ spl0_820
| ~ spl0_1564 ),
inference(superposition,[],[f7648,f12764]) ).
fof(f12764,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_1564 ),
inference(avatar_component_clause,[],[f12763]) ).
fof(f33049,plain,
( spl0_2563
| ~ spl0_675
| ~ spl0_1562 ),
inference(avatar_split_clause,[],[f13937,f12755,f7019,f33047]) ).
fof(f33047,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(f7019,plain,
( spl0_675
<=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f12755,plain,
( spl0_1562
<=> ! [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_1562])]) ).
fof(f13937,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2))
| ~ spl0_675
| ~ spl0_1562 ),
inference(resolution,[],[f12756,f7020]) ).
fof(f7020,plain,
( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
| ~ spl0_675 ),
inference(avatar_component_clause,[],[f7019]) ).
fof(f12756,plain,
( ! [X0,X1,X12,X13] :
( ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1562 ),
inference(avatar_component_clause,[],[f12755]) ).
fof(f33045,plain,
( spl0_2562
| ~ spl0_675
| ~ spl0_1559 ),
inference(avatar_split_clause,[],[f13917,f12743,f7019,f33043]) ).
fof(f33043,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(f12743,plain,
( spl0_1559
<=> ! [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_1559])]) ).
fof(f13917,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| ~ spl0_675
| ~ spl0_1559 ),
inference(resolution,[],[f12744,f7020]) ).
fof(f12744,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| c_lessequals(X13,X32,tc_set(X1)) )
| ~ spl0_1559 ),
inference(avatar_component_clause,[],[f12743]) ).
fof(f33041,plain,
( spl0_2561
| ~ spl0_675
| ~ spl0_1558 ),
inference(avatar_split_clause,[],[f13901,f12738,f7019,f33039]) ).
fof(f12738,plain,
( spl0_1558
<=> ! [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_1558])]) ).
fof(f13901,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| ~ spl0_675
| ~ spl0_1558 ),
inference(resolution,[],[f12739,f7020]) ).
fof(f12739,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| c_lessequals(X12,X32,tc_set(X1)) )
| ~ spl0_1558 ),
inference(avatar_component_clause,[],[f12738]) ).
fof(f33037,plain,
( spl0_2560
| ~ spl0_1028
| ~ spl0_1544 ),
inference(avatar_split_clause,[],[f13782,f12677,f8704,f33035]) ).
fof(f33035,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(f8704,plain,
( spl0_1028
<=> ! [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_1028])]) ).
fof(f12677,plain,
( spl0_1544
<=> ! [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_1544])]) ).
fof(f13782,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__1(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1028
| ~ spl0_1544 ),
inference(superposition,[],[f8705,f12678]) ).
fof(f12678,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_1544 ),
inference(avatar_component_clause,[],[f12677]) ).
fof(f8705,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat)
| ~ spl0_1028 ),
inference(avatar_component_clause,[],[f8704]) ).
fof(f33033,plain,
( spl0_2559
| ~ spl0_1029
| ~ spl0_1544 ),
inference(avatar_split_clause,[],[f13781,f12677,f8708,f33031]) ).
fof(f33031,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(f8708,plain,
( spl0_1029
<=> ! [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_1029])]) ).
fof(f13781,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_Main_Osurj__pair__2(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1029
| ~ spl0_1544 ),
inference(superposition,[],[f8709,f12678]) ).
fof(f8709,plain,
( ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat)
| ~ spl0_1029 ),
inference(avatar_component_clause,[],[f8708]) ).
fof(f33028,plain,
( spl0_2558
| ~ spl0_1028
| ~ spl0_1543 ),
inference(avatar_split_clause,[],[f13776,f12673,f8704,f33026]) ).
fof(f33026,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(f12673,plain,
( spl0_1543
<=> ! [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_1543])]) ).
fof(f13776,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_fst(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1028
| ~ spl0_1543 ),
inference(superposition,[],[f8705,f12674]) ).
fof(f12674,plain,
( ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3
| ~ spl0_1543 ),
inference(avatar_component_clause,[],[f12673]) ).
fof(f33024,plain,
( spl0_2557
| ~ spl0_1450
| ~ spl0_2514 ),
inference(avatar_split_clause,[],[f32975,f32704,f11264,f33021]) ).
fof(f33021,plain,
( spl0_2557
<=> c_in(c_Message_Omsg_OAgent(v_Ba),c_Event_Oused(v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2557])]) ).
fof(f11264,plain,
( spl0_1450
<=> ! [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_1450])]) ).
fof(f32975,plain,
( c_in(c_Message_Omsg_OAgent(v_Ba),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ spl0_1450
| ~ spl0_2514 ),
inference(resolution,[],[f32706,f11265]) ).
fof(f11265,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_1450 ),
inference(avatar_component_clause,[],[f11264]) ).
fof(f33018,plain,
( spl0_2556
| ~ spl0_1029
| ~ spl0_1543 ),
inference(avatar_split_clause,[],[f13775,f12673,f8708,f33016]) ).
fof(f33016,plain,
( spl0_2556
<=> ! [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_2556])]) ).
fof(f13775,plain,
( ! [X0] : c_Divides_Oop_Advd(c_GCD_Ogcd(X0),c_snd(X0,tc_nat,tc_nat),tc_nat)
| ~ spl0_1029
| ~ spl0_1543 ),
inference(superposition,[],[f8709,f12674]) ).
fof(f33014,plain,
( spl0_2555
| ~ spl0_820
| ~ spl0_1507 ),
inference(avatar_split_clause,[],[f13246,f12517,f7647,f33012]) ).
fof(f33012,plain,
( spl0_2555
<=> ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2555])]) ).
fof(f12517,plain,
( spl0_1507
<=> ! [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_1507])]) ).
fof(f13246,plain,
( ! [X2,X0,X1] : c_emptyset != c_List_Oset(c_List_Olist_OCons(X0,X1,X2),X2)
| ~ spl0_820
| ~ spl0_1507 ),
inference(superposition,[],[f7648,f12518]) ).
fof(f12518,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_1507 ),
inference(avatar_component_clause,[],[f12517]) ).
fof(f33010,plain,
( spl0_2554
| ~ spl0_782
| ~ spl0_1500 ),
inference(avatar_split_clause,[],[f13183,f12489,f7494,f33008]) ).
fof(f33008,plain,
( spl0_2554
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2554])]) ).
fof(f7494,plain,
( spl0_782
<=> ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f12489,plain,
( spl0_1500
<=> ! [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_1500])]) ).
fof(f13183,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) != X0
| c_List_Olist_ONil = X0 )
| ~ spl0_782
| ~ spl0_1500 ),
inference(superposition,[],[f7495,f12490]) ).
fof(f12490,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_1500 ),
inference(avatar_component_clause,[],[f12489]) ).
fof(f7495,plain,
( ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23
| ~ spl0_782 ),
inference(avatar_component_clause,[],[f7494]) ).
fof(f33006,plain,
( spl0_2553
| ~ spl0_1023
| ~ spl0_1493 ),
inference(avatar_split_clause,[],[f13121,f12461,f8553,f33004]) ).
fof(f33004,plain,
( spl0_2553
<=> ! [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_2553])]) ).
fof(f8553,plain,
( spl0_1023
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f12461,plain,
( spl0_1493
<=> ! [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_1493])]) ).
fof(f13121,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X1,c_1,tc_nat)
| c_Divides_Oop_Advd(X1,X0,tc_nat) )
| ~ spl0_1023
| ~ spl0_1493 ),
inference(superposition,[],[f12462,f8554]) ).
fof(f8554,plain,
( ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat))
| ~ spl0_1023 ),
inference(avatar_component_clause,[],[f8553]) ).
fof(f12462,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_1493 ),
inference(avatar_component_clause,[],[f12461]) ).
fof(f33002,plain,
( spl0_2552
| ~ spl0_738
| ~ spl0_1484 ),
inference(avatar_split_clause,[],[f13016,f12425,f7298,f33000]) ).
fof(f12425,plain,
( spl0_1484
<=> ! [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_1484])]) ).
fof(f13016,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_UNIV,X0,tc_set(X1))
| c_UNIV = X0 )
| ~ spl0_738
| ~ spl0_1484 ),
inference(resolution,[],[f12426,f7299]) ).
fof(f12426,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13 )
| ~ spl0_1484 ),
inference(avatar_component_clause,[],[f12425]) ).
fof(f32998,plain,
( spl0_2551
| ~ spl0_674
| ~ spl0_1482 ),
inference(avatar_split_clause,[],[f12988,f12417,f7015,f32996]) ).
fof(f32996,plain,
( spl0_2551
<=> ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2551])]) ).
fof(f12417,plain,
( spl0_1482
<=> ! [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_1482])]) ).
fof(f12988,plain,
( ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) )
| ~ spl0_674
| ~ spl0_1482 ),
inference(resolution,[],[f12418,f7016]) ).
fof(f12418,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13
| c_less(X12,X13,tc_set(X1)) )
| ~ spl0_1482 ),
inference(avatar_component_clause,[],[f12417]) ).
fof(f32994,plain,
( spl0_2550
| ~ spl0_738
| ~ spl0_1482 ),
inference(avatar_split_clause,[],[f12979,f12417,f7298,f32992]) ).
fof(f32992,plain,
( spl0_2550
<=> ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2550])]) ).
fof(f12979,plain,
( ! [X0,X1] :
( c_UNIV = X0
| c_less(X0,c_UNIV,tc_set(X1)) )
| ~ spl0_738
| ~ spl0_1482 ),
inference(resolution,[],[f12418,f7299]) ).
fof(f32990,plain,
( spl0_2549
| ~ spl0_790
| ~ spl0_873
| ~ spl0_1593 ),
inference(avatar_split_clause,[],[f12934,f12911,f7872,f7526,f32988]) ).
fof(f32988,plain,
( spl0_2549
<=> ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2549])]) ).
fof(f7526,plain,
( spl0_790
<=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f7872,plain,
( spl0_873
<=> ! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f12911,plain,
( spl0_1593
<=> ! [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_1593])]) ).
fof(f12934,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_1)
| c_0 = X0 )
| ~ spl0_790
| ~ spl0_873
| ~ spl0_1593 ),
inference(forward_demodulation,[],[f12921,f7527]) ).
fof(f7527,plain,
( ! [X3] : c_plus(X3,c_0,tc_nat) = X3
| ~ spl0_790 ),
inference(avatar_component_clause,[],[f7526]) ).
fof(f12921,plain,
( ! [X0] :
( c_List_Olist_ONil = c_List_Oupt(X0,c_plus(c_1,c_0,tc_nat))
| c_0 = X0 )
| ~ spl0_873
| ~ spl0_1593 ),
inference(resolution,[],[f12912,f7873]) ).
fof(f7873,plain,
( ! [X43] :
( ~ c_lessequals(X43,c_0,tc_nat)
| c_0 = X43 )
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f7872]) ).
fof(f12912,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_1593 ),
inference(avatar_component_clause,[],[f12911]) ).
fof(f32986,plain,
( spl0_2548
| ~ spl0_790
| ~ spl0_1000
| ~ spl0_1590 ),
inference(avatar_split_clause,[],[f12900,f12894,f8458,f7526,f32983]) ).
fof(f32983,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(f12894,plain,
( spl0_1590
<=> ! [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_1590])]) ).
fof(f12900,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_790
| ~ spl0_1000
| ~ spl0_1590 ),
inference(forward_demodulation,[],[f12897,f8460]) ).
fof(f12897,plain,
( c_insert(c_0,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(c_0,c_1,tc_nat)
| ~ spl0_790
| ~ spl0_1590 ),
inference(superposition,[],[f12895,f7527]) ).
fof(f12895,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_1590 ),
inference(avatar_component_clause,[],[f12894]) ).
fof(f32981,plain,
( spl0_2547
| ~ spl0_927
| ~ spl0_1590 ),
inference(avatar_split_clause,[],[f12899,f12894,f8161,f32979]) ).
fof(f32979,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(f8161,plain,
( spl0_927
<=> ! [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_927])]) ).
fof(f12899,plain,
( ! [X0] : c_in(c_insert(X0,c_emptyset,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_927
| ~ spl0_1590 ),
inference(superposition,[],[f8162,f12895]) ).
fof(f8162,plain,
( ! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_927 ),
inference(avatar_component_clause,[],[f8161]) ).
fof(f32974,plain,
( spl0_2546
| ~ spl0_895
| ~ spl0_1430 ),
inference(avatar_split_clause,[],[f12009,f11179,f7960,f32972]) ).
fof(f32972,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(f11179,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(f12009,plain,
( ! [X0,X1] :
( c_emptyset != X0
| c_lessequals(X0,c_emptyset,tc_set(X1)) )
| ~ spl0_895
| ~ spl0_1430 ),
inference(superposition,[],[f11180,f7961]) ).
fof(f11180,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_minus(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1430 ),
inference(avatar_component_clause,[],[f11179]) ).
fof(f32970,plain,
( spl0_2545
| ~ spl0_754
| ~ spl0_1422 ),
inference(avatar_split_clause,[],[f11983,f11147,f7381,f32968]) ).
fof(f32968,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(f11147,plain,
( spl0_1422
<=> ! [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_1422])]) ).
fof(f11983,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0) )
| ~ spl0_754
| ~ spl0_1422 ),
inference(duplicate_literal_removal,[],[f11950]) ).
fof(f11950,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_754
| ~ spl0_1422 ),
inference(resolution,[],[f11148,f7382]) ).
fof(f11148,plain,
( ! [X1,X26,X16] :
( ~ c_lessequals(X26,X16,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) )
| ~ spl0_1422 ),
inference(avatar_component_clause,[],[f11147]) ).
fof(f32960,plain,
( spl0_2544
| ~ spl0_79
| ~ spl0_121
| ~ spl0_1422 ),
inference(avatar_split_clause,[],[f11956,f11147,f4026,f3825,f32958]) ).
fof(f32958,plain,
( spl0_2544
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2544])]) ).
fof(f4026,plain,
( spl0_121
<=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f11956,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,c_0,tc_nat) )
| ~ spl0_121
| ~ spl0_1422 ),
inference(resolution,[],[f11148,f4027]) ).
fof(f4027,plain,
( ! [X21] : c_lessequals(c_0,X21,tc_nat)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f4026]) ).
fof(f32956,plain,
( spl0_2543
| ~ spl0_754
| ~ spl0_1413 ),
inference(avatar_split_clause,[],[f11928,f11108,f7381,f32954]) ).
fof(f32954,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(f11108,plain,
( spl0_1413
<=> ! [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_1413])]) ).
fof(f11928,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0) )
| ~ spl0_754
| ~ spl0_1413 ),
inference(duplicate_literal_removal,[],[f11895]) ).
fof(f11895,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_754
| ~ spl0_1413 ),
inference(resolution,[],[f11109,f7382]) ).
fof(f11109,plain,
( ! [X21,X1,X15] :
( ~ c_lessequals(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) )
| ~ spl0_1413 ),
inference(avatar_component_clause,[],[f11108]) ).
fof(f32938,plain,
( spl0_2542
| ~ spl0_79
| ~ spl0_121
| ~ spl0_1413 ),
inference(avatar_split_clause,[],[f11901,f11108,f4026,f3825,f32936]) ).
fof(f32936,plain,
( spl0_2542
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2542])]) ).
fof(f11901,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastLessThan(X0,c_0,tc_nat) )
| ~ spl0_121
| ~ spl0_1413 ),
inference(resolution,[],[f11109,f4027]) ).
fof(f32930,plain,
( spl0_2541
| ~ spl0_31
| ~ spl0_669
| ~ spl0_1412 ),
inference(avatar_split_clause,[],[f11876,f11104,f6230,f3585,f32927]) ).
fof(f32927,plain,
( spl0_2541
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2541])]) ).
fof(f6230,plain,
( spl0_669
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f11104,plain,
( spl0_1412
<=> ! [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_1412])]) ).
fof(f11876,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_669
| ~ spl0_1412 ),
inference(resolution,[],[f11105,f6232]) ).
fof(f6232,plain,
( c_less(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_669 ),
inference(avatar_component_clause,[],[f6230]) ).
fof(f11105,plain,
( ! [X21,X1,X15] :
( ~ c_less(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) )
| ~ spl0_1412 ),
inference(avatar_component_clause,[],[f11104]) ).
fof(f32919,plain,
( spl0_2540
| ~ spl0_79
| ~ spl0_655
| ~ spl0_1412 ),
inference(avatar_split_clause,[],[f11875,f11104,f6165,f3825,f32916]) ).
fof(f32916,plain,
( spl0_2540
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2540])]) ).
fof(f6165,plain,
( spl0_655
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f11875,plain,
( ~ class_Orderings_Oorder(tc_nat)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,tc_nat)
| ~ spl0_655
| ~ spl0_1412 ),
inference(resolution,[],[f11105,f6167]) ).
fof(f6167,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f6165]) ).
fof(f32912,plain,
( spl0_2538
| ~ spl0_2539
| ~ spl0_798
| ~ spl0_1324 ),
inference(avatar_split_clause,[],[f10771,f10355,f7558,f32909,f32906]) ).
fof(f32906,plain,
( spl0_2538
<=> ! [X0] : c_lessequals(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2538])]) ).
fof(f32909,plain,
( spl0_2539
<=> c_lessequals(c_1,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2539])]) ).
fof(f7558,plain,
( spl0_798
<=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f10355,plain,
( spl0_1324
<=> ! [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_1324])]) ).
fof(f10771,plain,
( ! [X0] :
( ~ c_lessequals(c_1,c_0,tc_nat)
| c_lessequals(c_1,X0,tc_nat) )
| ~ spl0_798
| ~ spl0_1324 ),
inference(superposition,[],[f10356,f7559]) ).
fof(f7559,plain,
( ! [X21] : c_0 = c_times(c_0,X21,tc_nat)
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f7558]) ).
fof(f10356,plain,
( ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) )
| ~ spl0_1324 ),
inference(avatar_component_clause,[],[f10355]) ).
fof(f32896,plain,
( spl0_2537
| ~ spl0_48
| ~ spl0_691
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10595,f10222,f7087,f3670,f32894]) ).
fof(f32894,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(f10595,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_IntDef_Oint(X0),tc_IntDef_Oint) )
| ~ spl0_691
| ~ spl0_1292 ),
inference(resolution,[],[f10223,f7088]) ).
fof(f32892,plain,
( spl0_2536
| ~ spl0_17
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f9945,f9577,f3515,f32890]) ).
fof(f32890,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(f9577,plain,
( spl0_1189
<=> ! [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_1189])]) ).
fof(f9945,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_17
| ~ spl0_1189 ),
inference(resolution,[],[f9578,f3517]) ).
fof(f9578,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) )
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f9577]) ).
fof(f32888,plain,
( spl0_2535
| ~ spl0_17
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f9934,f9561,f3515,f32886]) ).
fof(f32886,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(f9561,plain,
( spl0_1185
<=> ! [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_1185])]) ).
fof(f9934,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint)
| ~ spl0_17
| ~ spl0_1185 ),
inference(resolution,[],[f9562,f3517]) ).
fof(f9562,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) )
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f9561]) ).
fof(f32884,plain,
( spl0_2534
| ~ spl0_17
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f9930,f9549,f3515,f32882]) ).
fof(f32882,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(f9549,plain,
( spl0_1182
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f9930,plain,
( ! [X0] : c_0 = c_plus(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_17
| ~ spl0_1182 ),
inference(resolution,[],[f9550,f3517]) ).
fof(f9550,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) )
| ~ spl0_1182 ),
inference(avatar_component_clause,[],[f9549]) ).
fof(f32880,plain,
( spl0_2533
| ~ spl0_30
| ~ spl0_1156 ),
inference(avatar_split_clause,[],[f9820,f9444,f3580,f32878]) ).
fof(f32878,plain,
( spl0_2533
<=> ! [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_2533])]) ).
fof(f9444,plain,
( spl0_1156
<=> ! [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_1156])]) ).
fof(f9820,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,tc_IntDef_Oint) = c_IntDef_Oof__int(c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_30
| ~ spl0_1156 ),
inference(resolution,[],[f9445,f3582]) ).
fof(f9445,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_1156 ),
inference(avatar_component_clause,[],[f9444]) ).
fof(f32876,plain,
( spl0_2532
| ~ spl0_99
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f9811,f9423,f3925,f32874]) ).
fof(f32874,plain,
( spl0_2532
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2532])]) ).
fof(f3925,plain,
( spl0_99
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f9423,plain,
( spl0_1151
<=> ! [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_1151])]) ).
fof(f9811,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_99
| ~ spl0_1151 ),
inference(resolution,[],[f9424,f3927]) ).
fof(f3927,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f3925]) ).
fof(f9424,plain,
( ! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 )
| ~ spl0_1151 ),
inference(avatar_component_clause,[],[f9423]) ).
fof(f32872,plain,
( spl0_2531
| ~ spl0_1450
| ~ spl0_2513 ),
inference(avatar_split_clause,[],[f32822,f32621,f11264,f32869]) ).
fof(f32869,plain,
( spl0_2531
<=> c_in(c_Message_Omsg_OAgent(v_B),c_Event_Oused(v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).
fof(f32822,plain,
( c_in(c_Message_Omsg_OAgent(v_B),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ spl0_1450
| ~ spl0_2513 ),
inference(resolution,[],[f32623,f11265]) ).
fof(f32867,plain,
( spl0_2530
| ~ spl0_35
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f9810,f9423,f3605,f32865]) ).
fof(f32865,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(f3605,plain,
( spl0_35
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f9810,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_35
| ~ spl0_1151 ),
inference(resolution,[],[f9424,f3607]) ).
fof(f3607,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f3605]) ).
fof(f32863,plain,
( spl0_2529
| ~ spl0_99
| ~ spl0_1150 ),
inference(avatar_split_clause,[],[f9809,f9419,f3925,f32861]) ).
fof(f32861,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(f9419,plain,
( spl0_1150
<=> ! [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_1150])]) ).
fof(f9809,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_nat),tc_nat) = X0
| ~ spl0_99
| ~ spl0_1150 ),
inference(resolution,[],[f9420,f3927]) ).
fof(f9420,plain,
( ! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 )
| ~ spl0_1150 ),
inference(avatar_component_clause,[],[f9419]) ).
fof(f32859,plain,
( spl0_2528
| ~ spl0_35
| ~ spl0_1150 ),
inference(avatar_split_clause,[],[f9808,f9419,f3605,f32857]) ).
fof(f32857,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(f9808,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_35
| ~ spl0_1150 ),
inference(resolution,[],[f9420,f3607]) ).
fof(f32854,plain,
( spl0_2527
| ~ spl0_649
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f9727,f9724,f6138,f32851]) ).
fof(f9724,plain,
( spl0_1225
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f9727,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_1225 ),
inference(superposition,[],[f9725,f6140]) ).
fof(f9725,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1225 ),
inference(avatar_component_clause,[],[f9724]) ).
fof(f32849,plain,
( ~ spl0_2525
| spl0_2526
| ~ spl0_666
| ~ spl0_1126 ),
inference(avatar_split_clause,[],[f9346,f9105,f6216,f32846,f32842]) ).
fof(f32842,plain,
( spl0_2525
<=> c_less(c_1,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).
fof(f32846,plain,
( spl0_2526
<=> c_less(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).
fof(f9346,plain,
( c_less(c_1,c_1,tc_nat)
| ~ c_less(c_1,c_1,tc_IntDef_Oint)
| ~ spl0_666
| ~ spl0_1126 ),
inference(superposition,[],[f9106,f6218]) ).
fof(f32840,plain,
( spl0_2524
| ~ spl0_1001
| ~ spl0_1091 ),
inference(avatar_split_clause,[],[f9282,f8964,f8463,f32838]) ).
fof(f32838,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(f8463,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(f8964,plain,
( spl0_1091
<=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f9282,plain,
( ! [X0] : c_emptyset = c_Set_Ocontents(c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_1001
| ~ spl0_1091 ),
inference(superposition,[],[f8464,f8965]) ).
fof(f8965,plain,
( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
| ~ spl0_1091 ),
inference(avatar_component_clause,[],[f8964]) ).
fof(f8464,plain,
( ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3
| ~ spl0_1001 ),
inference(avatar_component_clause,[],[f8463]) ).
fof(f32836,plain,
( spl0_2523
| ~ spl0_872
| ~ spl0_1073 ),
inference(avatar_split_clause,[],[f9257,f8890,f7868,f32834]) ).
fof(f32834,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(f8890,plain,
( spl0_1073
<=> ! [X43,X59] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f9257,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_minus(X0,X1,tc_nat))
| ~ spl0_872
| ~ spl0_1073 ),
inference(resolution,[],[f8891,f7869]) ).
fof(f8891,plain,
( ! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) )
| ~ spl0_1073 ),
inference(avatar_component_clause,[],[f8890]) ).
fof(f32832,plain,
( spl0_2522
| ~ spl0_852
| ~ spl0_1073 ),
inference(avatar_split_clause,[],[f9256,f8890,f7788,f32830]) ).
fof(f32830,plain,
( spl0_2522
<=> ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).
fof(f9256,plain,
( ! [X0,X1] : c_List_Olist_ONil = c_List_Oupt(X0,c_div(X0,X1,tc_nat))
| ~ spl0_852
| ~ spl0_1073 ),
inference(resolution,[],[f8891,f7789]) ).
fof(f32828,plain,
( spl0_2521
| ~ spl0_1001
| ~ spl0_1063 ),
inference(avatar_split_clause,[],[f9229,f8850,f8463,f32826]) ).
fof(f32826,plain,
( spl0_2521
<=> ! [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_2521])]) ).
fof(f8850,plain,
( spl0_1063
<=> ! [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_1063])]) ).
fof(f9229,plain,
( ! [X0] : c_List_Olist_ONil = c_Set_Ocontents(c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_1001
| ~ spl0_1063 ),
inference(superposition,[],[f8464,f8851]) ).
fof(f8851,plain,
( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
| ~ spl0_1063 ),
inference(avatar_component_clause,[],[f8850]) ).
fof(f32821,plain,
( spl0_2520
| ~ spl0_858
| ~ spl0_1048 ),
inference(avatar_split_clause,[],[f9195,f8787,f7812,f32819]) ).
fof(f32819,plain,
( spl0_2520
<=> ! [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_2520])]) ).
fof(f8787,plain,
( spl0_1048
<=> ! [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_1048])]) ).
fof(f9195,plain,
( ! [X0,X1] : c_lessequals(c_0,c_Nat_Opower(c_IntDef_Oint(X0),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_858
| ~ spl0_1048 ),
inference(superposition,[],[f8788,f7813]) ).
fof(f8788,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_1048 ),
inference(avatar_component_clause,[],[f8787]) ).
fof(f32817,plain,
( spl0_2519
| ~ spl0_877
| ~ spl0_1043 ),
inference(avatar_split_clause,[],[f9173,f8767,f7888,f32815]) ).
fof(f32815,plain,
( spl0_2519
<=> ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2519])]) ).
fof(f8767,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(f9173,plain,
( ! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X0) )
| ~ spl0_877
| ~ spl0_1043 ),
inference(resolution,[],[f8768,f7889]) ).
fof(f8768,plain,
( ! [X48] :
( ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat)
| c_less(c_0,X48,tc_IntDef_Oint) )
| ~ spl0_1043 ),
inference(avatar_component_clause,[],[f8767]) ).
fof(f32813,plain,
( spl0_2518
| ~ spl0_742
| ~ spl0_1004 ),
inference(avatar_split_clause,[],[f8682,f8475,f7316,f32811]) ).
fof(f32811,plain,
( spl0_2518
<=> ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).
fof(f7316,plain,
( spl0_742
<=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f8682,plain,
( ! [X0,X1] :
( c_Message_OinvKey(X1) != X0
| c_Message_OinvKey(X0) = X1 )
| ~ spl0_742
| ~ spl0_1004 ),
inference(superposition,[],[f8476,f7317]) ).
fof(f7317,plain,
( ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3
| ~ spl0_742 ),
inference(avatar_component_clause,[],[f7316]) ).
fof(f32801,plain,
( spl0_2517
| ~ spl0_48
| ~ spl0_945
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f8642,f8372,f8235,f3670,f32799]) ).
fof(f32799,plain,
( spl0_2517
<=> ! [X0] : c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).
fof(f8235,plain,
( spl0_945
<=> ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f8642,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) )
| ~ spl0_945
| ~ spl0_979 ),
inference(resolution,[],[f8373,f8236]) ).
fof(f8236,plain,
( ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) )
| ~ spl0_945 ),
inference(avatar_component_clause,[],[f8235]) ).
fof(f32797,plain,
( spl0_2516
| ~ spl0_867
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f8591,f8259,f7848,f32795]) ).
fof(f32795,plain,
( spl0_2516
<=> ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).
fof(f7848,plain,
( spl0_867
<=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f8259,plain,
( spl0_951
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f8591,plain,
( ! [X0,X1] :
( c_List_Olist_ONil != X0
| c_List_Olist_ONil = c_List_Orev(X0,X1) )
| ~ spl0_867
| ~ spl0_951 ),
inference(superposition,[],[f8260,f7849]) ).
fof(f7849,plain,
( ! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3
| ~ spl0_867 ),
inference(avatar_component_clause,[],[f7848]) ).
fof(f8260,plain,
( ! [X1,X23] :
( c_List_Olist_ONil != c_List_Orev(X23,X1)
| c_List_Olist_ONil = X23 )
| ~ spl0_951 ),
inference(avatar_component_clause,[],[f8259]) ).
fof(f32735,plain,
( spl0_2515
| ~ spl0_117
| ~ spl0_2046 ),
inference(avatar_split_clause,[],[f22552,f22415,f4010,f32733]) ).
fof(f32733,plain,
( spl0_2515
<=> ! [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_2515])]) ).
fof(f4010,plain,
( spl0_117
<=> ! [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_117])]) ).
fof(f22415,plain,
( spl0_2046
<=> ! [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_2046])]) ).
fof(f22552,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_117
| ~ spl0_2046 ),
inference(resolution,[],[f22416,f4011]) ).
fof(f4011,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_117 ),
inference(avatar_component_clause,[],[f4010]) ).
fof(f22416,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_2046 ),
inference(avatar_component_clause,[],[f22415]) ).
fof(f32707,plain,
( spl0_2514
| ~ spl0_1214
| ~ spl0_2497 ),
inference(avatar_split_clause,[],[f32355,f32246,f9678,f32704]) ).
fof(f9678,plain,
( spl0_1214
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f32246,plain,
( spl0_2497
<=> 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_2497])]) ).
fof(f32355,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_1214
| ~ spl0_2497 ),
inference(resolution,[],[f32248,f9679]) ).
fof(f9679,plain,
( ! [X88,X86] :
( ~ c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) )
| ~ spl0_1214 ),
inference(avatar_component_clause,[],[f9678]) ).
fof(f32248,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_2497 ),
inference(avatar_component_clause,[],[f32246]) ).
fof(f32624,plain,
( spl0_2513
| ~ spl0_1214
| ~ spl0_2488 ),
inference(avatar_split_clause,[],[f32290,f32172,f9678,f32621]) ).
fof(f32172,plain,
( spl0_2488
<=> 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_2488])]) ).
fof(f32290,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_1214
| ~ spl0_2488 ),
inference(resolution,[],[f32174,f9679]) ).
fof(f32174,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_2488 ),
inference(avatar_component_clause,[],[f32172]) ).
fof(f32365,plain,
( spl0_2512
| ~ spl0_123
| ~ spl0_1891 ),
inference(avatar_split_clause,[],[f19880,f19213,f4034,f32363]) ).
fof(f32363,plain,
( spl0_2512
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).
fof(f4034,plain,
( spl0_123
<=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f19213,plain,
( spl0_1891
<=> ! [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_1891])]) ).
fof(f19880,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
| ~ spl0_123
| ~ spl0_1891 ),
inference(resolution,[],[f19214,f4035]) ).
fof(f4035,plain,
( ! [X0,X1] : c_in(X0,c_UNIV,X1)
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f4034]) ).
fof(f19214,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_1891 ),
inference(avatar_component_clause,[],[f19213]) ).
fof(f32361,plain,
( spl0_2511
| ~ spl0_123
| ~ spl0_1888 ),
inference(avatar_split_clause,[],[f19827,f19201,f4034,f32359]) ).
fof(f32359,plain,
( spl0_2511
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).
fof(f19201,plain,
( spl0_1888
<=> ! [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_1888])]) ).
fof(f19827,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
| ~ spl0_123
| ~ spl0_1888 ),
inference(resolution,[],[f19202,f4035]) ).
fof(f19202,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_1888 ),
inference(avatar_component_clause,[],[f19201]) ).
fof(f32303,plain,
( spl0_2510
| ~ spl0_655
| ~ spl0_792
| ~ spl0_1623 ),
inference(avatar_split_clause,[],[f14875,f14360,f7534,f6165,f32300]) ).
fof(f32300,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(f7534,plain,
( spl0_792
<=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f14360,plain,
( spl0_1623
<=> ! [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_1623])]) ).
fof(f14875,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_655
| ~ spl0_792
| ~ spl0_1623 ),
inference(forward_demodulation,[],[f14857,f7535]) ).
fof(f7535,plain,
( ! [X15] : c_0 = c_minus(X15,X15,tc_nat)
| ~ spl0_792 ),
inference(avatar_component_clause,[],[f7534]) ).
fof(f14857,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_655
| ~ spl0_1623 ),
inference(resolution,[],[f14361,f6167]) ).
fof(f14361,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_1623 ),
inference(avatar_component_clause,[],[f14360]) ).
fof(f32298,plain,
( spl0_2508
| spl0_2509
| ~ spl0_675
| ~ spl0_1616 ),
inference(avatar_split_clause,[],[f14778,f14329,f7019,f32296,f32293]) ).
fof(f32293,plain,
( spl0_2508
<=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).
fof(f14778,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
| ~ spl0_675
| ~ spl0_1616 ),
inference(resolution,[],[f14330,f7020]) ).
fof(f32289,plain,
( spl0_2507
| ~ spl0_852
| ~ spl0_1598 ),
inference(avatar_split_clause,[],[f14277,f12963,f7788,f32287]) ).
fof(f32287,plain,
( spl0_2507
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).
fof(f12963,plain,
( spl0_1598
<=> ! [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_1598])]) ).
fof(f14277,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_852
| ~ spl0_1598 ),
inference(superposition,[],[f7789,f12964]) ).
fof(f12964,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_1598 ),
inference(avatar_component_clause,[],[f12963]) ).
fof(f32285,plain,
( spl0_2506
| ~ spl0_1243
| ~ spl0_1543 ),
inference(avatar_split_clause,[],[f13772,f12673,f10025,f32283]) ).
fof(f32283,plain,
( spl0_2506
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f10025,plain,
( spl0_1243
<=> ! [X2,X27,X1,X18] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f13772,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1243
| ~ spl0_1543 ),
inference(superposition,[],[f10026,f12674]) ).
fof(f10026,plain,
( ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2))
| ~ spl0_1243 ),
inference(avatar_component_clause,[],[f10025]) ).
fof(f32281,plain,
( spl0_2505
| ~ spl0_799
| ~ spl0_823
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10766,f10343,f7659,f7562,f32279]) ).
fof(f32279,plain,
( spl0_2505
<=> ! [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_2505])]) ).
fof(f7562,plain,
( spl0_799
<=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f7659,plain,
( spl0_823
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f10766,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_799
| ~ spl0_823
| ~ spl0_1321 ),
inference(forward_demodulation,[],[f10755,f7563]) ).
fof(f7563,plain,
( ! [X3] : c_plus(c_0,X3,tc_nat) = X3
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7562]) ).
fof(f10755,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_823
| ~ spl0_1321 ),
inference(superposition,[],[f10344,f7660]) ).
fof(f7660,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg)
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f7659]) ).
fof(f32277,plain,
( spl0_2504
| ~ spl0_799
| ~ spl0_824
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10765,f10343,f7663,f7562,f32275]) ).
fof(f32275,plain,
( spl0_2504
<=> ! [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_2504])]) ).
fof(f7663,plain,
( spl0_824
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f10765,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_799
| ~ spl0_824
| ~ spl0_1321 ),
inference(forward_demodulation,[],[f10754,f7563]) ).
fof(f10754,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_824
| ~ spl0_1321 ),
inference(superposition,[],[f10344,f7664]) ).
fof(f7664,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg)
| ~ spl0_824 ),
inference(avatar_component_clause,[],[f7663]) ).
fof(f32273,plain,
( spl0_2503
| ~ spl0_799
| ~ spl0_825
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10764,f10343,f7667,f7562,f32271]) ).
fof(f32271,plain,
( spl0_2503
<=> ! [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_2503])]) ).
fof(f7667,plain,
( spl0_825
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f10764,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_799
| ~ spl0_825
| ~ spl0_1321 ),
inference(forward_demodulation,[],[f10753,f7563]) ).
fof(f10753,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_825
| ~ spl0_1321 ),
inference(superposition,[],[f10344,f7668]) ).
fof(f7668,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg)
| ~ spl0_825 ),
inference(avatar_component_clause,[],[f7667]) ).
fof(f32269,plain,
( spl0_2502
| ~ spl0_799
| ~ spl0_822
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10762,f10343,f7655,f7562,f32267]) ).
fof(f32267,plain,
( spl0_2502
<=> ! [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_2502])]) ).
fof(f7655,plain,
( spl0_822
<=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f10762,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
| ~ spl0_799
| ~ spl0_822
| ~ spl0_1321 ),
inference(forward_demodulation,[],[f10751,f7563]) ).
fof(f10751,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_822
| ~ spl0_1321 ),
inference(superposition,[],[f10344,f7656]) ).
fof(f7656,plain,
( ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg)
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f7655]) ).
fof(f32265,plain,
( spl0_2501
| ~ spl0_876
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10760,f10343,f7884,f32263]) ).
fof(f32263,plain,
( spl0_2501
<=> ! [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_2501])]) ).
fof(f10760,plain,
( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_876
| ~ spl0_1321 ),
inference(superposition,[],[f7885,f10344]) ).
fof(f32261,plain,
( spl0_2500
| ~ spl0_650
| ~ spl0_1206
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10750,f10339,f9646,f6143,f32259]) ).
fof(f32259,plain,
( spl0_2500
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).
fof(f9646,plain,
( spl0_1206
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f10339,plain,
( spl0_1320
<=> ! [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_1320])]) ).
fof(f10750,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_1206
| ~ spl0_1320 ),
inference(forward_demodulation,[],[f10747,f9647]) ).
fof(f9647,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1206 ),
inference(avatar_component_clause,[],[f9646]) ).
fof(f10747,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_650
| ~ spl0_1320 ),
inference(superposition,[],[f10340,f6145]) ).
fof(f10340,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_1320 ),
inference(avatar_component_clause,[],[f10339]) ).
fof(f32257,plain,
( spl0_2498
| ~ spl0_2499
| ~ spl0_121
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10566,f10210,f4026,f32254,f32251]) ).
fof(f32251,plain,
( spl0_2498
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).
fof(f32254,plain,
( spl0_2499
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f10566,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_121
| ~ spl0_1289 ),
inference(resolution,[],[f10211,f4027]) ).
fof(f32249,plain,
( spl0_2497
| ~ spl0_1458
| ~ spl0_2486 ),
inference(avatar_split_clause,[],[f32162,f32158,f11296,f32246]) ).
fof(f11296,plain,
( spl0_1458
<=> ! [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_1458])]) ).
fof(f32158,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(f32162,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_1458
| ~ spl0_2486 ),
inference(resolution,[],[f32160,f11297]) ).
fof(f11297,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_1458 ),
inference(avatar_component_clause,[],[f11296]) ).
fof(f32160,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,[],[f32158]) ).
fof(f32244,plain,
( spl0_2496
| ~ spl0_720
| ~ spl0_746
| ~ spl0_914
| ~ spl0_1284 ),
inference(avatar_split_clause,[],[f10553,f10190,f8037,f7334,f7221,f32241]) ).
fof(f32241,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(f7221,plain,
( spl0_720
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f7334,plain,
( spl0_746
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f10553,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_720
| ~ spl0_746
| ~ spl0_914
| ~ spl0_1284 ),
inference(forward_demodulation,[],[f10552,f7223]) ).
fof(f7223,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_720 ),
inference(avatar_component_clause,[],[f7221]) ).
fof(f10552,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_746
| ~ spl0_914
| ~ spl0_1284 ),
inference(forward_demodulation,[],[f10548,f8039]) ).
fof(f10548,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_746
| ~ spl0_1284 ),
inference(superposition,[],[f10191,f7336]) ).
fof(f7336,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_746 ),
inference(avatar_component_clause,[],[f7334]) ).
fof(f32239,plain,
( spl0_2495
| ~ spl0_655
| ~ spl0_1264 ),
inference(avatar_split_clause,[],[f10457,f10110,f6165,f32236]) ).
fof(f32236,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(f10110,plain,
( spl0_1264
<=> ! [X59,X3] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f10457,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_655
| ~ spl0_1264 ),
inference(resolution,[],[f10111,f6167]) ).
fof(f10111,plain,
( ! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 )
| ~ spl0_1264 ),
inference(avatar_component_clause,[],[f10110]) ).
fof(f32234,plain,
( spl0_2494
| ~ spl0_800
| ~ spl0_1180 ),
inference(avatar_split_clause,[],[f9912,f9541,f7566,f32232]) ).
fof(f32232,plain,
( spl0_2494
<=> ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).
fof(f7566,plain,
( spl0_800
<=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f9541,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(f9912,plain,
( ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_800
| ~ spl0_1180 ),
inference(superposition,[],[f9542,f7567]) ).
fof(f7567,plain,
( ! [X3] : c_minus(X3,c_0,tc_nat) = X3
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f7566]) ).
fof(f9542,plain,
( ! [X21,X15] :
( c_0 != c_minus(X15,X21,tc_nat)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1180 ),
inference(avatar_component_clause,[],[f9541]) ).
fof(f32230,plain,
( spl0_2493
| ~ spl0_1022
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f9308,f9016,f8549,f32228]) ).
fof(f32228,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(f8549,plain,
( spl0_1022
<=> ! [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_1022])]) ).
fof(f9016,plain,
( spl0_1104
<=> ! [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_1104])]) ).
fof(f9308,plain,
( ! [X0,X1] : ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oknows(X1,c_List_Olist_ONil),tc_Message_Omsg)
| ~ spl0_1022
| ~ spl0_1104 ),
inference(resolution,[],[f9017,f8550]) ).
fof(f8550,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_1022 ),
inference(avatar_component_clause,[],[f8549]) ).
fof(f9017,plain,
( ! [X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X86,X88,tc_Message_Omsg) )
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f9016]) ).
fof(f32226,plain,
( spl0_2492
| ~ spl0_898
| ~ spl0_1091 ),
inference(avatar_split_clause,[],[f9283,f8964,f7972,f32224]) ).
fof(f32224,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(f7972,plain,
( spl0_898
<=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f9283,plain,
( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_898
| ~ spl0_1091 ),
inference(superposition,[],[f7973,f8965]) ).
fof(f7973,plain,
( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_898 ),
inference(avatar_component_clause,[],[f7972]) ).
fof(f32222,plain,
( spl0_2491
| ~ spl0_17
| ~ spl0_1080 ),
inference(avatar_split_clause,[],[f9274,f8919,f3515,f32220]) ).
fof(f32220,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(f8919,plain,
( spl0_1080
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f9274,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_17
| ~ spl0_1080 ),
inference(resolution,[],[f8920,f3517]) ).
fof(f8920,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 )
| ~ spl0_1080 ),
inference(avatar_component_clause,[],[f8919]) ).
fof(f32218,plain,
( spl0_2490
| ~ spl0_60
| ~ spl0_1076 ),
inference(avatar_split_clause,[],[f9266,f8902,f3730,f32215]) ).
fof(f32215,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(f32179,plain,
( spl0_2489
| ~ spl0_117
| ~ spl0_2012 ),
inference(avatar_split_clause,[],[f21834,f20972,f4010,f32177]) ).
fof(f32177,plain,
( spl0_2489
<=> ! [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_2489])]) ).
fof(f20972,plain,
( spl0_2012
<=> ! [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_2012])]) ).
fof(f21834,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_117
| ~ spl0_2012 ),
inference(resolution,[],[f20973,f4011]) ).
fof(f20973,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_2012 ),
inference(avatar_component_clause,[],[f20972]) ).
fof(f32175,plain,
( spl0_2488
| ~ spl0_1458
| ~ spl0_2483 ),
inference(avatar_split_clause,[],[f32116,f32108,f11296,f32172]) ).
fof(f32108,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(f32116,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_1458
| ~ spl0_2483 ),
inference(resolution,[],[f32110,f11297]) ).
fof(f32110,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,[],[f32108]) ).
fof(f32170,plain,
( spl0_2487
| ~ spl0_753
| ~ spl0_1798 ),
inference(avatar_split_clause,[],[f18216,f17183,f7376,f32167]) ).
fof(f32167,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(f17183,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(f18216,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_753
| ~ spl0_1798 ),
inference(resolution,[],[f17184,f7378]) ).
fof(f17184,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,[],[f17183]) ).
fof(f32161,plain,
( ~ spl0_6
| spl0_2486
| ~ spl0_752
| ~ spl0_2084 ),
inference(avatar_split_clause,[],[f23555,f23061,f7371,f32158,f3460]) ).
fof(f23061,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(f23555,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_752
| ~ spl0_2084 ),
inference(resolution,[],[f23062,f7373]) ).
fof(f23062,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,[],[f23061]) ).
fof(f32128,plain,
( spl0_2485
| spl0_8
| ~ spl0_2012 ),
inference(avatar_split_clause,[],[f21900,f20972,f3470,f32126]) ).
fof(f32126,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(f21900,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_8
| ~ spl0_2012 ),
inference(resolution,[],[f20973,f3472]) ).
fof(f3472,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_8 ),
inference(avatar_component_clause,[],[f3470]) ).
fof(f32115,plain,
( spl0_2484
| ~ spl0_117
| ~ spl0_1995 ),
inference(avatar_split_clause,[],[f21500,f20903,f4010,f32113]) ).
fof(f32113,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(f20903,plain,
( spl0_1995
<=> ! [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_1995])]) ).
fof(f21500,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_117
| ~ spl0_1995 ),
inference(resolution,[],[f20904,f4011]) ).
fof(f20904,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_1995 ),
inference(avatar_component_clause,[],[f20903]) ).
fof(f32111,plain,
( spl0_2483
| ~ spl0_753
| ~ spl0_1842 ),
inference(avatar_split_clause,[],[f19017,f17375,f7376,f32108]) ).
fof(f17375,plain,
( spl0_1842
<=> ! [X102,X86,X12,X13] :
( c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f19017,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_753
| ~ spl0_1842 ),
inference(resolution,[],[f17376,f7378]) ).
fof(f17376,plain,
( ! [X86,X12,X102,X13] :
( ~ c_in(c_Event_Oevent_OSays(X12,X13,X86),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| c_in(X86,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg) )
| ~ spl0_1842 ),
inference(avatar_component_clause,[],[f17375]) ).
fof(f32083,plain,
( spl0_2482
| ~ spl0_1306
| ~ spl0_2133 ),
inference(avatar_split_clause,[],[f23944,f23834,f10278,f32081]) ).
fof(f32081,plain,
( spl0_2482
<=> ! [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_2482])]) ).
fof(f10278,plain,
( spl0_1306
<=> ! [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_1306])]) ).
fof(f23834,plain,
( spl0_2133
<=> ! [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_2133])]) ).
fof(f23944,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_1306
| ~ spl0_2133 ),
inference(superposition,[],[f10279,f23835]) ).
fof(f23835,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_2133 ),
inference(avatar_component_clause,[],[f23834]) ).
fof(f10279,plain,
( ! [X1,X4,X12,X13] :
( c_in(X4,c_union(X12,X13,X1),X1)
| ~ c_in(X4,X13,X1) )
| ~ spl0_1306 ),
inference(avatar_component_clause,[],[f10278]) ).
fof(f32053,plain,
( spl0_2481
| ~ spl0_6
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f22058,f20980,f3460,f32051]) ).
fof(f32051,plain,
( spl0_2481
<=> ! [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_2481])]) ).
fof(f22058,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_6
| ~ spl0_2014 ),
inference(resolution,[],[f20981,f3462]) ).
fof(f3462,plain,
( c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f3460]) ).
fof(f32049,plain,
( spl0_2480
| spl0_7
| ~ spl0_2012 ),
inference(avatar_split_clause,[],[f21891,f20972,f3465,f32047]) ).
fof(f32047,plain,
( spl0_2480
<=> ! [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_2480])]) ).
fof(f3465,plain,
( spl0_7
<=> c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f21891,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_7
| ~ spl0_2012 ),
inference(resolution,[],[f20973,f3467]) ).
fof(f3467,plain,
( ~ c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(v_evs3),tc_Message_Omsg)
| spl0_7 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f32028,plain,
( spl0_2479
| ~ spl0_5
| ~ spl0_2053 ),
inference(avatar_split_clause,[],[f22821,f22445,f3455,f32026]) ).
fof(f32026,plain,
( spl0_2479
<=> ! [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_2479])]) ).
fof(f22445,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(f22821,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_5
| ~ spl0_2053 ),
inference(resolution,[],[f22446,f3457]) ).
fof(f22446,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,[],[f22445]) ).
fof(f32015,plain,
spl0_2478,
inference(avatar_split_clause,[],[f6,f32013]) ).
fof(f32013,plain,
( spl0_2478
<=> ! [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_2478])]) ).
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(f31992,plain,
spl0_2477,
inference(avatar_split_clause,[],[f10,f31990]) ).
fof(f31990,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(f31969,plain,
( spl0_2476
| ~ spl0_1305
| ~ spl0_2122 ),
inference(avatar_split_clause,[],[f23884,f23790,f10274,f31967]) ).
fof(f31967,plain,
( spl0_2476
<=> ! [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_2476])]) ).
fof(f10274,plain,
( spl0_1305
<=> ! [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_1305])]) ).
fof(f23790,plain,
( spl0_2122
<=> ! [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_2122])]) ).
fof(f23884,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_1305
| ~ spl0_2122 ),
inference(superposition,[],[f10275,f23791]) ).
fof(f23791,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_2122 ),
inference(avatar_component_clause,[],[f23790]) ).
fof(f10275,plain,
( ! [X1,X4,X12,X13] :
( c_in(X4,c_union(X12,X13,X1),X1)
| ~ c_in(X4,X12,X1) )
| ~ spl0_1305 ),
inference(avatar_component_clause,[],[f10274]) ).
fof(f31946,plain,
spl0_2475,
inference(avatar_split_clause,[],[f9,f31944]) ).
fof(f31944,plain,
( spl0_2475
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2475])]) ).
fof(f9,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
fof(f31942,plain,
spl0_2474,
inference(avatar_split_clause,[],[f8,f31940]) ).
fof(f31940,plain,
( spl0_2474
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2474])]) ).
fof(f8,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
fof(f31919,plain,
spl0_2473,
inference(avatar_split_clause,[],[f7,f31917]) ).
fof(f31917,plain,
( spl0_2473
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2473])]) ).
fof(f7,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
fof(f31903,plain,
spl0_2472,
inference(avatar_split_clause,[],[f2959,f31901]) ).
fof(f31901,plain,
( spl0_2472
<=> ! [X102,X113,X13,X12,X91,X112] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_in(X13,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(X112,c_Message_Omsg_OMPair(X113,c_Message_Omsg_OKey(X91)))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OKey(X91))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).
fof(f2959,axiom,
! [X113,X91,X12,X102,X13,X112] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_in(X13,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X102)),tc_Message_Omsg)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(X112,c_Message_Omsg_OMPair(X113,c_Message_Omsg_OKey(X91)))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X12),c_Message_Omsg_OKey(X91))))),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__not__see__encrypted__key_0) ).
fof(f31882,plain,
spl0_2471,
inference(avatar_split_clause,[],[f3,f31880]) ).
fof(f31880,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(f31823,plain,
spl0_2470,
inference(avatar_split_clause,[],[f2962,f31821]) ).
fof(f31821,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(f31819,plain,
spl0_2469,
inference(avatar_split_clause,[],[f2961,f31817]) ).
fof(f31817,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(f31815,plain,
spl0_2468,
inference(avatar_split_clause,[],[f2941,f31813]) ).
fof(f31813,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(f31760,plain,
( spl0_2467
| ~ spl0_1588
| ~ spl0_2436 ),
inference(avatar_split_clause,[],[f31691,f31203,f12885,f31758]) ).
fof(f31758,plain,
( spl0_2467
<=> ! [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_2467])]) ).
fof(f12885,plain,
( spl0_1588
<=> ! [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_1588])]) ).
fof(f31203,plain,
( spl0_2436
<=> ! [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_2436])]) ).
fof(f31691,plain,
( ! [X0] : ~ c_in(v_Aa,c_minus(X0,c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1588
| ~ spl0_2436 ),
inference(trivial_inequality_removal,[],[f31688]) ).
fof(f31688,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_1588
| ~ spl0_2436 ),
inference(superposition,[],[f31204,f12886]) ).
fof(f12886,plain,
( ! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1)
| ~ spl0_1588 ),
inference(avatar_component_clause,[],[f12885]) ).
fof(f31204,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_2436 ),
inference(avatar_component_clause,[],[f31203]) ).
fof(f31756,plain,
spl0_2466,
inference(avatar_split_clause,[],[f2958,f31754]) ).
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(f31752,plain,
spl0_2465,
inference(avatar_split_clause,[],[f2957,f31750]) ).
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(f31748,plain,
spl0_2464,
inference(avatar_split_clause,[],[f2956,f31746]) ).
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(f31744,plain,
spl0_2463,
inference(avatar_split_clause,[],[f12,f31742]) ).
fof(f31742,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(f31740,plain,
spl0_2462,
inference(avatar_split_clause,[],[f11,f31738]) ).
fof(f31738,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(f31696,plain,
spl0_2461,
inference(avatar_split_clause,[],[f2966,f31694]) ).
fof(f31694,plain,
( spl0_2461
<=> ! [X86,X113,X120,X12,X91,X117,X112,X107,X111,X102,X13,X123] :
( X113 = X120
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).
fof(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(f31683,plain,
spl0_2460,
inference(avatar_split_clause,[],[f2965,f31681]) ).
fof(f31681,plain,
( spl0_2460
<=> ! [X86,X113,X120,X12,X91,X117,X112,X107,X111,X102,X13,X123] :
( X112 = X123
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2460])]) ).
fof(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(f31679,plain,
spl0_2459,
inference(avatar_split_clause,[],[f2964,f31677]) ).
fof(f31677,plain,
( spl0_2459
<=> ! [X86,X113,X120,X12,X91,X117,X112,X107,X111,X102,X13,X123] :
( X13 = X117
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2459])]) ).
fof(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(f31675,plain,
spl0_2458,
inference(avatar_split_clause,[],[f2963,f31673]) ).
fof(f31673,plain,
( spl0_2458
<=> ! [X120,X86,X113,X111,X12,X91,X117,X112,X107,X102,X13,X123] :
( X12 = X111
| ~ c_in(X102,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X13),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X112,X113)))),X86)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X111,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X111),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X117),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X123,X120)))),X107)),c_List_Oset(X102,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2458])]) ).
fof(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(f31631,plain,
( spl0_2457
| ~ spl0_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1813
| ~ spl0_1814
| ~ spl0_2456 ),
inference(avatar_split_clause,[],[f31627,f31622,f17248,f17244,f14597,f10190,f8915,f7570,f3730,f31629]) ).
fof(f31629,plain,
( spl0_2457
<=> ! [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_2457])]) ).
fof(f14597,plain,
( spl0_1682
<=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f17244,plain,
( spl0_1813
<=> ! [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_1813])]) ).
fof(f17248,plain,
( spl0_1814
<=> ! [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_1814])]) ).
fof(f31622,plain,
( spl0_2456
<=> ! [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_2456])]) ).
fof(f31627,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_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1813
| ~ spl0_1814
| ~ spl0_2456 ),
inference(forward_demodulation,[],[f31626,f18414]) ).
fof(f18414,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_60
| ~ spl0_1813 ),
inference(resolution,[],[f17245,f3732]) ).
fof(f17245,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_1813 ),
inference(avatar_component_clause,[],[f17244]) ).
fof(f31626,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_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1814
| ~ spl0_2456 ),
inference(forward_demodulation,[],[f31625,f15370]) ).
fof(f15370,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_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682 ),
inference(forward_demodulation,[],[f15369,f7572]) ).
fof(f15369,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_1079
| ~ spl0_1284
| ~ spl0_1682 ),
inference(forward_demodulation,[],[f15368,f8916]) ).
fof(f15368,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_1284
| ~ spl0_1682 ),
inference(superposition,[],[f10191,f14598]) ).
fof(f14598,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_1682 ),
inference(avatar_component_clause,[],[f14597]) ).
fof(f31625,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_60
| ~ spl0_1814
| ~ spl0_2456 ),
inference(forward_demodulation,[],[f31623,f18415]) ).
fof(f18415,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_60
| ~ spl0_1814 ),
inference(resolution,[],[f17249,f3732]) ).
fof(f17249,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_1814 ),
inference(avatar_component_clause,[],[f17248]) ).
fof(f31623,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_2456 ),
inference(avatar_component_clause,[],[f31622]) ).
fof(f31624,plain,
spl0_2456,
inference(avatar_split_clause,[],[f3411,f31622]) ).
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(f31490,plain,
spl0_2455,
inference(avatar_split_clause,[],[f1620,f31488]) ).
fof(f31488,plain,
( spl0_2455
<=> ! [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_2455])]) ).
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(f31486,plain,
spl0_2454,
inference(avatar_split_clause,[],[f1501,f31484]) ).
fof(f31484,plain,
( spl0_2454
<=> ! [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_2454])]) ).
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(f31482,plain,
spl0_2453,
inference(avatar_split_clause,[],[f5,f31480]) ).
fof(f31480,plain,
( spl0_2453
<=> ! [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_2453])]) ).
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(f31478,plain,
spl0_2452,
inference(avatar_split_clause,[],[f4,f31476]) ).
fof(f31476,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__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_2452])]) ).
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(f31438,plain,
spl0_2451,
inference(avatar_split_clause,[],[f1503,f31436]) ).
fof(f31436,plain,
( spl0_2451
<=> ! [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_2451])]) ).
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(f31434,plain,
spl0_2450,
inference(avatar_split_clause,[],[f1369,f31432]) ).
fof(f31432,plain,
( spl0_2450
<=> ! [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_2450])]) ).
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(f31430,plain,
spl0_2449,
inference(avatar_split_clause,[],[f1368,f31428]) ).
fof(f31428,plain,
( spl0_2449
<=> ! [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_2449])]) ).
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(f31426,plain,
( ~ spl0_2448
| ~ spl0_1465
| ~ spl0_2431 ),
inference(avatar_split_clause,[],[f31328,f31151,f11324,f31423]) ).
fof(f31423,plain,
( spl0_2448
<=> c_in(v_Aa,c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2448])]) ).
fof(f11324,plain,
( spl0_1465
<=> ! [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_1465])]) ).
fof(f31151,plain,
( spl0_2431
<=> ! [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_2431])]) ).
fof(f31328,plain,
( ~ c_in(v_Aa,c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1465
| ~ spl0_2431 ),
inference(trivial_inequality_removal,[],[f31327]) ).
fof(f31327,plain,
( c_emptyset != c_emptyset
| ~ c_in(v_Aa,c_uminus(c_Event_Obad,tc_set(tc_Message_Oagent)),tc_Message_Oagent)
| ~ spl0_1465
| ~ spl0_2431 ),
inference(superposition,[],[f31152,f11325]) ).
fof(f11325,plain,
( ! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1)
| ~ spl0_1465 ),
inference(avatar_component_clause,[],[f11324]) ).
fof(f31152,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_2431 ),
inference(avatar_component_clause,[],[f31151]) ).
fof(f31409,plain,
( spl0_2447
| ~ spl0_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1814
| ~ spl0_2446 ),
inference(avatar_split_clause,[],[f31405,f31401,f17248,f14597,f10190,f8915,f7570,f3730,f31407]) ).
fof(f31407,plain,
( spl0_2447
<=> ! [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_2447])]) ).
fof(f31401,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_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_2446])]) ).
fof(f31405,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_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1814
| ~ spl0_2446 ),
inference(forward_demodulation,[],[f31404,f15370]) ).
fof(f31404,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_60
| ~ spl0_1814
| ~ spl0_2446 ),
inference(forward_demodulation,[],[f31402,f18415]) ).
fof(f31402,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_2446 ),
inference(avatar_component_clause,[],[f31401]) ).
fof(f31403,plain,
spl0_2446,
inference(avatar_split_clause,[],[f3405,f31401]) ).
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(f31382,plain,
spl0_2445,
inference(avatar_split_clause,[],[f2960,f31380]) ).
fof(f31380,plain,
( spl0_2445
<=> ! [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_2445])]) ).
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(f31378,plain,
spl0_2444,
inference(avatar_split_clause,[],[f2955,f31376]) ).
fof(f31376,plain,
( spl0_2444
<=> ! [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_2444])]) ).
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(f31339,plain,
spl0_2443,
inference(avatar_split_clause,[],[f1791,f31337]) ).
fof(f31337,plain,
( spl0_2443
<=> ! [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_2443])]) ).
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(f31309,plain,
( spl0_2442
| ~ spl0_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1814
| ~ spl0_2441 ),
inference(avatar_split_clause,[],[f31305,f31301,f17248,f14597,f10190,f8915,f7570,f3730,f31307]) ).
fof(f31307,plain,
( spl0_2442
<=> ! [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_2442])]) ).
fof(f31301,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_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_2441])]) ).
fof(f31305,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_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1814
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f31304,f15370]) ).
fof(f31304,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_60
| ~ spl0_1814
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f31302,f18415]) ).
fof(f31302,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_2441 ),
inference(avatar_component_clause,[],[f31301]) ).
fof(f31303,plain,
spl0_2441,
inference(avatar_split_clause,[],[f3408,f31301]) ).
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(f31299,plain,
spl0_2440,
inference(avatar_split_clause,[],[f2948,f31297]) ).
fof(f31297,plain,
( spl0_2440
<=> ! [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_2440])]) ).
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(f31260,plain,
( spl0_2439
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_1813
| ~ spl0_2438 ),
inference(avatar_split_clause,[],[f31256,f31251,f17244,f8902,f3730,f31258]) ).
fof(f31258,plain,
( spl0_2439
<=> ! [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_2439])]) ).
fof(f31251,plain,
( spl0_2438
<=> ! [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_2438])]) ).
fof(f31256,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_60
| ~ spl0_1076
| ~ spl0_1813
| ~ spl0_2438 ),
inference(forward_demodulation,[],[f31255,f9266]) ).
fof(f31255,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_60
| ~ spl0_1813
| ~ spl0_2438 ),
inference(forward_demodulation,[],[f31254,f18414]) ).
fof(f31254,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_60
| ~ spl0_1813
| ~ spl0_2438 ),
inference(forward_demodulation,[],[f31252,f18414]) ).
fof(f31252,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_2438 ),
inference(avatar_component_clause,[],[f31251]) ).
fof(f31253,plain,
spl0_2438,
inference(avatar_split_clause,[],[f1451,f31251]) ).
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(f31218,plain,
spl0_2437,
inference(avatar_split_clause,[],[f1504,f31216]) ).
fof(f31216,plain,
( spl0_2437
<=> ! [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_2437])]) ).
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(f31205,plain,
( spl0_2436
| ~ spl0_1868
| ~ spl0_2361 ),
inference(avatar_split_clause,[],[f29561,f29192,f17810,f31203]) ).
fof(f17810,plain,
( spl0_1868
<=> ! [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_1868])]) ).
fof(f29192,plain,
( spl0_2361
<=> c_Event_Obad = c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2361])]) ).
fof(f29561,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_1868
| ~ spl0_2361 ),
inference(superposition,[],[f17811,f29194]) ).
fof(f29194,plain,
( c_Event_Obad = c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_2361 ),
inference(avatar_component_clause,[],[f29192]) ).
fof(f17811,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_1868 ),
inference(avatar_component_clause,[],[f17810]) ).
fof(f31187,plain,
( spl0_2435
| ~ spl0_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1814
| ~ spl0_2434 ),
inference(avatar_split_clause,[],[f31183,f31179,f17248,f14597,f10190,f8915,f7570,f3730,f31185]) ).
fof(f31185,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(f31179,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(f31183,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_60
| ~ spl0_801
| ~ spl0_1079
| ~ spl0_1284
| ~ spl0_1682
| ~ spl0_1814
| ~ spl0_2434 ),
inference(forward_demodulation,[],[f31182,f15370]) ).
fof(f31182,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_60
| ~ spl0_1814
| ~ spl0_2434 ),
inference(forward_demodulation,[],[f31180,f18415]) ).
fof(f31180,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,[],[f31179]) ).
fof(f31181,plain,
spl0_2434,
inference(avatar_split_clause,[],[f3402,f31179]) ).
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(f31177,plain,
spl0_2433,
inference(avatar_split_clause,[],[f54,f31175]) ).
fof(f31175,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(f31173,plain,
spl0_2432,
inference(avatar_split_clause,[],[f51,f31171]) ).
fof(f31171,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(f31153,plain,
( spl0_2431
| ~ spl0_1867
| ~ spl0_2361 ),
inference(avatar_split_clause,[],[f29560,f29192,f17806,f31151]) ).
fof(f17806,plain,
( spl0_1867
<=> ! [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_1867])]) ).
fof(f29560,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_1867
| ~ spl0_2361 ),
inference(superposition,[],[f17807,f29194]) ).
fof(f17807,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_1867 ),
inference(avatar_component_clause,[],[f17806]) ).
fof(f31149,plain,
( spl0_2430
| ~ spl0_1196
| ~ spl0_1544
| ~ spl0_2426 ),
inference(avatar_split_clause,[],[f31058,f31055,f12677,f9606,f31147]) ).
fof(f31147,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(f9606,plain,
( spl0_1196
<=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f31055,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(f31058,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_1196
| ~ spl0_1544
| ~ spl0_2426 ),
inference(forward_demodulation,[],[f31056,f13777]) ).
fof(f13777,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1196
| ~ spl0_1544 ),
inference(superposition,[],[f9607,f12678]) ).
fof(f9607,plain,
( ! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3
| ~ spl0_1196 ),
inference(avatar_component_clause,[],[f9606]) ).
fof(f31056,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,[],[f31055]) ).
fof(f31145,plain,
( spl0_2429
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2425 ),
inference(avatar_split_clause,[],[f31053,f31050,f12677,f9597,f31143]) ).
fof(f31143,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(f9597,plain,
( spl0_1194
<=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f31050,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(f31053,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2425 ),
inference(forward_demodulation,[],[f31051,f13778]) ).
fof(f13778,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1194
| ~ spl0_1544 ),
inference(superposition,[],[f9598,f12678]) ).
fof(f9598,plain,
( ! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3
| ~ spl0_1194 ),
inference(avatar_component_clause,[],[f9597]) ).
fof(f31051,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,[],[f31050]) ).
fof(f31141,plain,
( spl0_2428
| ~ spl0_1196
| ~ spl0_1544
| ~ spl0_2424 ),
inference(avatar_split_clause,[],[f31042,f31039,f12677,f9606,f31139]) ).
fof(f31139,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(f31039,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(f31042,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_1196
| ~ spl0_1544
| ~ spl0_2424 ),
inference(forward_demodulation,[],[f31040,f13777]) ).
fof(f31040,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,[],[f31039]) ).
fof(f31137,plain,
( spl0_2427
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2423 ),
inference(avatar_split_clause,[],[f31037,f31034,f12677,f9597,f31135]) ).
fof(f31135,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(f31034,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(f31037,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2423 ),
inference(forward_demodulation,[],[f31035,f13778]) ).
fof(f31035,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,[],[f31034]) ).
fof(f31057,plain,
spl0_2426,
inference(avatar_split_clause,[],[f3399,f31055]) ).
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(f31052,plain,
spl0_2425,
inference(avatar_split_clause,[],[f3398,f31050]) ).
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(f31041,plain,
spl0_2424,
inference(avatar_split_clause,[],[f3397,f31039]) ).
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(f31036,plain,
spl0_2423,
inference(avatar_split_clause,[],[f3396,f31034]) ).
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(f31032,plain,
spl0_2422,
inference(avatar_split_clause,[],[f1622,f31030]) ).
fof(f31030,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(f31028,plain,
spl0_2421,
inference(avatar_split_clause,[],[f1505,f31026]) ).
fof(f31026,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(f31024,plain,
spl0_2420,
inference(avatar_split_clause,[],[f1188,f31022]) ).
fof(f31022,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(f31020,plain,
spl0_2419,
inference(avatar_split_clause,[],[f1187,f31018]) ).
fof(f31018,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(f30992,plain,
( spl0_2418
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_2416 ),
inference(avatar_split_clause,[],[f30942,f30939,f8902,f3730,f30990]) ).
fof(f30990,plain,
( spl0_2418
<=> ! [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_2418])]) ).
fof(f30939,plain,
( spl0_2416
<=> ! [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_2416])]) ).
fof(f30942,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_60
| ~ spl0_1076
| ~ spl0_2416 ),
inference(forward_demodulation,[],[f30940,f9266]) ).
fof(f30940,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_2416 ),
inference(avatar_component_clause,[],[f30939]) ).
fof(f30988,plain,
spl0_2417,
inference(avatar_split_clause,[],[f1705,f30986]) ).
fof(f30986,plain,
( spl0_2417
<=> ! [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_2417])]) ).
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(f30974,plain,
( ~ spl0_820
| ~ spl0_2412 ),
inference(avatar_contradiction_clause,[],[f30973]) ).
fof(f30973,plain,
( $false
| ~ spl0_820
| ~ spl0_2412 ),
inference(trivial_inequality_removal,[],[f30952]) ).
fof(f30952,plain,
( c_emptyset != c_emptyset
| ~ spl0_820
| ~ spl0_2412 ),
inference(superposition,[],[f7648,f30782]) ).
fof(f30782,plain,
( c_emptyset = c_insert(v_Aa,c_emptyset,tc_Message_Oagent)
| ~ spl0_2412 ),
inference(avatar_component_clause,[],[f30780]) ).
fof(f30780,plain,
( spl0_2412
<=> c_emptyset = c_insert(v_Aa,c_emptyset,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2412])]) ).
fof(f30941,plain,
spl0_2416,
inference(avatar_split_clause,[],[f1449,f30939]) ).
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(f30794,plain,
spl0_2415,
inference(avatar_split_clause,[],[f1619,f30792]) ).
fof(f30792,plain,
( spl0_2415
<=> ! [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_2415])]) ).
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(f30790,plain,
spl0_2414,
inference(avatar_split_clause,[],[f1500,f30788]) ).
fof(f30788,plain,
( spl0_2414
<=> ! [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_2414])]) ).
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(f30786,plain,
( spl0_2412
| spl0_2413
| ~ spl0_1449
| ~ spl0_2351 ),
inference(avatar_split_clause,[],[f30723,f28858,f11260,f30784,f30780]) ).
fof(f30784,plain,
( spl0_2413
<=> ! [X0] : c_emptyset != c_union(X0,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2413])]) ).
fof(f11260,plain,
( spl0_1449
<=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f28858,plain,
( spl0_2351
<=> ! [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_2351])]) ).
fof(f30723,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_1449
| ~ spl0_2351 ),
inference(inner_rewriting,[],[f30721]) ).
fof(f30721,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_1449
| ~ spl0_2351 ),
inference(superposition,[],[f28859,f11261]) ).
fof(f11261,plain,
( ! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1)
| ~ spl0_1449 ),
inference(avatar_component_clause,[],[f11260]) ).
fof(f28859,plain,
( ! [X0] :
( c_emptyset != c_union(c_Event_Obad,X0,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_2351 ),
inference(avatar_component_clause,[],[f28858]) ).
fof(f30778,plain,
spl0_2411,
inference(avatar_split_clause,[],[f1383,f30776]) ).
fof(f30776,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(f30774,plain,
spl0_2410,
inference(avatar_split_clause,[],[f1382,f30772]) ).
fof(f30772,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(f30770,plain,
spl0_2409,
inference(avatar_split_clause,[],[f85,f30768]) ).
fof(f30768,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(f30766,plain,
spl0_2408,
inference(avatar_split_clause,[],[f53,f30764]) ).
fof(f30764,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(f30762,plain,
spl0_2407,
inference(avatar_split_clause,[],[f50,f30760]) ).
fof(f30760,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(f30715,plain,
( spl0_2406
| ~ spl0_1196
| ~ spl0_1544
| ~ spl0_2401 ),
inference(avatar_split_clause,[],[f30676,f30673,f12677,f9606,f30713]) ).
fof(f30713,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(f30673,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(f30676,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_1196
| ~ spl0_1544
| ~ spl0_2401 ),
inference(forward_demodulation,[],[f30674,f13777]) ).
fof(f30674,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,[],[f30673]) ).
fof(f30711,plain,
( spl0_2405
| ~ spl0_1196
| ~ spl0_1544
| ~ spl0_2400 ),
inference(avatar_split_clause,[],[f30671,f30668,f12677,f9606,f30709]) ).
fof(f30709,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(f30668,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(f30671,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_1196
| ~ spl0_1544
| ~ spl0_2400 ),
inference(forward_demodulation,[],[f30669,f13777]) ).
fof(f30669,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,[],[f30668]) ).
fof(f30707,plain,
( spl0_2404
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2399 ),
inference(avatar_split_clause,[],[f30666,f30663,f12677,f9597,f30705]) ).
fof(f30705,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(f30663,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(f30666,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2399 ),
inference(forward_demodulation,[],[f30664,f13778]) ).
fof(f30664,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,[],[f30663]) ).
fof(f30703,plain,
( spl0_2403
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2398 ),
inference(avatar_split_clause,[],[f30655,f30652,f12677,f9597,f30701]) ).
fof(f30701,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(f30652,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(f30655,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2398 ),
inference(forward_demodulation,[],[f30653,f13778]) ).
fof(f30653,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,[],[f30652]) ).
fof(f30680,plain,
spl0_2402,
inference(avatar_split_clause,[],[f1502,f30678]) ).
fof(f30678,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(f30675,plain,
spl0_2401,
inference(avatar_split_clause,[],[f1448,f30673]) ).
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(f30670,plain,
spl0_2400,
inference(avatar_split_clause,[],[f1444,f30668]) ).
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(f30665,plain,
spl0_2399,
inference(avatar_split_clause,[],[f1438,f30663]) ).
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(f30654,plain,
spl0_2398,
inference(avatar_split_clause,[],[f1434,f30652]) ).
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(f30650,plain,
spl0_2397,
inference(avatar_split_clause,[],[f55,f30648]) ).
fof(f30648,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(f30646,plain,
spl0_2396,
inference(avatar_split_clause,[],[f52,f30644]) ).
fof(f30644,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(f30508,plain,
spl0_2395,
inference(avatar_split_clause,[],[f1470,f30506]) ).
fof(f30506,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(f30504,plain,
spl0_2394,
inference(avatar_split_clause,[],[f83,f30502]) ).
fof(f30502,plain,
( spl0_2394
<=> ! [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_2394])]) ).
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(f30500,plain,
spl0_2393,
inference(avatar_split_clause,[],[f82,f30498]) ).
fof(f30498,plain,
( spl0_2393
<=> ! [X5,X31,X30,X6,X2,X1] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__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_2393])]) ).
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(f30496,plain,
spl0_2392,
inference(avatar_split_clause,[],[f20,f30494]) ).
fof(f30494,plain,
( spl0_2392
<=> ! [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_2392])]) ).
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(f30364,plain,
spl0_2391,
inference(avatar_split_clause,[],[f3303,f30362]) ).
fof(f30362,plain,
( spl0_2391
<=> ! [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_2391])]) ).
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(f30344,plain,
( spl0_2390
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2389 ),
inference(avatar_split_clause,[],[f30333,f30329,f21062,f11328,f10972,f7083,f6138,f30342]) ).
fof(f30342,plain,
( spl0_2390
<=> ! [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_2390])]) ).
fof(f10972,plain,
( spl0_1379
<=> ! [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_1379])]) ).
fof(f11328,plain,
( spl0_1466
<=> ! [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_1466])]) ).
fof(f21062,plain,
( spl0_2034
<=> ! [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_2034])]) ).
fof(f30329,plain,
( spl0_2389
<=> ! [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_2389])]) ).
fof(f30333,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2389 ),
inference(forward_demodulation,[],[f30332,f21063]) ).
fof(f21063,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_2034 ),
inference(avatar_component_clause,[],[f21062]) ).
fof(f30332,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2389 ),
inference(forward_demodulation,[],[f30330,f12329]) ).
fof(f12329,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466 ),
inference(forward_demodulation,[],[f12328,f7084]) ).
fof(f12328,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466 ),
inference(forward_demodulation,[],[f12290,f11636]) ).
fof(f11636,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_649
| ~ spl0_1379 ),
inference(superposition,[],[f10973,f6140]) ).
fof(f10973,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_1379 ),
inference(avatar_component_clause,[],[f10972]) ).
fof(f12290,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_690
| ~ spl0_1466 ),
inference(superposition,[],[f7084,f11329]) ).
fof(f11329,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_1466 ),
inference(avatar_component_clause,[],[f11328]) ).
fof(f30330,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_2389 ),
inference(avatar_component_clause,[],[f30329]) ).
fof(f30331,plain,
spl0_2389,
inference(avatar_split_clause,[],[f3300,f30329]) ).
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(f30327,plain,
spl0_2388,
inference(avatar_split_clause,[],[f3186,f30325]) ).
fof(f30325,plain,
( spl0_2388
<=> ! [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_2388])]) ).
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(f30323,plain,
spl0_2387,
inference(avatar_split_clause,[],[f3185,f30321]) ).
fof(f30321,plain,
( spl0_2387
<=> ! [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_2387])]) ).
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(f30319,plain,
spl0_2386,
inference(avatar_split_clause,[],[f1621,f30317]) ).
fof(f30317,plain,
( spl0_2386
<=> ! [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_2386])]) ).
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(f30315,plain,
spl0_2385,
inference(avatar_split_clause,[],[f1460,f30313]) ).
fof(f30313,plain,
( spl0_2385
<=> ! [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_2385])]) ).
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(f30311,plain,
spl0_2384,
inference(avatar_split_clause,[],[f19,f30309]) ).
fof(f30309,plain,
( spl0_2384
<=> ! [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_2384])]) ).
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(f30307,plain,
spl0_2383,
inference(avatar_split_clause,[],[f18,f30305]) ).
fof(f30305,plain,
( spl0_2383
<=> ! [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_2383])]) ).
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(f30204,plain,
( spl0_2382
| ~ spl0_1442
| ~ spl0_2361 ),
inference(avatar_split_clause,[],[f29554,f29192,f11231,f30202]) ).
fof(f30202,plain,
( spl0_2382
<=> ! [X0] :
( c_Event_Obad != c_insert(X0,c_emptyset,tc_Message_Oagent)
| v_Aa = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2382])]) ).
fof(f11231,plain,
( spl0_1442
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f29554,plain,
( ! [X0] :
( c_Event_Obad != c_insert(X0,c_emptyset,tc_Message_Oagent)
| v_Aa = X0 )
| ~ spl0_1442
| ~ spl0_2361 ),
inference(superposition,[],[f11232,f29194]) ).
fof(f11232,plain,
( ! [X18,X1,X27,X12] :
( c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1)
| X18 = X27 )
| ~ spl0_1442 ),
inference(avatar_component_clause,[],[f11231]) ).
fof(f30200,plain,
spl0_2381,
inference(avatar_split_clause,[],[f3230,f30198]) ).
fof(f30198,plain,
( spl0_2381
<=> ! [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_2381])]) ).
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(f30196,plain,
spl0_2380,
inference(avatar_split_clause,[],[f3155,f30194]) ).
fof(f30194,plain,
( spl0_2380
<=> ! [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_2380])]) ).
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(f30192,plain,
spl0_2379,
inference(avatar_split_clause,[],[f17,f30190]) ).
fof(f30190,plain,
( spl0_2379
<=> ! [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_2379])]) ).
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(f29904,plain,
( spl0_2378
| ~ spl0_1441
| ~ spl0_2361 ),
inference(avatar_split_clause,[],[f29553,f29192,f11227,f29902]) ).
fof(f11227,plain,
( spl0_1441
<=> ! [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_1441])]) ).
fof(f29553,plain,
( ! [X0] :
( ~ c_lessequals(c_Event_Obad,X0,tc_set(tc_Message_Oagent))
| c_in(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1441
| ~ spl0_2361 ),
inference(superposition,[],[f11228,f29194]) ).
fof(f11228,plain,
( ! [X0,X1,X12,X13] :
( ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1))
| c_in(X0,X13,X1) )
| ~ spl0_1441 ),
inference(avatar_component_clause,[],[f11227]) ).
fof(f29900,plain,
spl0_2377,
inference(avatar_split_clause,[],[f3099,f29898]) ).
fof(f29898,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(f29896,plain,
spl0_2376,
inference(avatar_split_clause,[],[f1998,f29894]) ).
fof(f29894,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(f29892,plain,
spl0_2375,
inference(avatar_split_clause,[],[f1992,f29890]) ).
fof(f29890,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(f29888,plain,
spl0_2374,
inference(avatar_split_clause,[],[f1986,f29886]) ).
fof(f29886,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(f29884,plain,
spl0_2373,
inference(avatar_split_clause,[],[f1980,f29882]) ).
fof(f29882,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(f29880,plain,
spl0_2372,
inference(avatar_split_clause,[],[f115,f29878]) ).
fof(f29878,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(f29876,plain,
spl0_2371,
inference(avatar_split_clause,[],[f84,f29874]) ).
fof(f29874,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(f29796,plain,
( spl0_2370
| ~ spl0_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2369 ),
inference(avatar_split_clause,[],[f29792,f29789,f21062,f7562,f7526,f29794]) ).
fof(f29794,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(f29789,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(f29792,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_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2369 ),
inference(forward_demodulation,[],[f29790,f21145]) ).
fof(f21145,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_790
| ~ spl0_799
| ~ spl0_2034 ),
inference(forward_demodulation,[],[f21066,f7527]) ).
fof(f21066,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_799
| ~ spl0_2034 ),
inference(superposition,[],[f21063,f7563]) ).
fof(f29790,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,[],[f29789]) ).
fof(f29791,plain,
spl0_2369,
inference(avatar_split_clause,[],[f3393,f29789]) ).
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(f29787,plain,
spl0_2368,
inference(avatar_split_clause,[],[f3173,f29785]) ).
fof(f29785,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(f29783,plain,
spl0_2367,
inference(avatar_split_clause,[],[f3172,f29781]) ).
fof(f29781,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(f29779,plain,
spl0_2366,
inference(avatar_split_clause,[],[f3070,f29777]) ).
fof(f29777,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(f29775,plain,
spl0_2365,
inference(avatar_split_clause,[],[f16,f29773]) ).
fof(f29773,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(f29763,plain,
( ~ spl0_2364
| ~ spl0_820
| ~ spl0_2361 ),
inference(avatar_split_clause,[],[f29549,f29192,f7647,f29760]) ).
fof(f29760,plain,
( spl0_2364
<=> c_emptyset = c_Event_Obad ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f29549,plain,
( c_emptyset != c_Event_Obad
| ~ spl0_820
| ~ spl0_2361 ),
inference(superposition,[],[f7648,f29194]) ).
fof(f29758,plain,
( spl0_2363
| ~ spl0_1196
| ~ spl0_1544
| ~ spl0_2360 ),
inference(avatar_split_clause,[],[f29016,f29013,f12677,f9606,f29756]) ).
fof(f29756,plain,
( spl0_2363
<=> ! [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_2363])]) ).
fof(f29013,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(f29016,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_1196
| ~ spl0_1544
| ~ spl0_2360 ),
inference(forward_demodulation,[],[f29014,f13777]) ).
fof(f29014,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,[],[f29013]) ).
fof(f29754,plain,
( spl0_2362
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2359 ),
inference(avatar_split_clause,[],[f29011,f29008,f12677,f9597,f29752]) ).
fof(f29752,plain,
( spl0_2362
<=> ! [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_2362])]) ).
fof(f29008,plain,
( spl0_2359
<=> ! [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_2359])]) ).
fof(f29011,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2359 ),
inference(forward_demodulation,[],[f29009,f13778]) ).
fof(f29009,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_2359 ),
inference(avatar_component_clause,[],[f29008]) ).
fof(f29195,plain,
( spl0_2361
| ~ spl0_817
| ~ spl0_2308
| ~ spl0_2330 ),
inference(avatar_split_clause,[],[f28980,f28766,f28166,f7635,f29192]) ).
fof(f7635,plain,
( spl0_817
<=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f28166,plain,
( spl0_2308
<=> ! [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_2308])]) ).
fof(f28766,plain,
( spl0_2330
<=> ! [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_2330])]) ).
fof(f28980,plain,
( c_Event_Obad = c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_817
| ~ spl0_2308
| ~ spl0_2330 ),
inference(forward_demodulation,[],[f28979,f7636]) ).
fof(f7636,plain,
( ! [X3,X1] : c_union(X3,X3,X1) = X3
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f7635]) ).
fof(f28979,plain,
( c_insert(v_Aa,c_Event_Obad,tc_Message_Oagent) = c_union(c_Event_Obad,c_Event_Obad,tc_Message_Oagent)
| ~ spl0_817
| ~ spl0_2308
| ~ spl0_2330 ),
inference(forward_demodulation,[],[f28956,f28167]) ).
fof(f28167,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_2308 ),
inference(avatar_component_clause,[],[f28166]) ).
fof(f28956,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_817
| ~ spl0_2330 ),
inference(superposition,[],[f28767,f7636]) ).
fof(f28767,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_2330 ),
inference(avatar_component_clause,[],[f28766]) ).
fof(f29015,plain,
spl0_2360,
inference(avatar_split_clause,[],[f3350,f29013]) ).
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(f29010,plain,
spl0_2359,
inference(avatar_split_clause,[],[f3349,f29008]) ).
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(f28955,plain,
( spl0_2358
| ~ spl0_649
| ~ spl0_690
| ~ spl0_790
| ~ spl0_799
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2357 ),
inference(avatar_split_clause,[],[f28951,f28947,f21062,f11328,f10972,f7562,f7526,f7083,f6138,f28953]) ).
fof(f28953,plain,
( spl0_2358
<=> ! [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_2358])]) ).
fof(f28947,plain,
( spl0_2357
<=> ! [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_2357])]) ).
fof(f28951,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_649
| ~ spl0_690
| ~ spl0_790
| ~ spl0_799
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2357 ),
inference(forward_demodulation,[],[f28950,f12329]) ).
fof(f28950,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_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2357 ),
inference(forward_demodulation,[],[f28948,f21145]) ).
fof(f28948,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_2357 ),
inference(avatar_component_clause,[],[f28947]) ).
fof(f28949,plain,
spl0_2357,
inference(avatar_split_clause,[],[f3297,f28947]) ).
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(f28900,plain,
( spl0_2356
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2355 ),
inference(avatar_split_clause,[],[f28896,f28892,f21062,f11328,f10972,f7083,f6138,f28898]) ).
fof(f28898,plain,
( spl0_2356
<=> ! [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_2356])]) ).
fof(f28892,plain,
( spl0_2355
<=> ! [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_2355])]) ).
fof(f28896,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2355 ),
inference(forward_demodulation,[],[f28895,f21063]) ).
fof(f28895,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2355 ),
inference(forward_demodulation,[],[f28893,f12329]) ).
fof(f28893,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_2355 ),
inference(avatar_component_clause,[],[f28892]) ).
fof(f28894,plain,
spl0_2355,
inference(avatar_split_clause,[],[f3287,f28892]) ).
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(f28878,plain,
( spl0_2354
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2353 ),
inference(avatar_split_clause,[],[f28874,f28870,f21062,f11328,f10972,f7083,f6138,f28876]) ).
fof(f28876,plain,
( spl0_2354
<=> ! [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_2354])]) ).
fof(f28870,plain,
( spl0_2353
<=> ! [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_2353])]) ).
fof(f28874,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2353 ),
inference(forward_demodulation,[],[f28873,f21063]) ).
fof(f28873,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2353 ),
inference(forward_demodulation,[],[f28871,f12329]) ).
fof(f28871,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_2353 ),
inference(avatar_component_clause,[],[f28870]) ).
fof(f28872,plain,
spl0_2353,
inference(avatar_split_clause,[],[f3284,f28870]) ).
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(f28864,plain,
( spl0_2352
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2350 ),
inference(avatar_split_clause,[],[f28856,f28852,f21062,f11328,f10972,f7083,f6138,f28862]) ).
fof(f28862,plain,
( spl0_2352
<=> ! [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_2352])]) ).
fof(f28852,plain,
( spl0_2350
<=> ! [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_2350])]) ).
fof(f28856,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2350 ),
inference(forward_demodulation,[],[f28855,f12329]) ).
fof(f28855,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_2034
| ~ spl0_2350 ),
inference(forward_demodulation,[],[f28853,f21063]) ).
fof(f28853,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_2350 ),
inference(avatar_component_clause,[],[f28852]) ).
fof(f28860,plain,
( spl0_2351
| ~ spl0_1093
| ~ spl0_2314 ),
inference(avatar_split_clause,[],[f28701,f28257,f8972,f28858]) ).
fof(f28257,plain,
( spl0_2314
<=> ! [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_2314])]) ).
fof(f28701,plain,
( ! [X0] :
( c_emptyset != c_union(c_Event_Obad,X0,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1093
| ~ spl0_2314 ),
inference(superposition,[],[f8973,f28258]) ).
fof(f28258,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_2314 ),
inference(avatar_component_clause,[],[f28257]) ).
fof(f28854,plain,
spl0_2350,
inference(avatar_split_clause,[],[f3281,f28852]) ).
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(f28846,plain,
( spl0_2349
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2348 ),
inference(avatar_split_clause,[],[f28842,f28838,f21062,f11328,f10972,f7083,f6138,f28844]) ).
fof(f28844,plain,
( spl0_2349
<=> ! [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_2349])]) ).
fof(f28838,plain,
( spl0_2348
<=> ! [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_2348])]) ).
fof(f28842,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2034
| ~ spl0_2348 ),
inference(forward_demodulation,[],[f28841,f12329]) ).
fof(f28841,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_2034
| ~ spl0_2348 ),
inference(forward_demodulation,[],[f28839,f21063]) ).
fof(f28839,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_2348 ),
inference(avatar_component_clause,[],[f28838]) ).
fof(f28840,plain,
spl0_2348,
inference(avatar_split_clause,[],[f3280,f28838]) ).
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(f28836,plain,
spl0_2347,
inference(avatar_split_clause,[],[f2951,f28834]) ).
fof(f28834,plain,
( spl0_2347
<=> ! [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_2347])]) ).
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(f28832,plain,
spl0_2346,
inference(avatar_split_clause,[],[f2003,f28830]) ).
fof(f28830,plain,
( spl0_2346
<=> ! [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_2346])]) ).
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(f28828,plain,
spl0_2345,
inference(avatar_split_clause,[],[f2002,f28826]) ).
fof(f28826,plain,
( spl0_2345
<=> ! [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_2345])]) ).
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(f28824,plain,
spl0_2344,
inference(avatar_split_clause,[],[f2000,f28822]) ).
fof(f28822,plain,
( spl0_2344
<=> ! [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_2344])]) ).
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(f28820,plain,
spl0_2343,
inference(avatar_split_clause,[],[f1999,f28818]) ).
fof(f28818,plain,
( spl0_2343
<=> ! [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_2343])]) ).
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(f28816,plain,
spl0_2342,
inference(avatar_split_clause,[],[f1997,f28814]) ).
fof(f28814,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_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_2342])]) ).
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(f28812,plain,
( spl0_2341
| ~ spl0_1092
| ~ spl0_2308 ),
inference(avatar_split_clause,[],[f28538,f28166,f8968,f28810]) ).
fof(f28810,plain,
( spl0_2341
<=> ! [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_2341])]) ).
fof(f28538,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Event_Obad,tc_Message_Oagent)
| c_emptyset = c_insert(v_Aa,X0,tc_Message_Oagent) )
| ~ spl0_1092
| ~ spl0_2308 ),
inference(superposition,[],[f8969,f28167]) ).
fof(f28808,plain,
spl0_2340,
inference(avatar_split_clause,[],[f1996,f28806]) ).
fof(f28806,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(f28804,plain,
spl0_2339,
inference(avatar_split_clause,[],[f1994,f28802]) ).
fof(f28802,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(f28800,plain,
spl0_2338,
inference(avatar_split_clause,[],[f1993,f28798]) ).
fof(f28798,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(f28796,plain,
spl0_2337,
inference(avatar_split_clause,[],[f1991,f28794]) ).
fof(f28794,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(f28792,plain,
spl0_2336,
inference(avatar_split_clause,[],[f1990,f28790]) ).
fof(f28790,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(f28788,plain,
spl0_2335,
inference(avatar_split_clause,[],[f1988,f28786]) ).
fof(f28786,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(f28784,plain,
spl0_2334,
inference(avatar_split_clause,[],[f1987,f28782]) ).
fof(f28782,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(f28780,plain,
spl0_2333,
inference(avatar_split_clause,[],[f1985,f28778]) ).
fof(f28778,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(f28776,plain,
spl0_2332,
inference(avatar_split_clause,[],[f1984,f28774]) ).
fof(f28774,plain,
( spl0_2332
<=> ! [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_2332])]) ).
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(f28772,plain,
spl0_2331,
inference(avatar_split_clause,[],[f1982,f28770]) ).
fof(f28770,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_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_2331])]) ).
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(f28768,plain,
( spl0_2330
| ~ spl0_1763
| ~ spl0_2308 ),
inference(avatar_split_clause,[],[f28536,f28166,f16036,f28766]) ).
fof(f16036,plain,
( spl0_1763
<=> ! [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_1763])]) ).
fof(f28536,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_1763
| ~ spl0_2308 ),
inference(superposition,[],[f28167,f16037]) ).
fof(f16037,plain,
( ! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1)
| ~ spl0_1763 ),
inference(avatar_component_clause,[],[f16036]) ).
fof(f28764,plain,
spl0_2329,
inference(avatar_split_clause,[],[f1981,f28762]) ).
fof(f28762,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(f28760,plain,
spl0_2328,
inference(avatar_split_clause,[],[f1979,f28758]) ).
fof(f28758,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(f28756,plain,
spl0_2327,
inference(avatar_split_clause,[],[f1978,f28754]) ).
fof(f28754,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(f28752,plain,
spl0_2326,
inference(avatar_split_clause,[],[f1948,f28750]) ).
fof(f28750,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(f28748,plain,
spl0_2325,
inference(avatar_split_clause,[],[f1947,f28746]) ).
fof(f28746,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(f28744,plain,
spl0_2324,
inference(avatar_split_clause,[],[f1862,f28742]) ).
fof(f28742,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(f28740,plain,
spl0_2323,
inference(avatar_split_clause,[],[f117,f28738]) ).
fof(f28738,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(f28736,plain,
spl0_2322,
inference(avatar_split_clause,[],[f116,f28734]) ).
fof(f28734,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(f28732,plain,
spl0_2321,
inference(avatar_split_clause,[],[f13,f28730]) ).
fof(f28730,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(f28577,plain,
( spl0_2320
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2319 ),
inference(avatar_split_clause,[],[f28573,f28570,f11328,f10972,f7083,f6138,f28575]) ).
fof(f28575,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(f28570,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(f28573,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2319 ),
inference(forward_demodulation,[],[f28571,f12329]) ).
fof(f28571,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,[],[f28570]) ).
fof(f28572,plain,
spl0_2319,
inference(avatar_split_clause,[],[f3100,f28570]) ).
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(f28568,plain,
spl0_2318,
inference(avatar_split_clause,[],[f2331,f28566]) ).
fof(f28566,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(f28564,plain,
spl0_2317,
inference(avatar_split_clause,[],[f2321,f28562]) ).
fof(f28562,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(f28560,plain,
spl0_2316,
inference(avatar_split_clause,[],[f1469,f28558]) ).
fof(f28558,plain,
( spl0_2316
<=> ! [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_2316])]) ).
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(f28556,plain,
spl0_2315,
inference(avatar_split_clause,[],[f77,f28554]) ).
fof(f28554,plain,
( spl0_2315
<=> ! [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_2315])]) ).
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(f28259,plain,
( spl0_2314
| ~ spl0_1557
| ~ spl0_2098 ),
inference(avatar_split_clause,[],[f28123,f23167,f12734,f28257]) ).
fof(f12734,plain,
( spl0_1557
<=> ! [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_1557])]) ).
fof(f23167,plain,
( spl0_2098
<=> ! [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_2098])]) ).
fof(f28123,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_1557
| ~ spl0_2098 ),
inference(forward_demodulation,[],[f28109,f12735]) ).
fof(f12735,plain,
( ! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1)
| ~ spl0_1557 ),
inference(avatar_component_clause,[],[f12734]) ).
fof(f28109,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_1557
| ~ spl0_2098 ),
inference(superposition,[],[f12735,f23168]) ).
fof(f23168,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_2098 ),
inference(avatar_component_clause,[],[f23167]) ).
fof(f28188,plain,
spl0_2313,
inference(avatar_split_clause,[],[f3229,f28186]) ).
fof(f28186,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(f28184,plain,
spl0_2312,
inference(avatar_split_clause,[],[f3228,f28182]) ).
fof(f28182,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(f28180,plain,
spl0_2311,
inference(avatar_split_clause,[],[f3227,f28178]) ).
fof(f28178,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(f28176,plain,
spl0_2310,
inference(avatar_split_clause,[],[f3226,f28174]) ).
fof(f28174,plain,
( spl0_2310
<=> ! [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_2310])]) ).
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(f28172,plain,
spl0_2309,
inference(avatar_split_clause,[],[f3224,f28170]) ).
fof(f28170,plain,
( spl0_2309
<=> ! [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_2309])]) ).
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(f28168,plain,
( spl0_2308
| ~ spl0_1556
| ~ spl0_2098 ),
inference(avatar_split_clause,[],[f28122,f23167,f12730,f28166]) ).
fof(f12730,plain,
( spl0_1556
<=> ! [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_1556])]) ).
fof(f28122,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_1556
| ~ spl0_2098 ),
inference(forward_demodulation,[],[f28108,f12731]) ).
fof(f12731,plain,
( ! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1)
| ~ spl0_1556 ),
inference(avatar_component_clause,[],[f12730]) ).
fof(f28108,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_1556
| ~ spl0_2098 ),
inference(superposition,[],[f12731,f23168]) ).
fof(f28164,plain,
spl0_2307,
inference(avatar_split_clause,[],[f2001,f28162]) ).
fof(f28162,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(f28160,plain,
spl0_2306,
inference(avatar_split_clause,[],[f1995,f28158]) ).
fof(f28158,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(f28156,plain,
spl0_2305,
inference(avatar_split_clause,[],[f1989,f28154]) ).
fof(f28154,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(f28152,plain,
spl0_2304,
inference(avatar_split_clause,[],[f1983,f28150]) ).
fof(f28150,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(f28148,plain,
spl0_2303,
inference(avatar_split_clause,[],[f1794,f28146]) ).
fof(f28146,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(f28144,plain,
spl0_2302,
inference(avatar_split_clause,[],[f1793,f28142]) ).
fof(f28142,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(f28140,plain,
spl0_2301,
inference(avatar_split_clause,[],[f1789,f28138]) ).
fof(f28138,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(f28136,plain,
spl0_2300,
inference(avatar_split_clause,[],[f1616,f28134]) ).
fof(f28134,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(f28132,plain,
spl0_2299,
inference(avatar_split_clause,[],[f1458,f28130]) ).
fof(f28130,plain,
( spl0_2299
<=> ! [X11] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).
fof(f1458,axiom,
! [X11] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
fof(f28128,plain,
spl0_2298,
inference(avatar_split_clause,[],[f118,f28126]) ).
fof(f28126,plain,
( spl0_2298
<=> ! [X13,X14,X12,X2,X1] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2298])]) ).
fof(f118,axiom,
! [X2,X1,X14,X12,X13] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f27937,plain,
spl0_2297,
inference(avatar_split_clause,[],[f3223,f27935]) ).
fof(f27935,plain,
( spl0_2297
<=> ! [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_2297])]) ).
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(f27933,plain,
spl0_2296,
inference(avatar_split_clause,[],[f3202,f27931]) ).
fof(f27931,plain,
( spl0_2296
<=> ! [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_2296])]) ).
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(f27923,plain,
spl0_2295,
inference(avatar_split_clause,[],[f3193,f27921]) ).
fof(f27921,plain,
( spl0_2295
<=> ! [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_2295])]) ).
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(f27919,plain,
spl0_2294,
inference(avatar_split_clause,[],[f3191,f27917]) ).
fof(f27917,plain,
( spl0_2294
<=> ! [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_2294])]) ).
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(f27915,plain,
spl0_2293,
inference(avatar_split_clause,[],[f2942,f27913]) ).
fof(f27913,plain,
( spl0_2293
<=> ! [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_2293])]) ).
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(f27911,plain,
spl0_2292,
inference(avatar_split_clause,[],[f2848,f27909]) ).
fof(f27909,plain,
( spl0_2292
<=> ! [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_2292])]) ).
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(f27907,plain,
spl0_2291,
inference(avatar_split_clause,[],[f1792,f27905]) ).
fof(f27905,plain,
( spl0_2291
<=> ! [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_2291])]) ).
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(f27903,plain,
spl0_2290,
inference(avatar_split_clause,[],[f1698,f27901]) ).
fof(f27901,plain,
( spl0_2290
<=> ! [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_2290])]) ).
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(f27857,plain,
( spl0_2289
| ~ spl0_60
| ~ spl0_1591
| ~ spl0_2285 ),
inference(avatar_split_clause,[],[f27333,f27330,f12902,f3730,f27855]) ).
fof(f27855,plain,
( spl0_2289
<=> ! [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_2289])]) ).
fof(f12902,plain,
( spl0_1591
<=> ! [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_1591])]) ).
fof(f27330,plain,
( spl0_2285
<=> ! [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_2285])]) ).
fof(f27333,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_60
| ~ spl0_1591
| ~ spl0_2285 ),
inference(forward_demodulation,[],[f27331,f14229]) ).
fof(f14229,plain,
( ! [X0] : c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1591 ),
inference(resolution,[],[f12903,f3732]) ).
fof(f12903,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_1591 ),
inference(avatar_component_clause,[],[f12902]) ).
fof(f27331,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_2285 ),
inference(avatar_component_clause,[],[f27330]) ).
fof(f27853,plain,
( spl0_2288
| ~ spl0_1588
| ~ spl0_2258 ),
inference(avatar_split_clause,[],[f27474,f26979,f12885,f27851]) ).
fof(f27851,plain,
( spl0_2288
<=> ! [X0] : ~ c_in(v_KAB,c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2288])]) ).
fof(f26979,plain,
( spl0_2258
<=> ! [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_2258])]) ).
fof(f27474,plain,
( ! [X0] : ~ c_in(v_KAB,c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),tc_nat)
| ~ spl0_1588
| ~ spl0_2258 ),
inference(trivial_inequality_removal,[],[f27471]) ).
fof(f27471,plain,
( ! [X0] :
( c_emptyset != c_emptyset
| ~ c_in(v_KAB,c_minus(X0,c_Message_OsymKeys,tc_set(tc_nat)),tc_nat) )
| ~ spl0_1588
| ~ spl0_2258 ),
inference(superposition,[],[f26980,f12886]) ).
fof(f26980,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_2258 ),
inference(avatar_component_clause,[],[f26979]) ).
fof(f27415,plain,
( spl0_2287
| ~ spl0_1196
| ~ spl0_1544
| ~ spl0_2266 ),
inference(avatar_split_clause,[],[f27161,f27158,f12677,f9606,f27413]) ).
fof(f27413,plain,
( spl0_2287
<=> ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).
fof(f27158,plain,
( spl0_2266
<=> ! [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_2266])]) ).
fof(f27161,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_1196
| ~ spl0_1544
| ~ spl0_2266 ),
inference(forward_demodulation,[],[f27159,f13777]) ).
fof(f27159,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_2266 ),
inference(avatar_component_clause,[],[f27158]) ).
fof(f27411,plain,
( spl0_2286
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2265 ),
inference(avatar_split_clause,[],[f27156,f27153,f12677,f9597,f27409]) ).
fof(f27409,plain,
( spl0_2286
<=> ! [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_2286])]) ).
fof(f27153,plain,
( spl0_2265
<=> ! [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_2265])]) ).
fof(f27156,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1194
| ~ spl0_1544
| ~ spl0_2265 ),
inference(forward_demodulation,[],[f27154,f13778]) ).
fof(f27154,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_2265 ),
inference(avatar_component_clause,[],[f27153]) ).
fof(f27332,plain,
spl0_2285,
inference(avatar_split_clause,[],[f3200,f27330]) ).
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(f27328,plain,
spl0_2284,
inference(avatar_split_clause,[],[f3109,f27326]) ).
fof(f27326,plain,
( spl0_2284
<=> ! [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_2284])]) ).
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(f27318,plain,
( spl0_2283
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2282 ),
inference(avatar_split_clause,[],[f27314,f27311,f11328,f10972,f7083,f6138,f27316]) ).
fof(f27316,plain,
( spl0_2283
<=> ! [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_2283])]) ).
fof(f27311,plain,
( spl0_2282
<=> ! [X41,X21,X85] : c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) = c_Nat_Opower(X85,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2282])]) ).
fof(f27314,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2282 ),
inference(forward_demodulation,[],[f27312,f12329]) ).
fof(f27312,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_2282 ),
inference(avatar_component_clause,[],[f27311]) ).
fof(f27313,plain,
spl0_2282,
inference(avatar_split_clause,[],[f3095,f27311]) ).
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(f27309,plain,
spl0_2281,
inference(avatar_split_clause,[],[f3090,f27307]) ).
fof(f27307,plain,
( spl0_2281
<=> ! [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_2281])]) ).
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(f27305,plain,
spl0_2280,
inference(avatar_split_clause,[],[f3083,f27303]) ).
fof(f27303,plain,
( spl0_2280
<=> ! [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_2280])]) ).
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(f27301,plain,
spl0_2279,
inference(avatar_split_clause,[],[f3082,f27299]) ).
fof(f27299,plain,
( spl0_2279
<=> ! [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_2279])]) ).
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(f27219,plain,
( spl0_2278
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2276 ),
inference(avatar_split_clause,[],[f27210,f27206,f11328,f10972,f7083,f6138,f27217]) ).
fof(f27217,plain,
( spl0_2278
<=> ! [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_2278])]) ).
fof(f27206,plain,
( spl0_2276
<=> ! [X16,X21] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).
fof(f27210,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2276 ),
inference(forward_demodulation,[],[f27209,f12329]) ).
fof(f27209,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2276 ),
inference(forward_demodulation,[],[f27207,f12329]) ).
fof(f27207,plain,
( ! [X21,X16] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2276 ),
inference(avatar_component_clause,[],[f27206]) ).
fof(f27215,plain,
( ~ spl0_2277
| ~ spl0_1465
| ~ spl0_2257 ),
inference(avatar_split_clause,[],[f27166,f26743,f11324,f27212]) ).
fof(f27212,plain,
( spl0_2277
<=> c_in(v_KAB,c_uminus(c_Message_OsymKeys,tc_set(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2277])]) ).
fof(f26743,plain,
( spl0_2257
<=> ! [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_2257])]) ).
fof(f27166,plain,
( ~ c_in(v_KAB,c_uminus(c_Message_OsymKeys,tc_set(tc_nat)),tc_nat)
| ~ spl0_1465
| ~ spl0_2257 ),
inference(trivial_inequality_removal,[],[f27164]) ).
fof(f27164,plain,
( c_emptyset != c_emptyset
| ~ c_in(v_KAB,c_uminus(c_Message_OsymKeys,tc_set(tc_nat)),tc_nat)
| ~ spl0_1465
| ~ spl0_2257 ),
inference(superposition,[],[f26744,f11325]) ).
fof(f26744,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_2257 ),
inference(avatar_component_clause,[],[f26743]) ).
fof(f27208,plain,
spl0_2276,
inference(avatar_split_clause,[],[f3076,f27206]) ).
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(f27202,plain,
spl0_2275,
inference(avatar_split_clause,[],[f3035,f27200]) ).
fof(f27200,plain,
( spl0_2275
<=> ! [X5,X1] : c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2275])]) ).
fof(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(f27198,plain,
spl0_2274,
inference(avatar_split_clause,[],[f2949,f27196]) ).
fof(f27196,plain,
( spl0_2274
<=> ! [X61,X102,X115,X12,X114,X91,X24] : c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X24),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X61,c_Message_Omsg_ONonce(X114))))),X115)),X102,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).
fof(f2949,axiom,
! [X91,X114,X24,X12,X61,X115,X102] : c_Yahalom_OKeyWithNonce(X91,X114,c_List_Olist_OCons(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X12,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X12),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X24),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X91),c_Message_Omsg_OMPair(X61,c_Message_Omsg_ONonce(X114))))),X115)),X102,tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_2) ).
fof(f27194,plain,
spl0_2273,
inference(avatar_split_clause,[],[f2934,f27192]) ).
fof(f27192,plain,
( spl0_2273
<=> ! [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_2273])]) ).
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(f27190,plain,
spl0_2272,
inference(avatar_split_clause,[],[f2316,f27188]) ).
fof(f27188,plain,
( spl0_2272
<=> ! [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_2272])]) ).
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(f27186,plain,
spl0_2271,
inference(avatar_split_clause,[],[f1826,f27184]) ).
fof(f27184,plain,
( spl0_2271
<=> ! [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_2271])]) ).
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(f27182,plain,
spl0_2270,
inference(avatar_split_clause,[],[f1695,f27180]) ).
fof(f27180,plain,
( spl0_2270
<=> ! [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_2270])]) ).
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(f27178,plain,
spl0_2269,
inference(avatar_split_clause,[],[f1573,f27176]) ).
fof(f27176,plain,
( spl0_2269
<=> ! [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_2269])]) ).
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(f27174,plain,
spl0_2268,
inference(avatar_split_clause,[],[f1571,f27172]) ).
fof(f27172,plain,
( spl0_2268
<=> ! [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_2268])]) ).
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(f27170,plain,
spl0_2267,
inference(avatar_split_clause,[],[f1526,f27168]) ).
fof(f27168,plain,
( spl0_2267
<=> ! [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_2267])]) ).
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(f27160,plain,
spl0_2266,
inference(avatar_split_clause,[],[f1447,f27158]) ).
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(f27155,plain,
spl0_2265,
inference(avatar_split_clause,[],[f1437,f27153]) ).
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(f27151,plain,
spl0_2264,
inference(avatar_split_clause,[],[f1381,f27149]) ).
fof(f27149,plain,
( spl0_2264
<=> ! [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_2264])]) ).
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(f27147,plain,
spl0_2263,
inference(avatar_split_clause,[],[f1269,f27145]) ).
fof(f27145,plain,
( spl0_2263
<=> ! [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_2263])]) ).
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(f27143,plain,
spl0_2262,
inference(avatar_split_clause,[],[f1266,f27141]) ).
fof(f27141,plain,
( spl0_2262
<=> ! [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_2262])]) ).
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(f27139,plain,
spl0_2261,
inference(avatar_split_clause,[],[f1262,f27137]) ).
fof(f27137,plain,
( spl0_2261
<=> ! [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_2261])]) ).
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(f27135,plain,
spl0_2260,
inference(avatar_split_clause,[],[f1259,f27133]) ).
fof(f27133,plain,
( spl0_2260
<=> ! [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_2260])]) ).
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(f27131,plain,
spl0_2259,
inference(avatar_split_clause,[],[f78,f27129]) ).
fof(f27129,plain,
( spl0_2259
<=> ! [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_2259])]) ).
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(f26981,plain,
( spl0_2258
| ~ spl0_1868
| ~ spl0_2190 ),
inference(avatar_split_clause,[],[f24660,f24557,f17810,f26979]) ).
fof(f24557,plain,
( spl0_2190
<=> c_Message_OsymKeys = c_insert(v_KAB,c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f24660,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_1868
| ~ spl0_2190 ),
inference(superposition,[],[f17811,f24559]) ).
fof(f24559,plain,
( c_Message_OsymKeys = c_insert(v_KAB,c_Message_OsymKeys,tc_nat)
| ~ spl0_2190 ),
inference(avatar_component_clause,[],[f24557]) ).
fof(f26745,plain,
( spl0_2257
| ~ spl0_1867
| ~ spl0_2190 ),
inference(avatar_split_clause,[],[f24659,f24557,f17806,f26743]) ).
fof(f24659,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_1867
| ~ spl0_2190 ),
inference(superposition,[],[f17807,f24559]) ).
fof(f26345,plain,
( spl0_2256
| ~ spl0_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2255 ),
inference(avatar_split_clause,[],[f26341,f26338,f21062,f7562,f7526,f26343]) ).
fof(f26343,plain,
( spl0_2256
<=> ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_plus(c_1,c_1,tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).
fof(f26338,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_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_2255])]) ).
fof(f26341,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_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2255 ),
inference(forward_demodulation,[],[f26339,f21145]) ).
fof(f26339,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_2255 ),
inference(avatar_component_clause,[],[f26338]) ).
fof(f26340,plain,
spl0_2255,
inference(avatar_split_clause,[],[f3390,f26338]) ).
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(f26336,plain,
spl0_2254,
inference(avatar_split_clause,[],[f3323,f26334]) ).
fof(f26334,plain,
( spl0_2254
<=> ! [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_2254])]) ).
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(f26332,plain,
spl0_2253,
inference(avatar_split_clause,[],[f3321,f26330]) ).
fof(f26330,plain,
( spl0_2253
<=> ! [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_2253])]) ).
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(f26282,plain,
( spl0_2252
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2251 ),
inference(avatar_split_clause,[],[f26278,f26275,f11328,f10972,f7083,f6138,f26280]) ).
fof(f26280,plain,
( spl0_2252
<=> ! [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_2252])]) ).
fof(f26275,plain,
( spl0_2251
<=> ! [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_2251])]) ).
fof(f26278,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2251 ),
inference(forward_demodulation,[],[f26276,f12329]) ).
fof(f26276,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_2251 ),
inference(avatar_component_clause,[],[f26275]) ).
fof(f26277,plain,
spl0_2251,
inference(avatar_split_clause,[],[f3190,f26275]) ).
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(f26247,plain,
( ~ spl0_820
| ~ spl0_2239 ),
inference(avatar_contradiction_clause,[],[f26246]) ).
fof(f26246,plain,
( $false
| ~ spl0_820
| ~ spl0_2239 ),
inference(trivial_inequality_removal,[],[f26227]) ).
fof(f26227,plain,
( c_emptyset != c_emptyset
| ~ spl0_820
| ~ spl0_2239 ),
inference(superposition,[],[f7648,f26172]) ).
fof(f26172,plain,
( c_emptyset = c_insert(v_KAB,c_emptyset,tc_nat)
| ~ spl0_2239 ),
inference(avatar_component_clause,[],[f26170]) ).
fof(f26170,plain,
( spl0_2239
<=> c_emptyset = c_insert(v_KAB,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).
fof(f26217,plain,
( spl0_2250
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2249 ),
inference(avatar_split_clause,[],[f26213,f26210,f11328,f10972,f7083,f6138,f26215]) ).
fof(f26215,plain,
( spl0_2250
<=> ! [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_2250])]) ).
fof(f26210,plain,
( spl0_2249
<=> ! [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_2249])]) ).
fof(f26213,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2249 ),
inference(forward_demodulation,[],[f26211,f12329]) ).
fof(f26211,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_2249 ),
inference(avatar_component_clause,[],[f26210]) ).
fof(f26212,plain,
spl0_2249,
inference(avatar_split_clause,[],[f3085,f26210]) ).
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(f26208,plain,
spl0_2248,
inference(avatar_split_clause,[],[f2952,f26206]) ).
fof(f26206,plain,
( spl0_2248
<=> ! [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_2248])]) ).
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(f26204,plain,
spl0_2247,
inference(avatar_split_clause,[],[f2829,f26202]) ).
fof(f26202,plain,
( spl0_2247
<=> ! [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_2247])]) ).
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(f26200,plain,
spl0_2246,
inference(avatar_split_clause,[],[f2385,f26198]) ).
fof(f26198,plain,
( spl0_2246
<=> ! [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_2246])]) ).
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(f26196,plain,
spl0_2245,
inference(avatar_split_clause,[],[f2384,f26194]) ).
fof(f26194,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(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(f26192,plain,
spl0_2244,
inference(avatar_split_clause,[],[f2332,f26190]) ).
fof(f26190,plain,
( spl0_2244
<=> ! [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_2244])]) ).
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(f26188,plain,
spl0_2243,
inference(avatar_split_clause,[],[f2322,f26186]) ).
fof(f26186,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_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
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(f26184,plain,
spl0_2242,
inference(avatar_split_clause,[],[f1877,f26182]) ).
fof(f26182,plain,
( spl0_2242
<=> ! [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_2242])]) ).
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(f26180,plain,
spl0_2241,
inference(avatar_split_clause,[],[f1828,f26178]) ).
fof(f26178,plain,
( spl0_2241
<=> ! [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_2241])]) ).
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(f26176,plain,
( spl0_2239
| spl0_2240
| ~ spl0_1449
| ~ spl0_2183 ),
inference(avatar_split_clause,[],[f26128,f24178,f11260,f26174,f26170]) ).
fof(f26174,plain,
( spl0_2240
<=> ! [X0] : c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f24178,plain,
( spl0_2183
<=> ! [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_2183])]) ).
fof(f26128,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat)
| c_emptyset = c_insert(v_KAB,c_emptyset,tc_nat) )
| ~ spl0_1449
| ~ spl0_2183 ),
inference(inner_rewriting,[],[f26126]) ).
fof(f26126,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_1449
| ~ spl0_2183 ),
inference(superposition,[],[f24179,f11261]) ).
fof(f24179,plain,
( ! [X0] :
( c_emptyset != c_union(c_Message_OsymKeys,X0,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) )
| ~ spl0_2183 ),
inference(avatar_component_clause,[],[f24178]) ).
fof(f26168,plain,
spl0_2238,
inference(avatar_split_clause,[],[f1273,f26166]) ).
fof(f26166,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(f26164,plain,
spl0_2237,
inference(avatar_split_clause,[],[f1271,f26162]) ).
fof(f26162,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(f26160,plain,
spl0_2236,
inference(avatar_split_clause,[],[f1270,f26158]) ).
fof(f26158,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(f26156,plain,
spl0_2235,
inference(avatar_split_clause,[],[f1268,f26154]) ).
fof(f26154,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(f26152,plain,
spl0_2234,
inference(avatar_split_clause,[],[f1267,f26150]) ).
fof(f26150,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(f26148,plain,
spl0_2233,
inference(avatar_split_clause,[],[f1264,f26146]) ).
fof(f26146,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(f26144,plain,
spl0_2232,
inference(avatar_split_clause,[],[f1263,f26142]) ).
fof(f26142,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(f26140,plain,
spl0_2231,
inference(avatar_split_clause,[],[f1261,f26138]) ).
fof(f26138,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(f26136,plain,
spl0_2230,
inference(avatar_split_clause,[],[f1260,f26134]) ).
fof(f26134,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(f26132,plain,
spl0_2229,
inference(avatar_split_clause,[],[f1258,f26130]) ).
fof(f26130,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(f26120,plain,
spl0_2228,
inference(avatar_split_clause,[],[f73,f26118]) ).
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(f26116,plain,
spl0_2227,
inference(avatar_split_clause,[],[f15,f26114]) ).
fof(f26114,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(f26112,plain,
spl0_2226,
inference(avatar_split_clause,[],[f14,f26110]) ).
fof(f26110,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(f25401,plain,
spl0_2225,
inference(avatar_split_clause,[],[f3199,f25399]) ).
fof(f25399,plain,
( spl0_2225
<=> ! [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_2225])]) ).
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(f25397,plain,
spl0_2224,
inference(avatar_split_clause,[],[f3198,f25395]) ).
fof(f25395,plain,
( spl0_2224
<=> ! [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_2224])]) ).
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(f25393,plain,
spl0_2223,
inference(avatar_split_clause,[],[f3171,f25391]) ).
fof(f25391,plain,
( spl0_2223
<=> ! [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_2223])]) ).
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(f25389,plain,
spl0_2222,
inference(avatar_split_clause,[],[f3050,f25387]) ).
fof(f25387,plain,
( spl0_2222
<=> ! [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_2222])]) ).
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(f25385,plain,
spl0_2221,
inference(avatar_split_clause,[],[f2849,f25383]) ).
fof(f25383,plain,
( spl0_2221
<=> ! [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_2221])]) ).
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(f25381,plain,
spl0_2220,
inference(avatar_split_clause,[],[f2562,f25379]) ).
fof(f25379,plain,
( spl0_2220
<=> ! [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_2220])]) ).
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(f25377,plain,
spl0_2219,
inference(avatar_split_clause,[],[f2356,f25375]) ).
fof(f25375,plain,
( spl0_2219
<=> ! [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_2219])]) ).
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(f25373,plain,
( spl0_2217
| ~ spl0_2218
| ~ spl0_1000
| ~ spl0_2193 ),
inference(avatar_split_clause,[],[f25324,f25077,f8458,f25370,f25366]) ).
fof(f25366,plain,
( spl0_2217
<=> c_0 = v_KAB ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f25370,plain,
( spl0_2218
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_Message_OsymKeys ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f25077,plain,
( spl0_2193
<=> ! [X0] :
( c_Message_OsymKeys != c_insert(X0,c_emptyset,tc_nat)
| v_KAB = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).
fof(f25324,plain,
( c_SetInterval_OatMost(c_0,tc_nat) != c_Message_OsymKeys
| c_0 = v_KAB
| ~ spl0_1000
| ~ spl0_2193 ),
inference(superposition,[],[f25078,f8460]) ).
fof(f25078,plain,
( ! [X0] :
( c_Message_OsymKeys != c_insert(X0,c_emptyset,tc_nat)
| v_KAB = X0 )
| ~ spl0_2193 ),
inference(avatar_component_clause,[],[f25077]) ).
fof(f25364,plain,
spl0_2216,
inference(avatar_split_clause,[],[f2355,f25362]) ).
fof(f25362,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(f25360,plain,
spl0_2215,
inference(avatar_split_clause,[],[f2351,f25358]) ).
fof(f25358,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(f25356,plain,
spl0_2214,
inference(avatar_split_clause,[],[f2350,f25354]) ).
fof(f25354,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(f25352,plain,
spl0_2213,
inference(avatar_split_clause,[],[f2336,f25350]) ).
fof(f25350,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(f25348,plain,
spl0_2212,
inference(avatar_split_clause,[],[f2333,f25346]) ).
fof(f25346,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(f25344,plain,
spl0_2211,
inference(avatar_split_clause,[],[f2330,f25342]) ).
fof(f25342,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(f25340,plain,
spl0_2210,
inference(avatar_split_clause,[],[f2328,f25338]) ).
fof(f25338,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(f25336,plain,
spl0_2209,
inference(avatar_split_clause,[],[f2325,f25334]) ).
fof(f25334,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(f25332,plain,
spl0_2208,
inference(avatar_split_clause,[],[f2319,f25330]) ).
fof(f25330,plain,
( spl0_2208
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f2319,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f25328,plain,
spl0_2207,
inference(avatar_split_clause,[],[f2168,f25326]) ).
fof(f25326,plain,
( spl0_2207
<=> ! [X48,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).
fof(f2168,axiom,
! [X48,X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f25323,plain,
spl0_2206,
inference(avatar_split_clause,[],[f2108,f25321]) ).
fof(f25321,plain,
( spl0_2206
<=> ! [X48,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2206])]) ).
fof(f2108,axiom,
! [X48,X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f25319,plain,
spl0_2205,
inference(avatar_split_clause,[],[f1861,f25317]) ).
fof(f25317,plain,
( spl0_2205
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f1861,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f25315,plain,
spl0_2204,
inference(avatar_split_clause,[],[f1834,f25313]) ).
fof(f25313,plain,
( spl0_2204
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f1834,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_0) ).
fof(f25311,plain,
spl0_2203,
inference(avatar_split_clause,[],[f1825,f25309]) ).
fof(f25309,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_plus(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(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(f25307,plain,
spl0_2202,
inference(avatar_split_clause,[],[f1635,f25305]) ).
fof(f25305,plain,
( spl0_2202
<=> ! [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_2202])]) ).
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(f25303,plain,
spl0_2201,
inference(avatar_split_clause,[],[f1634,f25301]) ).
fof(f25301,plain,
( spl0_2201
<=> ! [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_2201])]) ).
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(f25299,plain,
spl0_2200,
inference(avatar_split_clause,[],[f1355,f25297]) ).
fof(f25297,plain,
( spl0_2200
<=> ! [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_2200])]) ).
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(f25295,plain,
spl0_2199,
inference(avatar_split_clause,[],[f1294,f25293]) ).
fof(f25293,plain,
( spl0_2199
<=> ! [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_2199])]) ).
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(f25291,plain,
spl0_2198,
inference(avatar_split_clause,[],[f1293,f25289]) ).
fof(f25289,plain,
( spl0_2198
<=> ! [X2,X12,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omin(X3,c_Finite__Set_OMax(X12,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
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(f25287,plain,
spl0_2197,
inference(avatar_split_clause,[],[f1222,f25285]) ).
fof(f25285,plain,
( spl0_2197
<=> ! [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_2197])]) ).
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(f25275,plain,
spl0_2196,
inference(avatar_split_clause,[],[f1220,f25273]) ).
fof(f25273,plain,
( spl0_2196
<=> ! [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_2196])]) ).
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(f25271,plain,
spl0_2195,
inference(avatar_split_clause,[],[f121,f25269]) ).
fof(f25269,plain,
( spl0_2195
<=> ! [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_2195])]) ).
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(f25267,plain,
spl0_2194,
inference(avatar_split_clause,[],[f74,f25265]) ).
fof(f25265,plain,
( spl0_2194
<=> ! [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_2194])]) ).
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(f25079,plain,
( spl0_2193
| ~ spl0_1442
| ~ spl0_2190 ),
inference(avatar_split_clause,[],[f24653,f24557,f11231,f25077]) ).
fof(f24653,plain,
( ! [X0] :
( c_Message_OsymKeys != c_insert(X0,c_emptyset,tc_nat)
| v_KAB = X0 )
| ~ spl0_1442
| ~ spl0_2190 ),
inference(superposition,[],[f11232,f24559]) ).
fof(f24773,plain,
( spl0_2192
| ~ spl0_1441
| ~ spl0_2190 ),
inference(avatar_split_clause,[],[f24652,f24557,f11227,f24771]) ).
fof(f24771,plain,
( spl0_2192
<=> ! [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_2192])]) ).
fof(f24652,plain,
( ! [X0] :
( ~ c_lessequals(c_Message_OsymKeys,X0,tc_set(tc_nat))
| c_in(v_KAB,X0,tc_nat) )
| ~ spl0_1441
| ~ spl0_2190 ),
inference(superposition,[],[f11228,f24559]) ).
fof(f24670,plain,
( ~ spl0_2191
| ~ spl0_820
| ~ spl0_2190 ),
inference(avatar_split_clause,[],[f24648,f24557,f7647,f24667]) ).
fof(f24667,plain,
( spl0_2191
<=> c_emptyset = c_Message_OsymKeys ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f24648,plain,
( c_emptyset != c_Message_OsymKeys
| ~ spl0_820
| ~ spl0_2190 ),
inference(superposition,[],[f7648,f24559]) ).
fof(f24560,plain,
( spl0_2190
| ~ spl0_817
| ~ spl0_2122
| ~ spl0_2164 ),
inference(avatar_split_clause,[],[f24269,f23998,f23790,f7635,f24557]) ).
fof(f23998,plain,
( spl0_2164
<=> ! [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_2164])]) ).
fof(f24269,plain,
( c_Message_OsymKeys = c_insert(v_KAB,c_Message_OsymKeys,tc_nat)
| ~ spl0_817
| ~ spl0_2122
| ~ spl0_2164 ),
inference(forward_demodulation,[],[f24268,f7636]) ).
fof(f24268,plain,
( c_insert(v_KAB,c_Message_OsymKeys,tc_nat) = c_union(c_Message_OsymKeys,c_Message_OsymKeys,tc_nat)
| ~ spl0_817
| ~ spl0_2122
| ~ spl0_2164 ),
inference(forward_demodulation,[],[f24245,f23791]) ).
fof(f24245,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_817
| ~ spl0_2164 ),
inference(superposition,[],[f23999,f7636]) ).
fof(f23999,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_2164 ),
inference(avatar_component_clause,[],[f23998]) ).
fof(f24230,plain,
( spl0_2189
| ~ spl0_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2188 ),
inference(avatar_split_clause,[],[f24226,f24222,f21062,f7562,f7526,f24228]) ).
fof(f24228,plain,
( spl0_2189
<=> ! [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_2189])]) ).
fof(f24222,plain,
( spl0_2188
<=> ! [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_2188])]) ).
fof(f24226,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_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2188 ),
inference(forward_demodulation,[],[f24225,f21145]) ).
fof(f24225,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_790
| ~ spl0_799
| ~ spl0_2034
| ~ spl0_2188 ),
inference(forward_demodulation,[],[f24223,f21145]) ).
fof(f24223,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_2188 ),
inference(avatar_component_clause,[],[f24222]) ).
fof(f24224,plain,
spl0_2188,
inference(avatar_split_clause,[],[f3376,f24222]) ).
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(f24197,plain,
( spl0_2187
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2186 ),
inference(avatar_split_clause,[],[f24193,f24190,f11328,f10972,f7083,f6138,f24195]) ).
fof(f24195,plain,
( spl0_2187
<=> ! [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_2187])]) ).
fof(f24190,plain,
( spl0_2186
<=> ! [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_2186])]) ).
fof(f24193,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2186 ),
inference(forward_demodulation,[],[f24191,f12329]) ).
fof(f24191,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_2186 ),
inference(avatar_component_clause,[],[f24190]) ).
fof(f24192,plain,
spl0_2186,
inference(avatar_split_clause,[],[f3277,f24190]) ).
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(f24188,plain,
spl0_2185,
inference(avatar_split_clause,[],[f3222,f24186]) ).
fof(f24186,plain,
( spl0_2185
<=> ! [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_2185])]) ).
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(f24184,plain,
spl0_2184,
inference(avatar_split_clause,[],[f3221,f24182]) ).
fof(f24182,plain,
( spl0_2184
<=> ! [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_2184])]) ).
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(f24180,plain,
( spl0_2183
| ~ spl0_1093
| ~ spl0_2133 ),
inference(avatar_split_clause,[],[f23942,f23834,f8972,f24178]) ).
fof(f23942,plain,
( ! [X0] :
( c_emptyset != c_union(c_Message_OsymKeys,X0,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) )
| ~ spl0_1093
| ~ spl0_2133 ),
inference(superposition,[],[f8973,f23835]) ).
fof(f24176,plain,
spl0_2182,
inference(avatar_split_clause,[],[f3220,f24174]) ).
fof(f24174,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(f24172,plain,
spl0_2181,
inference(avatar_split_clause,[],[f3219,f24170]) ).
fof(f24170,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(f24168,plain,
spl0_2180,
inference(avatar_split_clause,[],[f3197,f24166]) ).
fof(f24166,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(f24164,plain,
spl0_2179,
inference(avatar_split_clause,[],[f3166,f24162]) ).
fof(f24162,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(f24160,plain,
spl0_2178,
inference(avatar_split_clause,[],[f3164,f24158]) ).
fof(f24158,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(f24095,plain,
( spl0_2177
| ~ spl0_649
| ~ spl0_690
| ~ spl0_785
| ~ spl0_790
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1855
| ~ spl0_2176 ),
inference(avatar_split_clause,[],[f24091,f24087,f17696,f11328,f10972,f7526,f7506,f7083,f6138,f24093]) ).
fof(f24093,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(f7506,plain,
( spl0_785
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f17696,plain,
( spl0_1855
<=> ! [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_1855])]) ).
fof(f24087,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(f24091,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_649
| ~ spl0_690
| ~ spl0_785
| ~ spl0_790
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1855
| ~ spl0_2176 ),
inference(forward_demodulation,[],[f24090,f17729]) ).
fof(f17729,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_785
| ~ spl0_790
| ~ spl0_1855 ),
inference(forward_demodulation,[],[f17699,f7527]) ).
fof(f17699,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_785
| ~ spl0_1855 ),
inference(superposition,[],[f17697,f7507]) ).
fof(f7507,plain,
( ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41)
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f7506]) ).
fof(f17697,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_1855 ),
inference(avatar_component_clause,[],[f17696]) ).
fof(f24090,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2176 ),
inference(forward_demodulation,[],[f24088,f12329]) ).
fof(f24088,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,[],[f24087]) ).
fof(f24089,plain,
spl0_2176,
inference(avatar_split_clause,[],[f3128,f24087]) ).
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(f24085,plain,
spl0_2175,
inference(avatar_split_clause,[],[f3089,f24083]) ).
fof(f24083,plain,
( spl0_2175
<=> ! [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_2175])]) ).
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(f24081,plain,
spl0_2174,
inference(avatar_split_clause,[],[f3088,f24079]) ).
fof(f24079,plain,
( spl0_2174
<=> ! [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_2174])]) ).
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(f24077,plain,
( spl0_2173
| ~ spl0_1092
| ~ spl0_2122 ),
inference(avatar_split_clause,[],[f23882,f23790,f8968,f24075]) ).
fof(f24075,plain,
( spl0_2173
<=> ! [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_2173])]) ).
fof(f23882,plain,
( ! [X0] :
( c_emptyset != c_union(X0,c_Message_OsymKeys,tc_nat)
| c_emptyset = c_insert(v_KAB,X0,tc_nat) )
| ~ spl0_1092
| ~ spl0_2122 ),
inference(superposition,[],[f8969,f23791]) ).
fof(f24073,plain,
spl0_2172,
inference(avatar_split_clause,[],[f3081,f24071]) ).
fof(f24071,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(f24050,plain,
( spl0_2171
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2170 ),
inference(avatar_split_clause,[],[f24046,f24041,f11328,f10972,f7083,f6138,f24048]) ).
fof(f24048,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(f24041,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(f24046,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2170 ),
inference(forward_demodulation,[],[f24045,f12329]) ).
fof(f24045,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2170 ),
inference(forward_demodulation,[],[f24044,f12329]) ).
fof(f24044,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2170 ),
inference(forward_demodulation,[],[f24042,f12329]) ).
fof(f24042,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,[],[f24041]) ).
fof(f24043,plain,
spl0_2170,
inference(avatar_split_clause,[],[f3057,f24041]) ).
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(f24023,plain,
( spl0_2169
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2168 ),
inference(avatar_split_clause,[],[f24019,f24014,f11328,f10972,f7083,f6138,f24021]) ).
fof(f24021,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(f24014,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(f24019,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2168 ),
inference(forward_demodulation,[],[f24018,f12329]) ).
fof(f24018,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2168 ),
inference(forward_demodulation,[],[f24017,f12329]) ).
fof(f24017,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2168 ),
inference(forward_demodulation,[],[f24015,f12329]) ).
fof(f24015,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,[],[f24014]) ).
fof(f24016,plain,
spl0_2168,
inference(avatar_split_clause,[],[f3056,f24014]) ).
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(f24012,plain,
spl0_2167,
inference(avatar_split_clause,[],[f2877,f24010]) ).
fof(f24010,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(f24008,plain,
spl0_2166,
inference(avatar_split_clause,[],[f2859,f24006]) ).
fof(f24006,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(f24004,plain,
spl0_2165,
inference(avatar_split_clause,[],[f2566,f24002]) ).
fof(f24002,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(f24000,plain,
( spl0_2164
| ~ spl0_1763
| ~ spl0_2122 ),
inference(avatar_split_clause,[],[f23880,f23790,f16036,f23998]) ).
fof(f23880,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_1763
| ~ spl0_2122 ),
inference(superposition,[],[f23791,f16037]) ).
fof(f23996,plain,
spl0_2163,
inference(avatar_split_clause,[],[f2564,f23994]) ).
fof(f23994,plain,
( spl0_2163
<=> ! [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_2163])]) ).
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(f23992,plain,
spl0_2162,
inference(avatar_split_clause,[],[f2563,f23990]) ).
fof(f23990,plain,
( spl0_2162
<=> ! [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_2162])]) ).
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(f23988,plain,
spl0_2161,
inference(avatar_split_clause,[],[f2376,f23986]) ).
fof(f23986,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(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(f23984,plain,
spl0_2160,
inference(avatar_split_clause,[],[f2375,f23982]) ).
fof(f23982,plain,
( spl0_2160
<=> ! [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_2160])]) ).
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(f23980,plain,
spl0_2159,
inference(avatar_split_clause,[],[f2335,f23978]) ).
fof(f23978,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_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
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(f23976,plain,
spl0_2158,
inference(avatar_split_clause,[],[f2318,f23974]) ).
fof(f23974,plain,
( spl0_2158
<=> ! [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_2158])]) ).
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(f23972,plain,
spl0_2157,
inference(avatar_split_clause,[],[f2174,f23970]) ).
fof(f23970,plain,
( spl0_2157
<=> ! [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_2157])]) ).
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(f23968,plain,
spl0_2156,
inference(avatar_split_clause,[],[f2121,f23966]) ).
fof(f23966,plain,
( spl0_2156
<=> ! [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_2156])]) ).
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(f23964,plain,
spl0_2155,
inference(avatar_split_clause,[],[f1810,f23962]) ).
fof(f23962,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(f23960,plain,
spl0_2154,
inference(avatar_split_clause,[],[f1672,f23958]) ).
fof(f23958,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(f23937,plain,
spl0_2153,
inference(avatar_split_clause,[],[f1671,f23935]) ).
fof(f23935,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(f23933,plain,
spl0_2152,
inference(avatar_split_clause,[],[f1670,f23931]) ).
fof(f23931,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(f23929,plain,
spl0_2151,
inference(avatar_split_clause,[],[f1669,f23927]) ).
fof(f23927,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(f23925,plain,
spl0_2150,
inference(avatar_split_clause,[],[f1668,f23923]) ).
fof(f23923,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(f23921,plain,
spl0_2149,
inference(avatar_split_clause,[],[f1667,f23919]) ).
fof(f23919,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(f23917,plain,
spl0_2148,
inference(avatar_split_clause,[],[f1666,f23915]) ).
fof(f23915,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(f23913,plain,
spl0_2147,
inference(avatar_split_clause,[],[f1665,f23911]) ).
fof(f23911,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(f23909,plain,
spl0_2146,
inference(avatar_split_clause,[],[f1664,f23907]) ).
fof(f23907,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(f23905,plain,
spl0_2145,
inference(avatar_split_clause,[],[f1663,f23903]) ).
fof(f23903,plain,
( spl0_2145
<=> ! [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_2145])]) ).
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(f23901,plain,
spl0_2144,
inference(avatar_split_clause,[],[f1662,f23899]) ).
fof(f23899,plain,
( spl0_2144
<=> ! [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_2144])]) ).
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(f23876,plain,
spl0_2143,
inference(avatar_split_clause,[],[f1661,f23874]) ).
fof(f23874,plain,
( spl0_2143
<=> ! [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_2143])]) ).
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(f23872,plain,
spl0_2142,
inference(avatar_split_clause,[],[f1660,f23870]) ).
fof(f23870,plain,
( spl0_2142
<=> ! [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_2142])]) ).
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(f23868,plain,
spl0_2141,
inference(avatar_split_clause,[],[f1659,f23866]) ).
fof(f23866,plain,
( spl0_2141
<=> ! [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_2141])]) ).
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(f23864,plain,
spl0_2140,
inference(avatar_split_clause,[],[f1658,f23862]) ).
fof(f23862,plain,
( spl0_2140
<=> ! [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_2140])]) ).
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(f23860,plain,
spl0_2139,
inference(avatar_split_clause,[],[f1657,f23858]) ).
fof(f23858,plain,
( spl0_2139
<=> ! [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_2139])]) ).
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(f23856,plain,
spl0_2138,
inference(avatar_split_clause,[],[f1656,f23854]) ).
fof(f23854,plain,
( spl0_2138
<=> ! [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_2138])]) ).
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(f23852,plain,
spl0_2137,
inference(avatar_split_clause,[],[f1655,f23850]) ).
fof(f23850,plain,
( spl0_2137
<=> ! [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_2137])]) ).
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(f23848,plain,
spl0_2136,
inference(avatar_split_clause,[],[f1654,f23846]) ).
fof(f23846,plain,
( spl0_2136
<=> ! [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_2136])]) ).
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(f23844,plain,
spl0_2135,
inference(avatar_split_clause,[],[f1653,f23842]) ).
fof(f23842,plain,
( spl0_2135
<=> ! [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_2135])]) ).
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(f23840,plain,
spl0_2134,
inference(avatar_split_clause,[],[f1652,f23838]) ).
fof(f23838,plain,
( spl0_2134
<=> ! [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_2134])]) ).
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(f23836,plain,
( spl0_2133
| ~ spl0_1557
| ~ spl0_2090 ),
inference(avatar_split_clause,[],[f23747,f23089,f12734,f23834]) ).
fof(f23089,plain,
( spl0_2090
<=> ! [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_2090])]) ).
fof(f23747,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_1557
| ~ spl0_2090 ),
inference(forward_demodulation,[],[f23732,f12735]) ).
fof(f23732,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_1557
| ~ spl0_2090 ),
inference(superposition,[],[f12735,f23090]) ).
fof(f23090,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_2090 ),
inference(avatar_component_clause,[],[f23089]) ).
fof(f23832,plain,
spl0_2132,
inference(avatar_split_clause,[],[f1651,f23830]) ).
fof(f23830,plain,
( spl0_2132
<=> ! [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_2132])]) ).
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(f23828,plain,
spl0_2131,
inference(avatar_split_clause,[],[f1650,f23826]) ).
fof(f23826,plain,
( spl0_2131
<=> ! [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_2131])]) ).
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(f23824,plain,
spl0_2130,
inference(avatar_split_clause,[],[f1649,f23822]) ).
fof(f23822,plain,
( spl0_2130
<=> ! [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_2130])]) ).
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(f23820,plain,
spl0_2129,
inference(avatar_split_clause,[],[f1648,f23818]) ).
fof(f23818,plain,
( spl0_2129
<=> ! [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_2129])]) ).
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(f23816,plain,
spl0_2128,
inference(avatar_split_clause,[],[f1647,f23814]) ).
fof(f23814,plain,
( spl0_2128
<=> ! [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_2128])]) ).
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(f23812,plain,
spl0_2127,
inference(avatar_split_clause,[],[f1646,f23810]) ).
fof(f23810,plain,
( spl0_2127
<=> ! [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_2127])]) ).
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(f23808,plain,
spl0_2126,
inference(avatar_split_clause,[],[f1645,f23806]) ).
fof(f23806,plain,
( spl0_2126
<=> ! [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_2126])]) ).
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(f23804,plain,
spl0_2125,
inference(avatar_split_clause,[],[f1644,f23802]) ).
fof(f23802,plain,
( spl0_2125
<=> ! [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_2125])]) ).
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(f23800,plain,
spl0_2124,
inference(avatar_split_clause,[],[f1643,f23798]) ).
fof(f23798,plain,
( spl0_2124
<=> ! [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_2124])]) ).
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(f23796,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1642,f23794]) ).
fof(f23794,plain,
( spl0_2123
<=> ! [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_2123])]) ).
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(f23792,plain,
( spl0_2122
| ~ spl0_1556
| ~ spl0_2090 ),
inference(avatar_split_clause,[],[f23746,f23089,f12730,f23790]) ).
fof(f23746,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_1556
| ~ spl0_2090 ),
inference(forward_demodulation,[],[f23731,f12731]) ).
fof(f23731,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_1556
| ~ spl0_2090 ),
inference(superposition,[],[f12731,f23090]) ).
fof(f23788,plain,
spl0_2121,
inference(avatar_split_clause,[],[f1641,f23786]) ).
fof(f23786,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(f23784,plain,
spl0_2120,
inference(avatar_split_clause,[],[f1629,f23782]) ).
fof(f23782,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(f23780,plain,
spl0_2119,
inference(avatar_split_clause,[],[f1614,f23778]) ).
fof(f23778,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(f23776,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1523,f23774]) ).
fof(f23774,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(f23772,plain,
spl0_2117,
inference(avatar_split_clause,[],[f1522,f23770]) ).
fof(f23770,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(f23768,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1521,f23766]) ).
fof(f23766,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(f23764,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1520,f23762]) ).
fof(f23762,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(f23760,plain,
spl0_2114,
inference(avatar_split_clause,[],[f1468,f23758]) ).
fof(f23758,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(f23756,plain,
spl0_2113,
inference(avatar_split_clause,[],[f1283,f23754]) ).
fof(f23754,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(f23752,plain,
spl0_2112,
inference(avatar_split_clause,[],[f1282,f23750]) ).
fof(f23750,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(f23724,plain,
spl0_2111,
inference(avatar_split_clause,[],[f79,f23722]) ).
fof(f23722,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(f23720,plain,
spl0_2110,
inference(avatar_split_clause,[],[f75,f23718]) ).
fof(f23718,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(f23716,plain,
spl0_2109,
inference(avatar_split_clause,[],[f69,f23714]) ).
fof(f23714,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(f23712,plain,
spl0_2108,
inference(avatar_split_clause,[],[f60,f23710]) ).
fof(f23710,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(f23708,plain,
spl0_2107,
inference(avatar_split_clause,[],[f22,f23706]) ).
fof(f23706,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(f23704,plain,
spl0_2106,
inference(avatar_split_clause,[],[f21,f23702]) ).
fof(f23702,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(f23580,plain,
( spl0_2105
| ~ spl0_60
| ~ spl0_1591
| ~ spl0_2087 ),
inference(avatar_split_clause,[],[f23077,f23074,f12902,f3730,f23578]) ).
fof(f23578,plain,
( spl0_2105
<=> ! [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_2105])]) ).
fof(f23074,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(f23077,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_60
| ~ spl0_1591
| ~ spl0_2087 ),
inference(forward_demodulation,[],[f23075,f14229]) ).
fof(f23075,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,[],[f23074]) ).
fof(f23576,plain,
( spl0_2104
| ~ spl0_60
| ~ spl0_1591
| ~ spl0_2086 ),
inference(avatar_split_clause,[],[f23072,f23069,f12902,f3730,f23574]) ).
fof(f23574,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(f23069,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(f23072,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_60
| ~ spl0_1591
| ~ spl0_2086 ),
inference(forward_demodulation,[],[f23070,f14229]) ).
fof(f23070,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,[],[f23069]) ).
fof(f23207,plain,
( spl0_2103
| ~ spl0_1671
| ~ spl0_2102 ),
inference(avatar_split_clause,[],[f23203,f23200,f14552,f23205]) ).
fof(f23205,plain,
( spl0_2103
<=> ! [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_2103])]) ).
fof(f14552,plain,
( spl0_1671
<=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f23200,plain,
( spl0_2102
<=> ! [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_2102])]) ).
fof(f23203,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_1671
| ~ spl0_2102 ),
inference(forward_demodulation,[],[f23201,f14554]) ).
fof(f14554,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1671 ),
inference(avatar_component_clause,[],[f14552]) ).
fof(f23201,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_2102 ),
inference(avatar_component_clause,[],[f23200]) ).
fof(f23202,plain,
spl0_2102,
inference(avatar_split_clause,[],[f3429,f23200]) ).
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(f23198,plain,
spl0_2101,
inference(avatar_split_clause,[],[f3427,f23196]) ).
fof(f23196,plain,
( spl0_2101
<=> ! [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_2101])]) ).
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(f23194,plain,
spl0_2100,
inference(avatar_split_clause,[],[f3425,f23192]) ).
fof(f23192,plain,
( spl0_2100
<=> ! [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_2100])]) ).
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(f23173,plain,
( spl0_2099
| ~ spl0_1671
| ~ spl0_2097 ),
inference(avatar_split_clause,[],[f23165,f23162,f14552,f23171]) ).
fof(f23171,plain,
( spl0_2099
<=> ! [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_2099])]) ).
fof(f23162,plain,
( spl0_2097
<=> ! [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_2097])]) ).
fof(f23165,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_1671
| ~ spl0_2097 ),
inference(forward_demodulation,[],[f23163,f14554]) ).
fof(f23163,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_2097 ),
inference(avatar_component_clause,[],[f23162]) ).
fof(f23169,plain,
( spl0_2098
| ~ spl0_5
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f22063,f20980,f3455,f23167]) ).
fof(f22063,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_5
| ~ spl0_2014 ),
inference(resolution,[],[f20981,f3457]) ).
fof(f23164,plain,
spl0_2097,
inference(avatar_split_clause,[],[f3422,f23162]) ).
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(f23143,plain,
( spl0_2096
| ~ spl0_1671
| ~ spl0_2095 ),
inference(avatar_split_clause,[],[f23139,f23136,f14552,f23141]) ).
fof(f23141,plain,
( spl0_2096
<=> ! [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_2096])]) ).
fof(f23136,plain,
( spl0_2095
<=> ! [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_2095])]) ).
fof(f23139,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_1671
| ~ spl0_2095 ),
inference(forward_demodulation,[],[f23137,f14554]) ).
fof(f23137,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_2095 ),
inference(avatar_component_clause,[],[f23136]) ).
fof(f23138,plain,
spl0_2095,
inference(avatar_split_clause,[],[f3419,f23136]) ).
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(f23134,plain,
spl0_2094,
inference(avatar_split_clause,[],[f3417,f23132]) ).
fof(f23132,plain,
( spl0_2094
<=> ! [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_2094])]) ).
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(f23130,plain,
spl0_2093,
inference(avatar_split_clause,[],[f3415,f23128]) ).
fof(f23128,plain,
( spl0_2093
<=> ! [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_2093])]) ).
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(f23117,plain,
( spl0_2092
| ~ spl0_1671
| ~ spl0_2091 ),
inference(avatar_split_clause,[],[f23113,f23110,f14552,f23115]) ).
fof(f23115,plain,
( spl0_2092
<=> ! [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_2092])]) ).
fof(f23110,plain,
( spl0_2091
<=> ! [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_2091])]) ).
fof(f23113,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_1671
| ~ spl0_2091 ),
inference(forward_demodulation,[],[f23111,f14554]) ).
fof(f23111,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_2091 ),
inference(avatar_component_clause,[],[f23110]) ).
fof(f23112,plain,
spl0_2091,
inference(avatar_split_clause,[],[f3412,f23110]) ).
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(f23091,plain,
( spl0_2090
| ~ spl0_4
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f22059,f20980,f3450,f23089]) ).
fof(f3450,plain,
( spl0_4
<=> c_in(v_KAB,c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f22059,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_4
| ~ spl0_2014 ),
inference(resolution,[],[f20981,f3452]) ).
fof(f3452,plain,
( c_in(v_KAB,c_Message_OsymKeys,tc_nat)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3450]) ).
fof(f23087,plain,
( spl0_2089
| ~ spl0_60
| ~ spl0_1471
| ~ spl0_2088 ),
inference(avatar_split_clause,[],[f23083,f23079,f11348,f3730,f23085]) ).
fof(f23085,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(f11348,plain,
( spl0_1471
<=> ! [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_1471])]) ).
fof(f23079,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(f23083,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_60
| ~ spl0_1471
| ~ spl0_2088 ),
inference(forward_demodulation,[],[f23082,f12396]) ).
fof(f12396,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint) = c_plus(c_1,c_1,tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1471 ),
inference(resolution,[],[f11349,f3732]) ).
fof(f11349,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_1471 ),
inference(avatar_component_clause,[],[f11348]) ).
fof(f23082,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_60
| ~ spl0_1471
| ~ spl0_2088 ),
inference(forward_demodulation,[],[f23080,f12396]) ).
fof(f23080,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,[],[f23079]) ).
fof(f23081,plain,
spl0_2088,
inference(avatar_split_clause,[],[f3370,f23079]) ).
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(f23076,plain,
spl0_2087,
inference(avatar_split_clause,[],[f3196,f23074]) ).
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(f23071,plain,
spl0_2086,
inference(avatar_split_clause,[],[f3195,f23069]) ).
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(f23067,plain,
spl0_2085,
inference(avatar_split_clause,[],[f2954,f23065]) ).
fof(f23065,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(f23063,plain,
spl0_2084,
inference(avatar_split_clause,[],[f2936,f23061]) ).
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(f23059,plain,
spl0_2083,
inference(avatar_split_clause,[],[f2352,f23057]) ).
fof(f23057,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(f23055,plain,
spl0_2082,
inference(avatar_split_clause,[],[f2327,f23053]) ).
fof(f23053,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(f23051,plain,
spl0_2081,
inference(avatar_split_clause,[],[f2320,f23049]) ).
fof(f23049,plain,
( spl0_2081
<=> ! [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_2081])]) ).
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(f23047,plain,
spl0_2080,
inference(avatar_split_clause,[],[f1973,f23045]) ).
fof(f23045,plain,
( spl0_2080
<=> ! [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_2080])]) ).
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(f23043,plain,
( spl0_2079
| spl0_3
| ~ spl0_2012 ),
inference(avatar_split_clause,[],[f21886,f20972,f3445,f23041]) ).
fof(f23041,plain,
( spl0_2079
<=> ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_Ba,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f3445,plain,
( spl0_3
<=> c_in(v_Ba,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f21886,plain,
( ! [X0] : c_minus(c_Event_Obad,X0,tc_set(tc_Message_Oagent)) = c_minus(c_Event_Obad,c_insert(v_Ba,X0,tc_Message_Oagent),tc_set(tc_Message_Oagent))
| spl0_3
| ~ spl0_2012 ),
inference(resolution,[],[f20973,f3447]) ).
fof(f3447,plain,
( ~ c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| spl0_3 ),
inference(avatar_component_clause,[],[f3445]) ).
fof(f23039,plain,
spl0_2078,
inference(avatar_split_clause,[],[f1972,f23037]) ).
fof(f23037,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(f23035,plain,
spl0_2077,
inference(avatar_split_clause,[],[f1969,f23033]) ).
fof(f23033,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(f23031,plain,
spl0_2076,
inference(avatar_split_clause,[],[f1968,f23029]) ).
fof(f23029,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(f23027,plain,
spl0_2075,
inference(avatar_split_clause,[],[f1962,f23025]) ).
fof(f23025,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(f23023,plain,
spl0_2074,
inference(avatar_split_clause,[],[f1961,f23021]) ).
fof(f23021,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(f23019,plain,
spl0_2073,
inference(avatar_split_clause,[],[f1946,f23017]) ).
fof(f23017,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(f23015,plain,
spl0_2072,
inference(avatar_split_clause,[],[f1945,f23013]) ).
fof(f23013,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(f23011,plain,
spl0_2071,
inference(avatar_split_clause,[],[f1876,f23009]) ).
fof(f23009,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(f23007,plain,
spl0_2070,
inference(avatar_split_clause,[],[f1755,f23005]) ).
fof(f23005,plain,
( spl0_2070
<=> ! [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_2070])]) ).
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(f23003,plain,
spl0_2069,
inference(avatar_split_clause,[],[f1274,f23001]) ).
fof(f23001,plain,
( spl0_2069
<=> ! [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_2069])]) ).
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(f22999,plain,
( spl0_2068
| spl0_2
| ~ spl0_2012 ),
inference(avatar_split_clause,[],[f21885,f20972,f3440,f22997]) ).
fof(f22997,plain,
( spl0_2068
<=> ! [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_2068])]) ).
fof(f3440,plain,
( spl0_2
<=> c_in(v_B,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f21885,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_2012 ),
inference(resolution,[],[f20973,f3442]) ).
fof(f3442,plain,
( ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent)
| spl0_2 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f22995,plain,
spl0_2067,
inference(avatar_split_clause,[],[f1256,f22993]) ).
fof(f22993,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(f22991,plain,
spl0_2066,
inference(avatar_split_clause,[],[f33,f22989]) ).
fof(f22989,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(f22987,plain,
spl0_2065,
inference(avatar_split_clause,[],[f32,f22985]) ).
fof(f22985,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(f22849,plain,
( spl0_2064
| spl0_1
| ~ spl0_2012 ),
inference(avatar_split_clause,[],[f21884,f20972,f3435,f22847]) ).
fof(f22847,plain,
( spl0_2064
<=> ! [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_2064])]) ).
fof(f21884,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_2012 ),
inference(resolution,[],[f20973,f3437]) ).
fof(f3437,plain,
( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| spl0_1 ),
inference(avatar_component_clause,[],[f3435]) ).
fof(f22579,plain,
( spl0_2063
| ~ spl0_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_2047 ),
inference(avatar_split_clause,[],[f22423,f22420,f17696,f7526,f7506,f22577]) ).
fof(f22577,plain,
( spl0_2063
<=> ! [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_2063])]) ).
fof(f22420,plain,
( spl0_2047
<=> ! [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_2047])]) ).
fof(f22423,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_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_2047 ),
inference(forward_demodulation,[],[f22421,f17729]) ).
fof(f22421,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_2047 ),
inference(avatar_component_clause,[],[f22420]) ).
fof(f22537,plain,
( spl0_2062
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_2044 ),
inference(avatar_split_clause,[],[f22409,f22406,f8902,f3730,f22535]) ).
fof(f22535,plain,
( spl0_2062
<=> ! [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_2062])]) ).
fof(f22406,plain,
( spl0_2044
<=> ! [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_2044])]) ).
fof(f22409,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_60
| ~ spl0_1076
| ~ spl0_2044 ),
inference(forward_demodulation,[],[f22407,f9266]) ).
fof(f22407,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_2044 ),
inference(avatar_component_clause,[],[f22406]) ).
fof(f22479,plain,
spl0_2061,
inference(avatar_split_clause,[],[f3343,f22477]) ).
fof(f22477,plain,
( spl0_2061
<=> ! [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_2061])]) ).
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(f22475,plain,
spl0_2060,
inference(avatar_split_clause,[],[f3163,f22473]) ).
fof(f22473,plain,
( spl0_2060
<=> ! [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_2060])]) ).
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(f22471,plain,
spl0_2059,
inference(avatar_split_clause,[],[f3161,f22469]) ).
fof(f22469,plain,
( spl0_2059
<=> ! [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_2059])]) ).
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(f22467,plain,
spl0_2058,
inference(avatar_split_clause,[],[f3108,f22465]) ).
fof(f22465,plain,
( spl0_2058
<=> ! [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_2058])]) ).
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(f22463,plain,
( spl0_2057
| ~ spl0_1004
| ~ spl0_2037 ),
inference(avatar_split_clause,[],[f21798,f21633,f8475,f22461]) ).
fof(f22461,plain,
( spl0_2057
<=> ! [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_2057])]) ).
fof(f21633,plain,
( spl0_2037
<=> 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_2037])]) ).
fof(f21798,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_2037 ),
inference(superposition,[],[f8476,f21635]) ).
fof(f21635,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_2037 ),
inference(avatar_component_clause,[],[f21633]) ).
fof(f22459,plain,
spl0_2056,
inference(avatar_split_clause,[],[f3079,f22457]) ).
fof(f22457,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(f22455,plain,
spl0_2055,
inference(avatar_split_clause,[],[f2858,f22453]) ).
fof(f22453,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(f22451,plain,
spl0_2054,
inference(avatar_split_clause,[],[f2846,f22449]) ).
fof(f22449,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(f22447,plain,
spl0_2053,
inference(avatar_split_clause,[],[f2797,f22445]) ).
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(f22443,plain,
spl0_2052,
inference(avatar_split_clause,[],[f2122,f22441]) ).
fof(f22441,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(f22439,plain,
spl0_2051,
inference(avatar_split_clause,[],[f1864,f22437]) ).
fof(f22437,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(f22435,plain,
spl0_2050,
inference(avatar_split_clause,[],[f1800,f22433]) ).
fof(f22433,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(f22431,plain,
spl0_2049,
inference(avatar_split_clause,[],[f1796,f22429]) ).
fof(f22429,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(f22427,plain,
spl0_2048,
inference(avatar_split_clause,[],[f1795,f22425]) ).
fof(f22425,plain,
( spl0_2048
<=> ! [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_2048])]) ).
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(f22422,plain,
spl0_2047,
inference(avatar_split_clause,[],[f1726,f22420]) ).
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(f22417,plain,
spl0_2046,
inference(avatar_split_clause,[],[f1714,f22415]) ).
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(f22413,plain,
spl0_2045,
inference(avatar_split_clause,[],[f1617,f22411]) ).
fof(f22411,plain,
( spl0_2045
<=> ! [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_2045])]) ).
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(f22408,plain,
spl0_2044,
inference(avatar_split_clause,[],[f1453,f22406]) ).
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(f22404,plain,
spl0_2043,
inference(avatar_split_clause,[],[f1219,f22402]) ).
fof(f22402,plain,
( spl0_2043
<=> ! [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_2043])]) ).
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(f22400,plain,
spl0_2042,
inference(avatar_split_clause,[],[f1218,f22398]) ).
fof(f22398,plain,
( spl0_2042
<=> ! [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_2042])]) ).
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(f22396,plain,
spl0_2041,
inference(avatar_split_clause,[],[f57,f22394]) ).
fof(f22394,plain,
( spl0_2041
<=> ! [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_2041])]) ).
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(f22392,plain,
spl0_2040,
inference(avatar_split_clause,[],[f56,f22390]) ).
fof(f22390,plain,
( spl0_2040
<=> ! [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_2040])]) ).
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(f22340,plain,
( ~ spl0_658
| ~ spl0_2038 ),
inference(avatar_contradiction_clause,[],[f22338]) ).
fof(f22338,plain,
( $false
| ~ spl0_658
| ~ spl0_2038 ),
inference(resolution,[],[f21639,f6180]) ).
fof(f21639,plain,
( c_in(v_KAB,c_emptyset,tc_nat)
| ~ spl0_2038 ),
inference(avatar_component_clause,[],[f21637]) ).
fof(f21637,plain,
( spl0_2038
<=> c_in(v_KAB,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f22148,plain,
( spl0_2039
| ~ spl0_742
| ~ spl0_1027
| ~ spl0_2037 ),
inference(avatar_split_clause,[],[f21805,f21633,f8698,f7316,f22145]) ).
fof(f22145,plain,
( spl0_2039
<=> 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_2039])]) ).
fof(f8698,plain,
( spl0_1027
<=> v_KAB = c_Message_OinvKey(v_KAB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f21805,plain,
( v_KAB = v_sko__uhi(c_insert(c_Message_Omsg_OKey(v_KAB),c_emptyset,tc_Message_Omsg),v_KAB)
| ~ spl0_742
| ~ spl0_1027
| ~ spl0_2037 ),
inference(forward_demodulation,[],[f21797,f8700]) ).
fof(f8700,plain,
( v_KAB = c_Message_OinvKey(v_KAB)
| ~ spl0_1027 ),
inference(avatar_component_clause,[],[f8698]) ).
fof(f21797,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_742
| ~ spl0_2037 ),
inference(superposition,[],[f7317,f21635]) ).
fof(f21640,plain,
( spl0_2037
| spl0_2038
| ~ spl0_661
| ~ spl0_2028 ),
inference(avatar_split_clause,[],[f21301,f21036,f6191,f21637,f21633]) ).
fof(f6191,plain,
( spl0_661
<=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f21036,plain,
( spl0_2028
<=> ! [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_2028])]) ).
fof(f21301,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_661
| ~ spl0_2028 ),
inference(superposition,[],[f21037,f6193]) ).
fof(f6193,plain,
( c_emptyset = c_Message_OkeysFor(c_emptyset)
| ~ spl0_661 ),
inference(avatar_component_clause,[],[f6191]) ).
fof(f21037,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_2028 ),
inference(avatar_component_clause,[],[f21036]) ).
fof(f21402,plain,
( spl0_2036
| ~ spl0_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_1993 ),
inference(avatar_split_clause,[],[f20897,f20893,f17696,f7526,f7506,f21400]) ).
fof(f21400,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)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f20893,plain,
( spl0_1993
<=> ! [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_1993])]) ).
fof(f20897,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_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_1993 ),
inference(forward_demodulation,[],[f20896,f17729]) ).
fof(f20896,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_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_1993 ),
inference(forward_demodulation,[],[f20894,f17729]) ).
fof(f20894,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_1993 ),
inference(avatar_component_clause,[],[f20893]) ).
fof(f21398,plain,
( spl0_2035
| ~ spl0_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_1992 ),
inference(avatar_split_clause,[],[f20891,f20887,f17696,f7526,f7506,f21396]) ).
fof(f21396,plain,
( spl0_2035
<=> ! [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_2035])]) ).
fof(f20887,plain,
( spl0_1992
<=> ! [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_1992])]) ).
fof(f20891,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_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_1992 ),
inference(forward_demodulation,[],[f20890,f17729]) ).
fof(f20890,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_785
| ~ spl0_790
| ~ spl0_1855
| ~ spl0_1992 ),
inference(forward_demodulation,[],[f20888,f17729]) ).
fof(f20888,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_1992 ),
inference(avatar_component_clause,[],[f20887]) ).
fof(f21064,plain,
( spl0_2034
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2033 ),
inference(avatar_split_clause,[],[f21060,f21056,f11328,f10972,f7083,f6138,f21062]) ).
fof(f21056,plain,
( spl0_2033
<=> ! [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_2033])]) ).
fof(f21060,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2033 ),
inference(forward_demodulation,[],[f21059,f12329]) ).
fof(f21059,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_2033 ),
inference(forward_demodulation,[],[f21057,f12329]) ).
fof(f21057,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_2033 ),
inference(avatar_component_clause,[],[f21056]) ).
fof(f21058,plain,
spl0_2033,
inference(avatar_split_clause,[],[f3265,f21056]) ).
fof(f21054,plain,
spl0_2032,
inference(avatar_split_clause,[],[f3189,f21052]) ).
fof(f21052,plain,
( spl0_2032
<=> ! [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_2032])]) ).
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(f21050,plain,
spl0_2031,
inference(avatar_split_clause,[],[f3184,f21048]) ).
fof(f21048,plain,
( spl0_2031
<=> ! [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_2031])]) ).
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(f21046,plain,
spl0_2030,
inference(avatar_split_clause,[],[f3183,f21044]) ).
fof(f21044,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(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(f21042,plain,
spl0_2029,
inference(avatar_split_clause,[],[f3133,f21040]) ).
fof(f21040,plain,
( spl0_2029
<=> ! [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_2029])]) ).
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(f21038,plain,
( spl0_2028
| ~ spl0_898
| ~ spl0_1101
| ~ spl0_1985 ),
inference(avatar_split_clause,[],[f20861,f20557,f9004,f7972,f21036]) ).
fof(f9004,plain,
( spl0_1101
<=> ! [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_1101])]) ).
fof(f20557,plain,
( spl0_1985
<=> ! [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_1985])]) ).
fof(f20861,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_898
| ~ spl0_1101
| ~ spl0_1985 ),
inference(forward_demodulation,[],[f20837,f9005]) ).
fof(f9005,plain,
( ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg))
| ~ spl0_1101 ),
inference(avatar_component_clause,[],[f9004]) ).
fof(f20837,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_898
| ~ spl0_1985 ),
inference(resolution,[],[f20558,f7973]) ).
fof(f20558,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_1985 ),
inference(avatar_component_clause,[],[f20557]) ).
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,
inference(avatar_split_clause,[],[f2838,f21000]) ).
fof(f21000,plain,
( spl0_2019
<=> ! [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_2019])]) ).
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(f20998,plain,
spl0_2018,
inference(avatar_split_clause,[],[f2805,f20996]) ).
fof(f20996,plain,
( spl0_2018
<=> ! [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_2018])]) ).
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(f20994,plain,
spl0_2017,
inference(avatar_split_clause,[],[f2804,f20992]) ).
fof(f20992,plain,
( spl0_2017
<=> ! [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_2017])]) ).
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(f20990,plain,
spl0_2016,
inference(avatar_split_clause,[],[f2802,f20988]) ).
fof(f20988,plain,
( spl0_2016
<=> ! [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_2016])]) ).
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(f20986,plain,
spl0_2015,
inference(avatar_split_clause,[],[f2791,f20984]) ).
fof(f20984,plain,
( spl0_2015
<=> ! [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_2015])]) ).
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(f20982,plain,
spl0_2014,
inference(avatar_split_clause,[],[f2674,f20980]) ).
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(f20978,plain,
spl0_2013,
inference(avatar_split_clause,[],[f2647,f20976]) ).
fof(f20976,plain,
( spl0_2013
<=> ! [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_2013])]) ).
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(f20974,plain,
spl0_2012,
inference(avatar_split_clause,[],[f2597,f20972]) ).
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(f20970,plain,
spl0_2011,
inference(avatar_split_clause,[],[f2337,f20968]) ).
fof(f20968,plain,
( spl0_2011
<=> ! [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_2011])]) ).
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(f20966,plain,
spl0_2010,
inference(avatar_split_clause,[],[f2329,f20964]) ).
fof(f20964,plain,
( spl0_2010
<=> ! [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_2010])]) ).
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(f20962,plain,
spl0_2009,
inference(avatar_split_clause,[],[f2326,f20960]) ).
fof(f20960,plain,
( spl0_2009
<=> ! [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_2009])]) ).
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(f20958,plain,
spl0_2008,
inference(avatar_split_clause,[],[f2323,f20956]) ).
fof(f20956,plain,
( spl0_2008
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
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(f20954,plain,
spl0_2007,
inference(avatar_split_clause,[],[f2077,f20952]) ).
fof(f20952,plain,
( spl0_2007
<=> ! [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_2007])]) ).
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(f20950,plain,
spl0_2006,
inference(avatar_split_clause,[],[f2074,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(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
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(f20946,plain,
spl0_2005,
inference(avatar_split_clause,[],[f2069,f20944]) ).
fof(f20944,plain,
( spl0_2005
<=> ! [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_2005])]) ).
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(f20942,plain,
spl0_2004,
inference(avatar_split_clause,[],[f2066,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(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
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(f20938,plain,
spl0_2003,
inference(avatar_split_clause,[],[f1929,f20936]) ).
fof(f20936,plain,
( spl0_2003
<=> ! [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_2003])]) ).
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(f20934,plain,
spl0_2002,
inference(avatar_split_clause,[],[f1830,f20932]) ).
fof(f20932,plain,
( spl0_2002
<=> ! [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_2002])]) ).
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(f20930,plain,
spl0_2001,
inference(avatar_split_clause,[],[f1829,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(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(f20926,plain,
spl0_2000,
inference(avatar_split_clause,[],[f1721,f20924]) ).
fof(f20924,plain,
( spl0_2000
<=> ! [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_2000])]) ).
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(f20922,plain,
spl0_1999,
inference(avatar_split_clause,[],[f1704,f20920]) ).
fof(f20920,plain,
( spl0_1999
<=> ! [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_1999])]) ).
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(f20918,plain,
spl0_1998,
inference(avatar_split_clause,[],[f1697,f20916]) ).
fof(f20916,plain,
( spl0_1998
<=> ! [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_1998])]) ).
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(f20914,plain,
( spl0_1996
| spl0_1997
| ~ spl0_123
| ~ spl0_1985 ),
inference(avatar_split_clause,[],[f20847,f20557,f4034,f20911,f20907]) ).
fof(f20907,plain,
( spl0_1996
<=> c_in(v_KAB,c_Message_OkeysFor(c_UNIV),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).
fof(f20911,plain,
( spl0_1997
<=> v_KAB = c_Message_OinvKey(v_sko__uhi(c_UNIV,v_KAB)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).
fof(f20847,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_123
| ~ spl0_1985 ),
inference(resolution,[],[f20558,f4035]) ).
fof(f20905,plain,
spl0_1995,
inference(avatar_split_clause,[],[f1630,f20903]) ).
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(f20901,plain,
spl0_1994,
inference(avatar_split_clause,[],[f1599,f20899]) ).
fof(f20899,plain,
( spl0_1994
<=> ! [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_1994])]) ).
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(f20895,plain,
spl0_1993,
inference(avatar_split_clause,[],[f1517,f20893]) ).
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(f20889,plain,
spl0_1992,
inference(avatar_split_clause,[],[f1516,f20887]) ).
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(f20885,plain,
spl0_1991,
inference(avatar_split_clause,[],[f1481,f20883]) ).
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(f20881,plain,
spl0_1990,
inference(avatar_split_clause,[],[f1480,f20879]) ).
fof(f20879,plain,
( spl0_1990
<=> ! [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_1990])]) ).
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(f20877,plain,
spl0_1989,
inference(avatar_split_clause,[],[f1473,f20875]) ).
fof(f20875,plain,
( spl0_1989
<=> ! [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_1989])]) ).
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(f20873,plain,
spl0_1988,
inference(avatar_split_clause,[],[f1472,f20871]) ).
fof(f20871,plain,
( spl0_1988
<=> ! [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_1988])]) ).
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(f20869,plain,
spl0_1987,
inference(avatar_split_clause,[],[f1292,f20867]) ).
fof(f20867,plain,
( spl0_1987
<=> ! [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_1987])]) ).
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(f20865,plain,
spl0_1986,
inference(avatar_split_clause,[],[f1288,f20863]) ).
fof(f20863,plain,
( spl0_1986
<=> ! [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_1986])]) ).
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(f20559,plain,
( spl0_1985
| ~ spl0_1478
| ~ spl0_1936 ),
inference(avatar_split_clause,[],[f20440,f19420,f12268,f20557]) ).
fof(f12268,plain,
( spl0_1478
<=> ! [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_1478])]) ).
fof(f19420,plain,
( spl0_1936
<=> ! [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_1936])]) ).
fof(f20440,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_1478
| ~ spl0_1936 ),
inference(resolution,[],[f19421,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_1478 ),
inference(avatar_component_clause,[],[f12268]) ).
fof(f19421,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_1936 ),
inference(avatar_component_clause,[],[f19420]) ).
fof(f20423,plain,
( spl0_1984
| ~ spl0_1181
| ~ spl0_1883 ),
inference(avatar_split_clause,[],[f18844,f18529,f9545,f20420]) ).
fof(f20420,plain,
( spl0_1984
<=> 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_1984])]) ).
fof(f18529,plain,
( spl0_1883
<=> 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_1883])]) ).
fof(f18844,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_1181
| ~ spl0_1883 ),
inference(resolution,[],[f18531,f9546]) ).
fof(f18531,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_1883 ),
inference(avatar_component_clause,[],[f18529]) ).
fof(f19899,plain,
( spl0_1983
| ~ spl0_1450
| ~ spl0_1898 ),
inference(avatar_split_clause,[],[f19387,f19241,f11264,f19897]) ).
fof(f19897,plain,
( spl0_1983
<=> ! [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_Ba,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f19241,plain,
( spl0_1898
<=> ! [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_Ba,X1),X0,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f19387,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_Ba,X0),X1,tc_Event_Oevent)),tc_Message_Omsg) )
| ~ spl0_1450
| ~ spl0_1898 ),
inference(superposition,[],[f11265,f19242]) ).
fof(f19242,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_Ba,X1),X0,tc_Event_Oevent))
| ~ spl0_1898 ),
inference(avatar_component_clause,[],[f19241]) ).
fof(f19805,plain,
spl0_1982,
inference(avatar_split_clause,[],[f3428,f19803]) ).
fof(f19803,plain,
( spl0_1982
<=> ! [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_1982])]) ).
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(f19801,plain,
spl0_1981,
inference(avatar_split_clause,[],[f3426,f19799]) ).
fof(f19799,plain,
( spl0_1981
<=> ! [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_1981])]) ).
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(f19797,plain,
( spl0_1980
| ~ spl0_1450
| ~ spl0_1887 ),
inference(avatar_split_clause,[],[f19338,f19197,f11264,f19795]) ).
fof(f19795,plain,
( spl0_1980
<=> ! [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_1980])]) ).
fof(f19197,plain,
( spl0_1887
<=> ! [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_1887])]) ).
fof(f19338,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_1450
| ~ spl0_1887 ),
inference(superposition,[],[f11265,f19198]) ).
fof(f19198,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_1887 ),
inference(avatar_component_clause,[],[f19197]) ).
fof(f19793,plain,
spl0_1979,
inference(avatar_split_clause,[],[f3418,f19791]) ).
fof(f19791,plain,
( spl0_1979
<=> ! [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_1979])]) ).
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(f19789,plain,
spl0_1978,
inference(avatar_split_clause,[],[f3416,f19787]) ).
fof(f19787,plain,
( spl0_1978
<=> ! [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_1978])]) ).
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(f19785,plain,
spl0_1977,
inference(avatar_split_clause,[],[f3384,f19783]) ).
fof(f19783,plain,
( spl0_1977
<=> ! [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_1977])]) ).
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(f19776,plain,
( spl0_1976
| ~ spl0_1671
| ~ spl0_1975 ),
inference(avatar_split_clause,[],[f19772,f19769,f14552,f19774]) ).
fof(f19774,plain,
( spl0_1976
<=> ! [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_1976])]) ).
fof(f19769,plain,
( spl0_1975
<=> ! [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_1975])]) ).
fof(f19772,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_1671
| ~ spl0_1975 ),
inference(forward_demodulation,[],[f19770,f14554]) ).
fof(f19770,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_1975 ),
inference(avatar_component_clause,[],[f19769]) ).
fof(f19771,plain,
spl0_1975,
inference(avatar_split_clause,[],[f3383,f19769]) ).
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(f19767,plain,
spl0_1974,
inference(avatar_split_clause,[],[f3378,f19765]) ).
fof(f19765,plain,
( spl0_1974
<=> ! [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_1974])]) ).
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(f19754,plain,
( spl0_1973
| ~ spl0_1671
| ~ spl0_1972 ),
inference(avatar_split_clause,[],[f19750,f19747,f14552,f19752]) ).
fof(f19752,plain,
( spl0_1973
<=> ! [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_1973])]) ).
fof(f19747,plain,
( spl0_1972
<=> ! [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_1972])]) ).
fof(f19750,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_1671
| ~ spl0_1972 ),
inference(forward_demodulation,[],[f19748,f14554]) ).
fof(f19748,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_1972 ),
inference(avatar_component_clause,[],[f19747]) ).
fof(f19749,plain,
spl0_1972,
inference(avatar_split_clause,[],[f3377,f19747]) ).
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(f19745,plain,
( spl0_1971
| ~ spl0_1450
| ~ spl0_1884 ),
inference(avatar_split_clause,[],[f19289,f19026,f11264,f19743]) ).
fof(f19743,plain,
( spl0_1971
<=> ! [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_1971])]) ).
fof(f19026,plain,
( spl0_1884
<=> ! [X0,X1] : c_Event_Oknows(c_Message_Oagent_OSpy,X0) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,X1),X0,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f19289,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_1450
| ~ spl0_1884 ),
inference(superposition,[],[f11265,f19027]) ).
fof(f19027,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_1884 ),
inference(avatar_component_clause,[],[f19026]) ).
fof(f19739,plain,
( spl0_1970
| ~ spl0_60
| ~ spl0_1471
| ~ spl0_1969 ),
inference(avatar_split_clause,[],[f19735,f19732,f11348,f3730,f19737]) ).
fof(f19737,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(f19732,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(f19735,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_60
| ~ spl0_1471
| ~ spl0_1969 ),
inference(forward_demodulation,[],[f19733,f12396]) ).
fof(f19733,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,[],[f19732]) ).
fof(f19734,plain,
spl0_1969,
inference(avatar_split_clause,[],[f3346,f19732]) ).
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(f19728,plain,
( spl0_1968
| ~ spl0_60
| ~ spl0_1471
| ~ spl0_1967 ),
inference(avatar_split_clause,[],[f19724,f19721,f11348,f3730,f19726]) ).
fof(f19726,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(f19721,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(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_60
| ~ spl0_1471
| ~ spl0_1967 ),
inference(forward_demodulation,[],[f19722,f12396]) ).
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_1967 ),
inference(avatar_component_clause,[],[f19721]) ).
fof(f19723,plain,
spl0_1967,
inference(avatar_split_clause,[],[f3342,f19721]) ).
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(f19718,plain,
( spl0_1966
| ~ spl0_1671
| ~ spl0_1965 ),
inference(avatar_split_clause,[],[f19714,f19711,f14552,f19716]) ).
fof(f19716,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(f19711,plain,
( spl0_1965
<=> ! [X1,X47] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_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_1965])]) ).
fof(f19714,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_1671
| ~ spl0_1965 ),
inference(forward_demodulation,[],[f19712,f14554]) ).
fof(f19712,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_1965 ),
inference(avatar_component_clause,[],[f19711]) ).
fof(f19713,plain,
spl0_1965,
inference(avatar_split_clause,[],[f3311,f19711]) ).
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(f19709,plain,
spl0_1964,
inference(avatar_split_clause,[],[f3310,f19707]) ).
fof(f19707,plain,
( spl0_1964
<=> ! [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_1964])]) ).
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(f19697,plain,
spl0_1963,
inference(avatar_split_clause,[],[f3278,f19695]) ).
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(f19693,plain,
spl0_1962,
inference(avatar_split_clause,[],[f3269,f19691]) ).
fof(f19691,plain,
( spl0_1962
<=> ! [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_1962])]) ).
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(f19671,plain,
( spl0_1961
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1960 ),
inference(avatar_split_clause,[],[f19667,f19664,f11328,f10972,f7083,f6138,f19669]) ).
fof(f19669,plain,
( spl0_1961
<=> ! [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_1961])]) ).
fof(f19664,plain,
( spl0_1960
<=> ! [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_1960])]) ).
fof(f19667,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1960 ),
inference(forward_demodulation,[],[f19665,f12329]) ).
fof(f19665,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_1960 ),
inference(avatar_component_clause,[],[f19664]) ).
fof(f19666,plain,
spl0_1960,
inference(avatar_split_clause,[],[f3156,f19664]) ).
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(f19662,plain,
spl0_1959,
inference(avatar_split_clause,[],[f3080,f19660]) ).
fof(f19660,plain,
( spl0_1959
<=> ! [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_1959])]) ).
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(f19658,plain,
spl0_1958,
inference(avatar_split_clause,[],[f3078,f19656]) ).
fof(f19656,plain,
( spl0_1958
<=> ! [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_1958])]) ).
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(f19654,plain,
spl0_1957,
inference(avatar_split_clause,[],[f3074,f19652]) ).
fof(f19652,plain,
( spl0_1957
<=> ! [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_1957])]) ).
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(f19649,plain,
( spl0_1956
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1954 ),
inference(avatar_split_clause,[],[f19640,f19637,f11328,f10972,f7083,f6138,f19647]) ).
fof(f19647,plain,
( spl0_1956
<=> ! [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_1956])]) ).
fof(f19637,plain,
( spl0_1954
<=> ! [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_1954])]) ).
fof(f19640,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1954 ),
inference(forward_demodulation,[],[f19638,f12329]) ).
fof(f19638,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_1954 ),
inference(avatar_component_clause,[],[f19637]) ).
fof(f19645,plain,
( spl0_1955
| ~ spl0_1073
| ~ spl0_1883 ),
inference(avatar_split_clause,[],[f18845,f18529,f8890,f19642]) ).
fof(f19642,plain,
( spl0_1955
<=> 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_1955])]) ).
fof(f18845,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_1073
| ~ spl0_1883 ),
inference(resolution,[],[f18531,f8891]) ).
fof(f19639,plain,
spl0_1954,
inference(avatar_split_clause,[],[f3073,f19637]) ).
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(f19634,plain,
( spl0_1953
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1952 ),
inference(avatar_split_clause,[],[f19630,f19627,f11328,f10972,f7083,f6138,f19632]) ).
fof(f19632,plain,
( spl0_1953
<=> ! [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_1953])]) ).
fof(f19627,plain,
( spl0_1952
<=> ! [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_1952])]) ).
fof(f19630,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1952 ),
inference(forward_demodulation,[],[f19628,f12329]) ).
fof(f19628,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_1952 ),
inference(avatar_component_clause,[],[f19627]) ).
fof(f19629,plain,
spl0_1952,
inference(avatar_split_clause,[],[f3072,f19627]) ).
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(f19624,plain,
( spl0_1951
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1950 ),
inference(avatar_split_clause,[],[f19620,f19617,f11328,f10972,f7083,f6138,f19622]) ).
fof(f19622,plain,
( spl0_1951
<=> ! [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_1951])]) ).
fof(f19617,plain,
( spl0_1950
<=> ! [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_1950])]) ).
fof(f19620,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1950 ),
inference(forward_demodulation,[],[f19618,f12329]) ).
fof(f19618,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_1950 ),
inference(avatar_component_clause,[],[f19617]) ).
fof(f19619,plain,
spl0_1950,
inference(avatar_split_clause,[],[f3071,f19617]) ).
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(f19615,plain,
spl0_1949,
inference(avatar_split_clause,[],[f3059,f19613]) ).
fof(f19613,plain,
( spl0_1949
<=> ! [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_1949])]) ).
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(f19611,plain,
spl0_1948,
inference(avatar_split_clause,[],[f3051,f19609]) ).
fof(f19609,plain,
( spl0_1948
<=> ! [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_1948])]) ).
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(f19575,plain,
( spl0_1947
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1946 ),
inference(avatar_split_clause,[],[f19571,f19568,f11328,f10972,f7083,f6138,f19573]) ).
fof(f19573,plain,
( spl0_1947
<=> ! [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_1947])]) ).
fof(f19568,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_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f19571,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1946 ),
inference(forward_demodulation,[],[f19569,f12329]) ).
fof(f19569,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_1946 ),
inference(avatar_component_clause,[],[f19568]) ).
fof(f19570,plain,
spl0_1946,
inference(avatar_split_clause,[],[f3049,f19568]) ).
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(f19485,plain,
( spl0_1945
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1944 ),
inference(avatar_split_clause,[],[f19481,f19477,f11328,f10972,f7083,f6138,f19483]) ).
fof(f19483,plain,
( spl0_1945
<=> ! [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_1945])]) ).
fof(f19477,plain,
( spl0_1944
<=> ! [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_1944])]) ).
fof(f19481,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1944 ),
inference(forward_demodulation,[],[f19480,f12329]) ).
fof(f19480,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1944 ),
inference(forward_demodulation,[],[f19478,f12329]) ).
fof(f19478,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_1944 ),
inference(avatar_component_clause,[],[f19477]) ).
fof(f19479,plain,
spl0_1944,
inference(avatar_split_clause,[],[f3048,f19477]) ).
fof(f19453,plain,
( spl0_1943
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1942 ),
inference(avatar_split_clause,[],[f19449,f19445,f11328,f10972,f7083,f6138,f19451]) ).
fof(f19451,plain,
( spl0_1943
<=> ! [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_1943])]) ).
fof(f19445,plain,
( spl0_1942
<=> ! [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_1942])]) ).
fof(f19449,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1942 ),
inference(forward_demodulation,[],[f19448,f12329]) ).
fof(f19448,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1942 ),
inference(forward_demodulation,[],[f19446,f12329]) ).
fof(f19446,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_1942 ),
inference(avatar_component_clause,[],[f19445]) ).
fof(f19447,plain,
spl0_1942,
inference(avatar_split_clause,[],[f3047,f19445]) ).
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(f19443,plain,
spl0_1941,
inference(avatar_split_clause,[],[f2947,f19441]) ).
fof(f19441,plain,
( spl0_1941
<=> ! [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_1941])]) ).
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(f19439,plain,
spl0_1940,
inference(avatar_split_clause,[],[f2887,f19437]) ).
fof(f19437,plain,
( spl0_1940
<=> ! [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_1940])]) ).
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(f19435,plain,
( spl0_1939
| ~ spl0_1498
| ~ spl0_1883 ),
inference(avatar_split_clause,[],[f18850,f18529,f12481,f19432]) ).
fof(f19432,plain,
( spl0_1939
<=> 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_1939])]) ).
fof(f12481,plain,
( spl0_1498
<=> ! [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_1498])]) ).
fof(f18850,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_1498
| ~ spl0_1883 ),
inference(resolution,[],[f18531,f12482]) ).
fof(f12482,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_1498 ),
inference(avatar_component_clause,[],[f12481]) ).
fof(f19430,plain,
spl0_1938,
inference(avatar_split_clause,[],[f2884,f19428]) ).
fof(f19428,plain,
( spl0_1938
<=> ! [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_1938])]) ).
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(f19426,plain,
spl0_1937,
inference(avatar_split_clause,[],[f2801,f19424]) ).
fof(f19424,plain,
( spl0_1937
<=> ! [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_1937])]) ).
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(f19422,plain,
spl0_1936,
inference(avatar_split_clause,[],[f2792,f19420]) ).
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(f19418,plain,
spl0_1935,
inference(avatar_split_clause,[],[f2697,f19416]) ).
fof(f19416,plain,
( spl0_1935
<=> ! [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_1935])]) ).
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(f19414,plain,
spl0_1934,
inference(avatar_split_clause,[],[f2696,f19412]) ).
fof(f19412,plain,
( spl0_1934
<=> ! [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_1934])]) ).
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(f19410,plain,
spl0_1933,
inference(avatar_split_clause,[],[f2690,f19408]) ).
fof(f19408,plain,
( spl0_1933
<=> ! [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_1933])]) ).
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(f19406,plain,
spl0_1932,
inference(avatar_split_clause,[],[f2573,f19404]) ).
fof(f19404,plain,
( spl0_1932
<=> ! [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_1932])]) ).
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(f19402,plain,
spl0_1931,
inference(avatar_split_clause,[],[f2565,f19400]) ).
fof(f19400,plain,
( spl0_1931
<=> ! [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_1931])]) ).
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(f19398,plain,
spl0_1930,
inference(avatar_split_clause,[],[f2556,f19396]) ).
fof(f19396,plain,
( spl0_1930
<=> ! [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_1930])]) ).
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(f19394,plain,
spl0_1929,
inference(avatar_split_clause,[],[f2553,f19392]) ).
fof(f19392,plain,
( spl0_1929
<=> ! [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_1929])]) ).
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(f19381,plain,
spl0_1928,
inference(avatar_split_clause,[],[f2526,f19379]) ).
fof(f19379,plain,
( spl0_1928
<=> ! [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_1928])]) ).
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(f19377,plain,
spl0_1927,
inference(avatar_split_clause,[],[f2521,f19375]) ).
fof(f19375,plain,
( spl0_1927
<=> ! [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_1927])]) ).
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(f19373,plain,
spl0_1926,
inference(avatar_split_clause,[],[f2324,f19371]) ).
fof(f19371,plain,
( spl0_1926
<=> ! [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_1926])]) ).
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(f19369,plain,
spl0_1925,
inference(avatar_split_clause,[],[f2307,f19367]) ).
fof(f19367,plain,
( spl0_1925
<=> ! [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_1925])]) ).
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(f19365,plain,
spl0_1924,
inference(avatar_split_clause,[],[f2305,f19363]) ).
fof(f19363,plain,
( spl0_1924
<=> ! [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_1924])]) ).
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(f19361,plain,
spl0_1923,
inference(avatar_split_clause,[],[f2266,f19359]) ).
fof(f19359,plain,
( spl0_1923
<=> ! [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_1923])]) ).
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(f19357,plain,
spl0_1922,
inference(avatar_split_clause,[],[f2261,f19355]) ).
fof(f19355,plain,
( spl0_1922
<=> ! [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_1922])]) ).
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(f19353,plain,
spl0_1921,
inference(avatar_split_clause,[],[f2258,f19351]) ).
fof(f19351,plain,
( spl0_1921
<=> ! [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_1921])]) ).
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(f19349,plain,
spl0_1920,
inference(avatar_split_clause,[],[f2255,f19347]) ).
fof(f19347,plain,
( spl0_1920
<=> ! [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_1920])]) ).
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(f19345,plain,
spl0_1919,
inference(avatar_split_clause,[],[f2237,f19343]) ).
fof(f19343,plain,
( spl0_1919
<=> ! [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_1919])]) ).
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(f19332,plain,
spl0_1918,
inference(avatar_split_clause,[],[f2228,f19330]) ).
fof(f19330,plain,
( spl0_1918
<=> ! [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_1918])]) ).
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(f19328,plain,
spl0_1917,
inference(avatar_split_clause,[],[f2214,f19326]) ).
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(f19324,plain,
spl0_1916,
inference(avatar_split_clause,[],[f1843,f19322]) ).
fof(f19322,plain,
( spl0_1916
<=> ! [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_1916])]) ).
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(f19320,plain,
spl0_1915,
inference(avatar_split_clause,[],[f1836,f19318]) ).
fof(f19318,plain,
( spl0_1915
<=> ! [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_1915])]) ).
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(f19316,plain,
spl0_1914,
inference(avatar_split_clause,[],[f1824,f19314]) ).
fof(f19314,plain,
( spl0_1914
<=> ! [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_1914])]) ).
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(f19312,plain,
spl0_1913,
inference(avatar_split_clause,[],[f1821,f19310]) ).
fof(f19310,plain,
( spl0_1913
<=> ! [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_1913])]) ).
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(f19308,plain,
spl0_1912,
inference(avatar_split_clause,[],[f1809,f19306]) ).
fof(f19306,plain,
( spl0_1912
<=> ! [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_1912])]) ).
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(f19304,plain,
spl0_1911,
inference(avatar_split_clause,[],[f1781,f19302]) ).
fof(f19302,plain,
( spl0_1911
<=> ! [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_1911])]) ).
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(f19300,plain,
spl0_1910,
inference(avatar_split_clause,[],[f1699,f19298]) ).
fof(f19298,plain,
( spl0_1910
<=> ! [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_1910])]) ).
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(f19296,plain,
spl0_1909,
inference(avatar_split_clause,[],[f1633,f19294]) ).
fof(f19294,plain,
( spl0_1909
<=> ! [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_1909])]) ).
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(f19283,plain,
spl0_1908,
inference(avatar_split_clause,[],[f1592,f19281]) ).
fof(f19281,plain,
( spl0_1908
<=> ! [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_1908])]) ).
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(f19279,plain,
spl0_1907,
inference(avatar_split_clause,[],[f1525,f19277]) ).
fof(f19277,plain,
( spl0_1907
<=> ! [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_1907])]) ).
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(f19275,plain,
spl0_1906,
inference(avatar_split_clause,[],[f1524,f19273]) ).
fof(f19273,plain,
( spl0_1906
<=> ! [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_1906])]) ).
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(f19271,plain,
spl0_1905,
inference(avatar_split_clause,[],[f1417,f19269]) ).
fof(f19269,plain,
( spl0_1905
<=> ! [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_1905])]) ).
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(f19267,plain,
spl0_1904,
inference(avatar_split_clause,[],[f1403,f19265]) ).
fof(f19265,plain,
( spl0_1904
<=> ! [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_1904])]) ).
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(f19263,plain,
spl0_1903,
inference(avatar_split_clause,[],[f1402,f19261]) ).
fof(f19261,plain,
( spl0_1903
<=> ! [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_1903])]) ).
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(f19259,plain,
spl0_1902,
inference(avatar_split_clause,[],[f1366,f19257]) ).
fof(f19257,plain,
( spl0_1902
<=> ! [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_1902])]) ).
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(f19255,plain,
spl0_1901,
inference(avatar_split_clause,[],[f1365,f19253]) ).
fof(f19253,plain,
( spl0_1901
<=> ! [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_1901])]) ).
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(f19251,plain,
spl0_1900,
inference(avatar_split_clause,[],[f1362,f19249]) ).
fof(f19249,plain,
( spl0_1900
<=> ! [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_1900])]) ).
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(f19247,plain,
spl0_1899,
inference(avatar_split_clause,[],[f1360,f19245]) ).
fof(f19245,plain,
( spl0_1899
<=> ! [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_1899])]) ).
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(f19243,plain,
( spl0_1898
| spl0_3
| ~ spl0_1837 ),
inference(avatar_split_clause,[],[f18950,f17355,f3445,f19241]) ).
fof(f17355,plain,
( spl0_1837
<=> ! [X102,X86,X12] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f18950,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_Ba,X1),X0,tc_Event_Oevent))
| spl0_3
| ~ spl0_1837 ),
inference(resolution,[],[f17356,f3447]) ).
fof(f17356,plain,
( ! [X86,X12,X102] :
( c_in(X12,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,X102) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(X12,X86),X102,tc_Event_Oevent)) )
| ~ spl0_1837 ),
inference(avatar_component_clause,[],[f17355]) ).
fof(f19239,plain,
spl0_1897,
inference(avatar_split_clause,[],[f1359,f19237]) ).
fof(f19237,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_plus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
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(f19235,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1306,f19233]) ).
fof(f19233,plain,
( spl0_1896
<=> ! [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_1896])]) ).
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(f19231,plain,
spl0_1895,
inference(avatar_split_clause,[],[f1290,f19229]) ).
fof(f19229,plain,
( spl0_1895
<=> ! [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_1895])]) ).
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(f19227,plain,
spl0_1894,
inference(avatar_split_clause,[],[f1289,f19225]) ).
fof(f19225,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(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(f19223,plain,
spl0_1893,
inference(avatar_split_clause,[],[f114,f19221]) ).
fof(f19221,plain,
( spl0_1893
<=> ! [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_1893])]) ).
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(f19219,plain,
spl0_1892,
inference(avatar_split_clause,[],[f113,f19217]) ).
fof(f19217,plain,
( spl0_1892
<=> ! [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_1892])]) ).
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(f19215,plain,
spl0_1891,
inference(avatar_split_clause,[],[f76,f19213]) ).
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(f19211,plain,
spl0_1890,
inference(avatar_split_clause,[],[f72,f19209]) ).
fof(f19209,plain,
( spl0_1890
<=> ! [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_1890])]) ).
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(f19207,plain,
spl0_1889,
inference(avatar_split_clause,[],[f71,f19205]) ).
fof(f19205,plain,
( spl0_1889
<=> ! [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_1889])]) ).
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(f19203,plain,
spl0_1888,
inference(avatar_split_clause,[],[f70,f19201]) ).
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(f19199,plain,
( spl0_1887
| spl0_2
| ~ spl0_1837 ),
inference(avatar_split_clause,[],[f18949,f17355,f3440,f19197]) ).
fof(f18949,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_1837 ),
inference(resolution,[],[f17356,f3442]) ).
fof(f19195,plain,
spl0_1886,
inference(avatar_split_clause,[],[f58,f19193]) ).
fof(f19193,plain,
( spl0_1886
<=> ! [X12,X0,X1,X26] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f58,axiom,
! [X0,X1,X26,X12] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f19191,plain,
spl0_1885,
inference(avatar_split_clause,[],[f46,f19189]) ).
fof(f19189,plain,
( spl0_1885
<=> ! [X24,X23,X12,X1] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f46,axiom,
! [X1,X24,X12,X23] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f19028,plain,
( spl0_1884
| spl0_1
| ~ spl0_1837 ),
inference(avatar_split_clause,[],[f18948,f17355,f3435,f19026]) ).
fof(f18948,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_1837 ),
inference(resolution,[],[f17356,f3437]) ).
fof(f18532,plain,
( spl0_1883
| ~ spl0_1062
| ~ spl0_1334
| ~ spl0_1764
| ~ spl0_1855
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f18400,f18226,f17696,f16040,f10789,f8846,f18529]) ).
fof(f10789,plain,
( spl0_1334
<=> ! [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_1334])]) ).
fof(f16040,plain,
( spl0_1764
<=> ! [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_1764])]) ).
fof(f18226,plain,
( spl0_1882
<=> 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_1882])]) ).
fof(f18400,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_1062
| ~ spl0_1334
| ~ spl0_1764
| ~ spl0_1855
| ~ spl0_1882 ),
inference(forward_demodulation,[],[f18399,f17731]) ).
fof(f17731,plain,
( ! [X1] : c_plus(X1,c_1,tc_nat) = c_plus(c_1,X1,tc_nat)
| ~ spl0_1062
| ~ spl0_1764
| ~ spl0_1855 ),
inference(forward_demodulation,[],[f17730,f8847]) ).
fof(f17730,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_1062
| ~ spl0_1764
| ~ spl0_1855 ),
inference(forward_demodulation,[],[f17719,f8847]) ).
fof(f17719,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_1764
| ~ spl0_1855 ),
inference(superposition,[],[f16041,f17697]) ).
fof(f16041,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_1764 ),
inference(avatar_component_clause,[],[f16040]) ).
fof(f18399,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_1334
| ~ spl0_1764
| ~ spl0_1882 ),
inference(forward_demodulation,[],[f18395,f16041]) ).
fof(f18395,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_1334
| ~ spl0_1882 ),
inference(superposition,[],[f10790,f18228]) ).
fof(f18228,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_1882 ),
inference(avatar_component_clause,[],[f18226]) ).
fof(f10790,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_1334 ),
inference(avatar_component_clause,[],[f10789]) ).
fof(f18229,plain,
( spl0_1882
| ~ spl0_752
| ~ spl0_1798 ),
inference(avatar_split_clause,[],[f18217,f17183,f7371,f18226]) ).
fof(f18217,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_752
| ~ spl0_1798 ),
inference(resolution,[],[f17184,f7373]) ).
fof(f18072,plain,
( spl0_1881
| ~ spl0_898
| ~ spl0_1063 ),
inference(avatar_split_clause,[],[f9230,f8850,f7972,f18070]) ).
fof(f18070,plain,
( spl0_1881
<=> ! [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_1881])]) ).
fof(f9230,plain,
( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_898
| ~ spl0_1063 ),
inference(superposition,[],[f7973,f8851]) ).
fof(f17906,plain,
( spl0_1880
| ~ spl0_1000
| ~ spl0_1001 ),
inference(avatar_split_clause,[],[f8677,f8463,f8458,f17903]) ).
fof(f17903,plain,
( spl0_1880
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f8677,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_1000
| ~ spl0_1001 ),
inference(superposition,[],[f8464,f8460]) ).
fof(f17901,plain,
( spl0_1877
| spl0_1879 ),
inference(avatar_split_clause,[],[f3433,f17899,f17878]) ).
fof(f17878,plain,
( spl0_1877
<=> ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f17899,plain,
( spl0_1879
<=> ! [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_1879])]) ).
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(f17887,plain,
( ~ spl0_718
| ~ spl0_1877 ),
inference(avatar_contradiction_clause,[],[f17886]) ).
fof(f17886,plain,
( $false
| ~ spl0_718
| ~ spl0_1877 ),
inference(trivial_inequality_removal,[],[f17884]) ).
fof(f17884,plain,
( c_0 != c_0
| ~ spl0_718
| ~ spl0_1877 ),
inference(superposition,[],[f17879,f7213]) ).
fof(f7213,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_718 ),
inference(avatar_component_clause,[],[f7211]) ).
fof(f7211,plain,
( spl0_718
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f17879,plain,
( ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ spl0_1877 ),
inference(avatar_component_clause,[],[f17878]) ).
fof(f17883,plain,
( spl0_1877
| spl0_1878 ),
inference(avatar_split_clause,[],[f3432,f17881,f17878]) ).
fof(f17881,plain,
( spl0_1878
<=> ! [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_1878])]) ).
fof(f3432,plain,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_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(f17850,plain,
( spl0_1876
| ~ spl0_649
| ~ spl0_690
| ~ spl0_790
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1759
| ~ spl0_1875 ),
inference(avatar_split_clause,[],[f17846,f17842,f15989,f11328,f10972,f7526,f7083,f6138,f17848]) ).
fof(f17848,plain,
( spl0_1876
<=> ! [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_1876])]) ).
fof(f17842,plain,
( spl0_1875
<=> ! [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_1875])]) ).
fof(f17846,plain,
( ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_649
| ~ spl0_690
| ~ spl0_790
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1759
| ~ spl0_1875 ),
inference(forward_demodulation,[],[f17845,f15992]) ).
fof(f15992,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_790
| ~ spl0_1759 ),
inference(superposition,[],[f15990,f7527]) ).
fof(f17845,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1875 ),
inference(forward_demodulation,[],[f17843,f12329]) ).
fof(f17843,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_1875 ),
inference(avatar_component_clause,[],[f17842]) ).
fof(f17844,plain,
spl0_1875,
inference(avatar_split_clause,[],[f3326,f17842]) ).
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(f17840,plain,
spl0_1874,
inference(avatar_split_clause,[],[f3159,f17838]) ).
fof(f17838,plain,
( spl0_1874
<=> ! [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_1874])]) ).
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(f17836,plain,
spl0_1873,
inference(avatar_split_clause,[],[f3158,f17834]) ).
fof(f17834,plain,
( spl0_1873
<=> ! [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_1873])]) ).
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(f17832,plain,
spl0_1872,
inference(avatar_split_clause,[],[f3154,f17830]) ).
fof(f17830,plain,
( spl0_1872
<=> ! [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_1872])]) ).
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(f17828,plain,
spl0_1871,
inference(avatar_split_clause,[],[f3153,f17826]) ).
fof(f17826,plain,
( spl0_1871
<=> ! [X20,X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(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(f17822,plain,
spl0_1870,
inference(avatar_split_clause,[],[f3146,f17820]) ).
fof(f17820,plain,
( spl0_1870
<=> ! [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_1870])]) ).
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(f17816,plain,
spl0_1869,
inference(avatar_split_clause,[],[f3142,f17814]) ).
fof(f17814,plain,
( spl0_1869
<=> ! [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_1869])]) ).
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(f17812,plain,
spl0_1868,
inference(avatar_split_clause,[],[f3139,f17810]) ).
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(f17808,plain,
spl0_1867,
inference(avatar_split_clause,[],[f3137,f17806]) ).
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(f17802,plain,
spl0_1866,
inference(avatar_split_clause,[],[f3132,f17800]) ).
fof(f17800,plain,
( spl0_1866
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(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(f17796,plain,
spl0_1865,
inference(avatar_split_clause,[],[f3127,f17794]) ).
fof(f17794,plain,
( spl0_1865
<=> ! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(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(f17792,plain,
spl0_1864,
inference(avatar_split_clause,[],[f3115,f17790]) ).
fof(f17790,plain,
( spl0_1864
<=> ! [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_1864])]) ).
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(f17784,plain,
( spl0_1862
| ~ spl0_1863
| ~ spl0_873
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f8641,f8372,f7872,f17781,f17778]) ).
fof(f17778,plain,
( spl0_1862
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f17781,plain,
( spl0_1863
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f8641,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_873
| ~ spl0_979 ),
inference(resolution,[],[f8373,f7873]) ).
fof(f17776,plain,
( spl0_1861
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1860 ),
inference(avatar_split_clause,[],[f17772,f17769,f11328,f10972,f7083,f6138,f17774]) ).
fof(f17774,plain,
( spl0_1861
<=> ! [X41,X15] :
( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f17769,plain,
( spl0_1860
<=> ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f17772,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1860 ),
inference(forward_demodulation,[],[f17770,f12329]) ).
fof(f17770,plain,
( ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) )
| ~ spl0_1860 ),
inference(avatar_component_clause,[],[f17769]) ).
fof(f17771,plain,
spl0_1860,
inference(avatar_split_clause,[],[f3111,f17769]) ).
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(f17763,plain,
( spl0_1859
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1858 ),
inference(avatar_split_clause,[],[f17759,f17756,f11328,f10972,f7083,f6138,f17761]) ).
fof(f17761,plain,
( spl0_1859
<=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(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_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f17759,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1858 ),
inference(forward_demodulation,[],[f17757,f12329]) ).
fof(f17757,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_1858 ),
inference(avatar_component_clause,[],[f17756]) ).
fof(f17758,plain,
spl0_1858,
inference(avatar_split_clause,[],[f3068,f17756]) ).
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(f17740,plain,
( spl0_1857
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1856 ),
inference(avatar_split_clause,[],[f17736,f17733,f11328,f10972,f7083,f6138,f17738]) ).
fof(f17738,plain,
( spl0_1857
<=> ! [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_1857])]) ).
fof(f17733,plain,
( spl0_1856
<=> ! [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_1856])]) ).
fof(f17736,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1856 ),
inference(forward_demodulation,[],[f17734,f12329]) ).
fof(f17734,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_1856 ),
inference(avatar_component_clause,[],[f17733]) ).
fof(f17735,plain,
spl0_1856,
inference(avatar_split_clause,[],[f3067,f17733]) ).
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(f17698,plain,
( spl0_1855
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1853 ),
inference(avatar_split_clause,[],[f17690,f17687,f11328,f10972,f7083,f6138,f17696]) ).
fof(f17687,plain,
( spl0_1853
<=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f17690,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1853 ),
inference(forward_demodulation,[],[f17688,f12329]) ).
fof(f17688,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41)
| ~ spl0_1853 ),
inference(avatar_component_clause,[],[f17687]) ).
fof(f17694,plain,
( spl0_1854
| ~ spl0_649
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8581,f8239,f6138,f17692]) ).
fof(f17692,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(f8239,plain,
( spl0_946
<=> ! [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_946])]) ).
fof(f8581,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_946 ),
inference(superposition,[],[f8240,f6140]) ).
fof(f8240,plain,
( ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f8239]) ).
fof(f17689,plain,
spl0_1853,
inference(avatar_split_clause,[],[f3065,f17687]) ).
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(f17590,plain,
( spl0_1852
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1851 ),
inference(avatar_split_clause,[],[f17586,f17583,f11328,f10972,f7083,f6138,f17588]) ).
fof(f17588,plain,
( spl0_1852
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f17583,plain,
( spl0_1851
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f17586,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f17584,f12329]) ).
fof(f17584,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
| ~ spl0_1851 ),
inference(avatar_component_clause,[],[f17583]) ).
fof(f17585,plain,
spl0_1851,
inference(avatar_split_clause,[],[f3064,f17583]) ).
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(f17490,plain,
( spl0_1850
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1849 ),
inference(avatar_split_clause,[],[f17486,f17483,f11328,f10972,f7083,f6138,f17488]) ).
fof(f17488,plain,
( spl0_1850
<=> ! [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_1850])]) ).
fof(f17483,plain,
( spl0_1849
<=> ! [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_1849])]) ).
fof(f17486,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1849 ),
inference(forward_demodulation,[],[f17484,f12329]) ).
fof(f17484,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_1849 ),
inference(avatar_component_clause,[],[f17483]) ).
fof(f17485,plain,
spl0_1849,
inference(avatar_split_clause,[],[f3063,f17483]) ).
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(f17427,plain,
( spl0_1848
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1847 ),
inference(avatar_split_clause,[],[f17423,f17420,f11328,f10972,f7083,f6138,f17425]) ).
fof(f17425,plain,
( spl0_1848
<=> ! [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_1848])]) ).
fof(f17420,plain,
( spl0_1847
<=> ! [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_1847])]) ).
fof(f17423,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1847 ),
inference(forward_demodulation,[],[f17421,f12329]) ).
fof(f17421,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_1847 ),
inference(avatar_component_clause,[],[f17420]) ).
fof(f17422,plain,
spl0_1847,
inference(avatar_split_clause,[],[f3062,f17420]) ).
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(f17418,plain,
( spl0_1846
| ~ spl0_650
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8580,f8239,f6143,f17416]) ).
fof(f17416,plain,
( spl0_1846
<=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f8580,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_946 ),
inference(superposition,[],[f8240,f6145]) ).
fof(f17390,plain,
( spl0_1845
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1844 ),
inference(avatar_split_clause,[],[f17386,f17383,f11328,f10972,f7083,f6138,f17388]) ).
fof(f17388,plain,
( spl0_1845
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(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_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f17386,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1844 ),
inference(forward_demodulation,[],[f17384,f12329]) ).
fof(f17384,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_1844 ),
inference(avatar_component_clause,[],[f17383]) ).
fof(f17385,plain,
spl0_1844,
inference(avatar_split_clause,[],[f3061,f17383]) ).
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(f17381,plain,
spl0_1843,
inference(avatar_split_clause,[],[f3060,f17379]) ).
fof(f17379,plain,
( spl0_1843
<=> ! [X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(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(f17377,plain,
spl0_1842,
inference(avatar_split_clause,[],[f2933,f17375]) ).
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(f17373,plain,
spl0_1841,
inference(avatar_split_clause,[],[f2866,f17371]) ).
fof(f17371,plain,
( spl0_1841
<=> ! [X20,X88] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f2866,axiom,
! [X88,X20] : c_Message_Oanalz(c_union(c_Message_Osynth(X20),X88,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(X20,X88,tc_Message_Omsg)),c_Message_Osynth(X20),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
fof(f17369,plain,
spl0_1840,
inference(avatar_split_clause,[],[f2828,f17367]) ).
fof(f17367,plain,
( spl0_1840
<=> ! [X86,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f2828,axiom,
! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
fof(f17365,plain,
spl0_1839,
inference(avatar_split_clause,[],[f2807,f17363]) ).
fof(f17363,plain,
( spl0_1839
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_Message_Osynth(c_Message_Oanalz(X88)) = c_Message_Osynth(c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f2807,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Osynth(c_Message_Oanalz(X88)),tc_Message_Omsg)
| c_Message_Osynth(c_Message_Oanalz(X88)) = c_Message_Osynth(c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).
fof(f17361,plain,
spl0_1838,
inference(avatar_split_clause,[],[f2799,f17359]) ).
fof(f17359,plain,
( spl0_1838
<=> ! [X102,X13,X12,X86] : c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f2799,axiom,
! [X86,X102,X12,X13] : c_insert(X86,c_Event_Oknows(c_Message_Oagent_OSpy,X102),tc_Message_Omsg) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(X12,X13,X86),X102,tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Says_0) ).
fof(f17357,plain,
spl0_1837,
inference(avatar_split_clause,[],[f2798,f17355]) ).
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(f17353,plain,
( spl0_1836
| ~ spl0_649
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8579,f8239,f6138,f17351]) ).
fof(f17351,plain,
( spl0_1836
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f8579,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_946 ),
inference(superposition,[],[f8240,f6140]) ).
fof(f17349,plain,
spl0_1835,
inference(avatar_split_clause,[],[f2675,f17347]) ).
fof(f17347,plain,
( spl0_1835
<=> ! [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_1835])]) ).
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(f17345,plain,
spl0_1834,
inference(avatar_split_clause,[],[f2650,f17343]) ).
fof(f17343,plain,
( spl0_1834
<=> ! [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_1834])]) ).
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(f17341,plain,
spl0_1833,
inference(avatar_split_clause,[],[f2596,f17339]) ).
fof(f17339,plain,
( spl0_1833
<=> ! [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_1833])]) ).
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(f17337,plain,
spl0_1832,
inference(avatar_split_clause,[],[f2585,f17335]) ).
fof(f17335,plain,
( spl0_1832
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(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(f17333,plain,
spl0_1831,
inference(avatar_split_clause,[],[f2584,f17331]) ).
fof(f17331,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(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(f17329,plain,
spl0_1830,
inference(avatar_split_clause,[],[f2574,f17327]) ).
fof(f17327,plain,
( spl0_1830
<=> ! [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_1830])]) ).
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(f17325,plain,
spl0_1829,
inference(avatar_split_clause,[],[f2360,f17323]) ).
fof(f17323,plain,
( spl0_1829
<=> ! [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_1829])]) ).
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(f17321,plain,
spl0_1828,
inference(avatar_split_clause,[],[f2359,f17319]) ).
fof(f17319,plain,
( spl0_1828
<=> ! [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_1828])]) ).
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(f17317,plain,
spl0_1827,
inference(avatar_split_clause,[],[f2194,f17315]) ).
fof(f17315,plain,
( spl0_1827
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(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(f17313,plain,
spl0_1826,
inference(avatar_split_clause,[],[f2193,f17311]) ).
fof(f17311,plain,
( spl0_1826
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
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(f17309,plain,
( spl0_1825
| ~ spl0_649
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8570,f8227,f6138,f17307]) ).
fof(f17307,plain,
( spl0_1825
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f8227,plain,
( spl0_943
<=> ! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f8570,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_649
| ~ spl0_943 ),
inference(superposition,[],[f8228,f6140]) ).
fof(f8228,plain,
( ! [X21,X15] :
( c_IntDef_Oint(X21) != c_IntDef_Oint(X15)
| X15 = X21 )
| ~ spl0_943 ),
inference(avatar_component_clause,[],[f8227]) ).
fof(f17305,plain,
spl0_1824,
inference(avatar_split_clause,[],[f2192,f17303]) ).
fof(f17303,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(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
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(f17301,plain,
spl0_1823,
inference(avatar_split_clause,[],[f2191,f17299]) ).
fof(f17299,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(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(f17297,plain,
spl0_1822,
inference(avatar_split_clause,[],[f2189,f17295]) ).
fof(f17295,plain,
( spl0_1822
<=> ! [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_1822])]) ).
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(f17293,plain,
spl0_1821,
inference(avatar_split_clause,[],[f2188,f17291]) ).
fof(f17291,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(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(f17289,plain,
spl0_1820,
inference(avatar_split_clause,[],[f2187,f17287]) ).
fof(f17287,plain,
( spl0_1820
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(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(f17285,plain,
spl0_1819,
inference(avatar_split_clause,[],[f2186,f17283]) ).
fof(f17283,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(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(f17281,plain,
spl0_1818,
inference(avatar_split_clause,[],[f2146,f17279]) ).
fof(f17279,plain,
( spl0_1818
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(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(f17277,plain,
spl0_1817,
inference(avatar_split_clause,[],[f2145,f17275]) ).
fof(f17275,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(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(f17273,plain,
spl0_1816,
inference(avatar_split_clause,[],[f2138,f17271]) ).
fof(f17271,plain,
( spl0_1816
<=> ! [X11,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(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(f17269,plain,
spl0_1815,
inference(avatar_split_clause,[],[f2137,f17267]) ).
fof(f17267,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(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(f17250,plain,
spl0_1814,
inference(avatar_split_clause,[],[f2119,f17248]) ).
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(f17246,plain,
spl0_1813,
inference(avatar_split_clause,[],[f2116,f17244]) ).
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(f17242,plain,
spl0_1812,
inference(avatar_split_clause,[],[f1971,f17240]) ).
fof(f17240,plain,
( spl0_1812
<=> ! [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_1812])]) ).
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(f17238,plain,
spl0_1811,
inference(avatar_split_clause,[],[f1970,f17236]) ).
fof(f17236,plain,
( spl0_1811
<=> ! [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_1811])]) ).
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(f17234,plain,
spl0_1810,
inference(avatar_split_clause,[],[f1967,f17232]) ).
fof(f17232,plain,
( spl0_1810
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f1967,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f17230,plain,
spl0_1809,
inference(avatar_split_clause,[],[f1966,f17228]) ).
fof(f17228,plain,
( spl0_1809
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f1966,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f17226,plain,
spl0_1808,
inference(avatar_split_clause,[],[f1960,f17224]) ).
fof(f17224,plain,
( spl0_1808
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f1960,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f17222,plain,
spl0_1807,
inference(avatar_split_clause,[],[f1959,f17220]) ).
fof(f17220,plain,
( spl0_1807
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f1959,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f17218,plain,
spl0_1806,
inference(avatar_split_clause,[],[f1944,f17216]) ).
fof(f17216,plain,
( spl0_1806
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f1944,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f17214,plain,
spl0_1805,
inference(avatar_split_clause,[],[f1943,f17212]) ).
fof(f17212,plain,
( spl0_1805
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f1943,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f17210,plain,
( spl0_1804
| ~ spl0_815
| ~ spl0_1750 ),
inference(avatar_split_clause,[],[f16784,f15931,f7627,f17208]) ).
fof(f17208,plain,
( spl0_1804
<=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f15931,plain,
( spl0_1750
<=> ! [X18,X13,X12,X1] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f16784,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_815
| ~ spl0_1750 ),
inference(forward_demodulation,[],[f16754,f7628]) ).
fof(f16754,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_815
| ~ spl0_1750 ),
inference(superposition,[],[f15932,f7628]) ).
fof(f15932,plain,
( ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1)
| ~ spl0_1750 ),
inference(avatar_component_clause,[],[f15931]) ).
fof(f17206,plain,
spl0_1803,
inference(avatar_split_clause,[],[f1869,f17204]) ).
fof(f17204,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(f17202,plain,
spl0_1802,
inference(avatar_split_clause,[],[f1780,f17200]) ).
fof(f17200,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(f17198,plain,
spl0_1801,
inference(avatar_split_clause,[],[f1764,f17196]) ).
fof(f17196,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(f17193,plain,
spl0_1800,
inference(avatar_split_clause,[],[f1727,f17191]) ).
fof(f17191,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(f17189,plain,
spl0_1799,
inference(avatar_split_clause,[],[f1724,f17187]) ).
fof(f17187,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(f17185,plain,
spl0_1798,
inference(avatar_split_clause,[],[f1713,f17183]) ).
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(f17181,plain,
spl0_1797,
inference(avatar_split_clause,[],[f1701,f17179]) ).
fof(f17179,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(f17177,plain,
spl0_1796,
inference(avatar_split_clause,[],[f1700,f17175]) ).
fof(f17175,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(f17173,plain,
spl0_1795,
inference(avatar_split_clause,[],[f1618,f17171]) ).
fof(f17171,plain,
( spl0_1795
<=> ! [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_1795])]) ).
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(f17169,plain,
spl0_1794,
inference(avatar_split_clause,[],[f1605,f17167]) ).
fof(f17167,plain,
( spl0_1794
<=> ! [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_1794])]) ).
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(f17112,plain,
spl0_1793,
inference(avatar_split_clause,[],[f1546,f17110]) ).
fof(f17110,plain,
( spl0_1793
<=> ! [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_1793])]) ).
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(f17108,plain,
spl0_1792,
inference(avatar_split_clause,[],[f1545,f17106]) ).
fof(f17106,plain,
( spl0_1792
<=> ! [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_1792])]) ).
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(f17104,plain,
spl0_1791,
inference(avatar_split_clause,[],[f1538,f17102]) ).
fof(f17102,plain,
( spl0_1791
<=> ! [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_1791])]) ).
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(f17100,plain,
spl0_1790,
inference(avatar_split_clause,[],[f1519,f17098]) ).
fof(f17098,plain,
( spl0_1790
<=> ! [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_1790])]) ).
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(f17096,plain,
spl0_1789,
inference(avatar_split_clause,[],[f1515,f17094]) ).
fof(f17094,plain,
( spl0_1789
<=> ! [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_1789])]) ).
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(f17092,plain,
spl0_1788,
inference(avatar_split_clause,[],[f1506,f17090]) ).
fof(f17090,plain,
( spl0_1788
<=> ! [X5,X1,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f1506,axiom,
! [X1,X5,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f17088,plain,
spl0_1787,
inference(avatar_split_clause,[],[f1311,f17086]) ).
fof(f17086,plain,
( spl0_1787
<=> ! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f1311,axiom,
! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f17084,plain,
spl0_1786,
inference(avatar_split_clause,[],[f1303,f17082]) ).
fof(f17082,plain,
( spl0_1786
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f1303,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f17080,plain,
spl0_1785,
inference(avatar_split_clause,[],[f1302,f17078]) ).
fof(f17078,plain,
( spl0_1785
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f1302,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f17076,plain,
spl0_1784,
inference(avatar_split_clause,[],[f1301,f17074]) ).
fof(f17074,plain,
( spl0_1784
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f1301,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f17072,plain,
spl0_1783,
inference(avatar_split_clause,[],[f1272,f17070]) ).
fof(f17070,plain,
( spl0_1783
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f1272,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f17068,plain,
spl0_1782,
inference(avatar_split_clause,[],[f1257,f17066]) ).
fof(f17066,plain,
( spl0_1782
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f1257,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f17064,plain,
spl0_1781,
inference(avatar_split_clause,[],[f81,f17062]) ).
fof(f17062,plain,
( spl0_1781
<=> ! [X12,X1,X18] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f81,axiom,
! [X18,X1,X12] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f17060,plain,
spl0_1780,
inference(avatar_split_clause,[],[f47,f17058]) ).
fof(f17058,plain,
( spl0_1780
<=> ! [X12,X1,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f47,axiom,
! [X1,X12,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f16993,plain,
( spl0_1779
| ~ spl0_753
| ~ spl0_1754 ),
inference(avatar_split_clause,[],[f16852,f15947,f7376,f16990]) ).
fof(f16990,plain,
( spl0_1779
<=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f15947,plain,
( spl0_1754
<=> ! [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_1754])]) ).
fof(f16852,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_753
| ~ spl0_1754 ),
inference(resolution,[],[f15948,f7378]) ).
fof(f15948,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_1754 ),
inference(avatar_component_clause,[],[f15947]) ).
fof(f16748,plain,
( spl0_1778
| ~ spl0_675
| ~ spl0_1743 ),
inference(avatar_split_clause,[],[f16662,f15903,f7019,f16746]) ).
fof(f16746,plain,
( spl0_1778
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f15903,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(f16662,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_675
| ~ spl0_1743 ),
inference(resolution,[],[f15904,f7020]) ).
fof(f15904,plain,
( ! [X3,X0,X1] :
( ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
| c_lessequals(X3,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_1743 ),
inference(avatar_component_clause,[],[f15903]) ).
fof(f16571,plain,
( spl0_1777
| ~ spl0_761
| ~ spl0_1717 ),
inference(avatar_split_clause,[],[f16415,f15790,f7409,f16569]) ).
fof(f16569,plain,
( spl0_1777
<=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f15790,plain,
( spl0_1717
<=> ! [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_1717])]) ).
fof(f16415,plain,
( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
| ~ spl0_761
| ~ spl0_1717 ),
inference(trivial_inequality_removal,[],[f16405]) ).
fof(f16405,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_0,X0,X1) = X0 )
| ~ spl0_761
| ~ spl0_1717 ),
inference(superposition,[],[f15791,f7410]) ).
fof(f15791,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_1717 ),
inference(avatar_component_clause,[],[f15790]) ).
fof(f16243,plain,
( ~ spl0_1775
| spl0_1776
| ~ spl0_117
| ~ spl0_1707 ),
inference(avatar_split_clause,[],[f16199,f15749,f4010,f16241,f16237]) ).
fof(f16237,plain,
( spl0_1775
<=> c_List_Odistinct(v_evs3,tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f16241,plain,
( spl0_1776
<=> ! [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_1776])]) ).
fof(f15749,plain,
( spl0_1707
<=> ! [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_1707])]) ).
fof(f16199,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_117
| ~ spl0_1707 ),
inference(resolution,[],[f15750,f4011]) ).
fof(f15750,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_1707 ),
inference(avatar_component_clause,[],[f15749]) ).
fof(f16085,plain,
( spl0_1774
| ~ spl0_650
| ~ spl0_924 ),
inference(avatar_split_clause,[],[f8567,f8149,f6143,f16083]) ).
fof(f16083,plain,
( spl0_1774
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f8149,plain,
( spl0_924
<=> ! [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_924])]) ).
fof(f8567,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_924 ),
inference(superposition,[],[f8150,f6145]) ).
fof(f8150,plain,
( ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_924 ),
inference(avatar_component_clause,[],[f8149]) ).
fof(f16078,plain,
spl0_1773,
inference(avatar_split_clause,[],[f3431,f16076]) ).
fof(f16076,plain,
( spl0_1773
<=> ! [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_1773])]) ).
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(f16074,plain,
spl0_1772,
inference(avatar_split_clause,[],[f3424,f16072]) ).
fof(f16072,plain,
( spl0_1772
<=> ! [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_1772])]) ).
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(f16070,plain,
spl0_1771,
inference(avatar_split_clause,[],[f3421,f16068]) ).
fof(f16068,plain,
( spl0_1771
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(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(f16066,plain,
spl0_1770,
inference(avatar_split_clause,[],[f3414,f16064]) ).
fof(f16064,plain,
( spl0_1770
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(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(f16062,plain,
spl0_1769,
inference(avatar_split_clause,[],[f3395,f16060]) ).
fof(f16060,plain,
( spl0_1769
<=> ! [X21,X15] :
( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(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(f16058,plain,
spl0_1768,
inference(avatar_split_clause,[],[f3309,f16056]) ).
fof(f16056,plain,
( spl0_1768
<=> ! [X1,X47] :
( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(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(f16054,plain,
spl0_1767,
inference(avatar_split_clause,[],[f3308,f16052]) ).
fof(f16052,plain,
( spl0_1767
<=> ! [X11,X1] :
( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(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(f16050,plain,
spl0_1766,
inference(avatar_split_clause,[],[f3279,f16048]) ).
fof(f16048,plain,
( spl0_1766
<=> ! [X5,X1] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(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(f16046,plain,
( spl0_1765
| ~ spl0_649
| ~ spl0_924 ),
inference(avatar_split_clause,[],[f8566,f8149,f6138,f16044]) ).
fof(f16044,plain,
( spl0_1765
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f8566,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_924 ),
inference(superposition,[],[f8150,f6140]) ).
fof(f16042,plain,
spl0_1764,
inference(avatar_split_clause,[],[f3275,f16040]) ).
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(f16038,plain,
spl0_1763,
inference(avatar_split_clause,[],[f3271,f16036]) ).
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(f16034,plain,
spl0_1762,
inference(avatar_split_clause,[],[f3170,f16032]) ).
fof(f16032,plain,
( spl0_1762
<=> ! [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_1762])]) ).
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(f16014,plain,
( spl0_1761
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1760 ),
inference(avatar_split_clause,[],[f16010,f16007,f11328,f10972,f7083,f6138,f16012]) ).
fof(f16012,plain,
( spl0_1761
<=> ! [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_1761])]) ).
fof(f16007,plain,
( spl0_1760
<=> ! [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_1760])]) ).
fof(f16010,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1760 ),
inference(forward_demodulation,[],[f16008,f12329]) ).
fof(f16008,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_1760 ),
inference(avatar_component_clause,[],[f16007]) ).
fof(f16009,plain,
spl0_1760,
inference(avatar_split_clause,[],[f3055,f16007]) ).
fof(f15991,plain,
( spl0_1759
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1758 ),
inference(avatar_split_clause,[],[f15987,f15984,f11328,f10972,f7083,f6138,f15989]) ).
fof(f15984,plain,
( spl0_1758
<=> ! [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_1758])]) ).
fof(f15987,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1758 ),
inference(forward_demodulation,[],[f15985,f12329]) ).
fof(f15985,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_1758 ),
inference(avatar_component_clause,[],[f15984]) ).
fof(f15986,plain,
spl0_1758,
inference(avatar_split_clause,[],[f3054,f15984]) ).
fof(f15962,plain,
( spl0_1757
| ~ spl0_649
| ~ spl0_924 ),
inference(avatar_split_clause,[],[f8564,f8149,f6138,f15960]) ).
fof(f15960,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(f8564,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_924 ),
inference(superposition,[],[f8150,f6140]) ).
fof(f15958,plain,
( spl0_1756
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1755 ),
inference(avatar_split_clause,[],[f15954,f15951,f11328,f10972,f7083,f6138,f15956]) ).
fof(f15956,plain,
( spl0_1756
<=> ! [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_1756])]) ).
fof(f15951,plain,
( spl0_1755
<=> ! [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_1755])]) ).
fof(f15954,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1755 ),
inference(forward_demodulation,[],[f15952,f12329]) ).
fof(f15952,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_1755 ),
inference(avatar_component_clause,[],[f15951]) ).
fof(f15953,plain,
spl0_1755,
inference(avatar_split_clause,[],[f3053,f15951]) ).
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(f15949,plain,
spl0_1754,
inference(avatar_split_clause,[],[f2953,f15947]) ).
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(f15945,plain,
spl0_1753,
inference(avatar_split_clause,[],[f2722,f15943]) ).
fof(f15943,plain,
( spl0_1753
<=> ! [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_1753])]) ).
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(f15941,plain,
spl0_1752,
inference(avatar_split_clause,[],[f2719,f15939]) ).
fof(f15939,plain,
( spl0_1752
<=> ! [X5,X1,X0,X3] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f2719,axiom,
! [X3,X0,X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f15937,plain,
spl0_1751,
inference(avatar_split_clause,[],[f2657,f15935]) ).
fof(f15935,plain,
( spl0_1751
<=> ! [X24,X12,X32,X1] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f2657,axiom,
! [X1,X24,X12,X32] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f15933,plain,
spl0_1750,
inference(avatar_split_clause,[],[f2644,f15931]) ).
fof(f15929,plain,
spl0_1749,
inference(avatar_split_clause,[],[f2640,f15927]) ).
fof(f15927,plain,
( spl0_1749
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f2640,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f15925,plain,
spl0_1748,
inference(avatar_split_clause,[],[f2620,f15923]) ).
fof(f15923,plain,
( spl0_1748
<=> ! [X24,X12,X32,X1] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f2620,axiom,
! [X1,X24,X12,X32] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f15921,plain,
spl0_1747,
inference(avatar_split_clause,[],[f2593,f15919]) ).
fof(f15919,plain,
( spl0_1747
<=> ! [X13,X12,X1] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f2593,axiom,
! [X1,X12,X13] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f15917,plain,
spl0_1746,
inference(avatar_split_clause,[],[f2572,f15915]) ).
fof(f15915,plain,
( spl0_1746
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f2572,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f15913,plain,
spl0_1745,
inference(avatar_split_clause,[],[f2571,f15911]) ).
fof(f15911,plain,
( spl0_1745
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f2571,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f15909,plain,
spl0_1744,
inference(avatar_split_clause,[],[f2561,f15907]) ).
fof(f15907,plain,
( spl0_1744
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f2561,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f15905,plain,
spl0_1743,
inference(avatar_split_clause,[],[f2560,f15903]) ).
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(f15901,plain,
spl0_1742,
inference(avatar_split_clause,[],[f2548,f15899]) ).
fof(f15899,plain,
( spl0_1742
<=> ! [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_1742])]) ).
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(f15897,plain,
spl0_1741,
inference(avatar_split_clause,[],[f2541,f15895]) ).
fof(f15895,plain,
( spl0_1741
<=> ! [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_1741])]) ).
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(f15893,plain,
spl0_1740,
inference(avatar_split_clause,[],[f2539,f15891]) ).
fof(f15891,plain,
( spl0_1740
<=> ! [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_1740])]) ).
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(f15889,plain,
spl0_1739,
inference(avatar_split_clause,[],[f2538,f15887]) ).
fof(f15887,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(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(f15885,plain,
spl0_1738,
inference(avatar_split_clause,[],[f2533,f15883]) ).
fof(f15883,plain,
( spl0_1738
<=> ! [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_1738])]) ).
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(f15881,plain,
spl0_1737,
inference(avatar_split_clause,[],[f2532,f15879]) ).
fof(f15879,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(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(f15868,plain,
spl0_1736,
inference(avatar_split_clause,[],[f2490,f15866]) ).
fof(f15866,plain,
( spl0_1736
<=> ! [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_1736])]) ).
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(f15864,plain,
spl0_1735,
inference(avatar_split_clause,[],[f2489,f15862]) ).
fof(f15862,plain,
( spl0_1735
<=> ! [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_1735])]) ).
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(f15860,plain,
spl0_1734,
inference(avatar_split_clause,[],[f2467,f15858]) ).
fof(f15858,plain,
( spl0_1734
<=> ! [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_1734])]) ).
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(f15856,plain,
spl0_1733,
inference(avatar_split_clause,[],[f2312,f15854]) ).
fof(f15854,plain,
( spl0_1733
<=> ! [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_1733])]) ).
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(f15852,plain,
spl0_1732,
inference(avatar_split_clause,[],[f2306,f15850]) ).
fof(f15850,plain,
( spl0_1732
<=> ! [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_1732])]) ).
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(f15848,plain,
spl0_1731,
inference(avatar_split_clause,[],[f2304,f15846]) ).
fof(f15846,plain,
( spl0_1731
<=> ! [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_1731])]) ).
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(f15844,plain,
spl0_1730,
inference(avatar_split_clause,[],[f2209,f15842]) ).
fof(f15842,plain,
( spl0_1730
<=> ! [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_1730])]) ).
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(f15840,plain,
spl0_1729,
inference(avatar_split_clause,[],[f2208,f15838]) ).
fof(f15838,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(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(f15836,plain,
spl0_1728,
inference(avatar_split_clause,[],[f2080,f15834]) ).
fof(f15834,plain,
( spl0_1728
<=> ! [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_1728])]) ).
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(f15832,plain,
spl0_1727,
inference(avatar_split_clause,[],[f2060,f15830]) ).
fof(f15830,plain,
( spl0_1727
<=> ! [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_1727])]) ).
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(f15828,plain,
spl0_1726,
inference(avatar_split_clause,[],[f2058,f15826]) ).
fof(f15826,plain,
( spl0_1726
<=> ! [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_1726])]) ).
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(f15824,plain,
spl0_1725,
inference(avatar_split_clause,[],[f2037,f15822]) ).
fof(f15822,plain,
( spl0_1725
<=> ! [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_1725])]) ).
fof(f15820,plain,
spl0_1724,
inference(avatar_split_clause,[],[f2028,f15818]) ).
fof(f15818,plain,
( spl0_1724
<=> ! [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_1724])]) ).
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(f15816,plain,
spl0_1723,
inference(avatar_split_clause,[],[f1863,f15814]) ).
fof(f15814,plain,
( spl0_1723
<=> ! [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_1723])]) ).
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(f15812,plain,
spl0_1722,
inference(avatar_split_clause,[],[f1860,f15810]) ).
fof(f15810,plain,
( spl0_1722
<=> ! [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_1722])]) ).
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(f15808,plain,
spl0_1721,
inference(avatar_split_clause,[],[f1831,f15806]) ).
fof(f15806,plain,
( spl0_1721
<=> ! [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_1721])]) ).
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(f15804,plain,
spl0_1720,
inference(avatar_split_clause,[],[f1827,f15802]) ).
fof(f15802,plain,
( spl0_1720
<=> ! [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_1720])]) ).
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(f15800,plain,
spl0_1719,
inference(avatar_split_clause,[],[f1801,f15798]) ).
fof(f15798,plain,
( spl0_1719
<=> ! [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_1719])]) ).
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(f15796,plain,
spl0_1718,
inference(avatar_split_clause,[],[f1749,f15794]) ).
fof(f15794,plain,
( spl0_1718
<=> ! [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_1718])]) ).
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(f15792,plain,
spl0_1717,
inference(avatar_split_clause,[],[f1739,f15790]) ).
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(f15788,plain,
( ~ spl0_47
| ~ spl0_1716
| ~ spl0_1386
| spl0_1538 ),
inference(avatar_split_clause,[],[f14332,f12652,f11000,f15785,f3665]) ).
fof(f3665,plain,
( spl0_47
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f15785,plain,
( spl0_1716
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f11000,plain,
( spl0_1386
<=> ! [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_1386])]) ).
fof(f12652,plain,
( spl0_1538
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f14332,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| ~ spl0_1386
| spl0_1538 ),
inference(resolution,[],[f12654,f11001]) ).
fof(f11001,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_1386 ),
inference(avatar_component_clause,[],[f11000]) ).
fof(f12654,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_1538 ),
inference(avatar_component_clause,[],[f12652]) ).
fof(f15783,plain,
spl0_1715,
inference(avatar_split_clause,[],[f1725,f15781]) ).
fof(f15781,plain,
( spl0_1715
<=> ! [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_1715])]) ).
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(f15779,plain,
spl0_1714,
inference(avatar_split_clause,[],[f1708,f15777]) ).
fof(f15777,plain,
( spl0_1714
<=> ! [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_1714])]) ).
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(f15775,plain,
spl0_1713,
inference(avatar_split_clause,[],[f1696,f15773]) ).
fof(f15773,plain,
( spl0_1713
<=> ! [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_1713])]) ).
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(f15771,plain,
spl0_1712,
inference(avatar_split_clause,[],[f1691,f15769]) ).
fof(f15769,plain,
( spl0_1712
<=> ! [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_1712])]) ).
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(f15767,plain,
spl0_1711,
inference(avatar_split_clause,[],[f1690,f15765]) ).
fof(f15765,plain,
( spl0_1711
<=> ! [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_1711])]) ).
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(f15763,plain,
spl0_1710,
inference(avatar_split_clause,[],[f1601,f15761]) ).
fof(f15761,plain,
( spl0_1710
<=> ! [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_1710])]) ).
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(f15759,plain,
spl0_1709,
inference(avatar_split_clause,[],[f1577,f15757]) ).
fof(f15757,plain,
( spl0_1709
<=> ! [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_1709])]) ).
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(f15755,plain,
spl0_1708,
inference(avatar_split_clause,[],[f1574,f15753]) ).
fof(f15753,plain,
( spl0_1708
<=> ! [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_1708])]) ).
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(f15751,plain,
spl0_1707,
inference(avatar_split_clause,[],[f1554,f15749]) ).
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(f15747,plain,
spl0_1706,
inference(avatar_split_clause,[],[f1547,f15745]) ).
fof(f15745,plain,
( spl0_1706
<=> ! [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_1706])]) ).
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(f15743,plain,
( spl0_1705
| ~ spl0_915
| ~ spl0_1375 ),
inference(avatar_split_clause,[],[f12879,f10955,f8042,f15740]) ).
fof(f15740,plain,
( spl0_1705
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f10955,plain,
( spl0_1375
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f12879,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_915
| ~ spl0_1375 ),
inference(superposition,[],[f10957,f8043]) ).
fof(f10957,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_1375 ),
inference(avatar_component_clause,[],[f10955]) ).
fof(f15738,plain,
spl0_1704,
inference(avatar_split_clause,[],[f1518,f15736]) ).
fof(f15736,plain,
( spl0_1704
<=> ! [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_1704])]) ).
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(f15734,plain,
spl0_1703,
inference(avatar_split_clause,[],[f1508,f15732]) ).
fof(f15732,plain,
( spl0_1703
<=> ! [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_1703])]) ).
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(f15730,plain,
spl0_1702,
inference(avatar_split_clause,[],[f1495,f15728]) ).
fof(f15728,plain,
( spl0_1702
<=> ! [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_1702])]) ).
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(f15726,plain,
spl0_1701,
inference(avatar_split_clause,[],[f1239,f15724]) ).
fof(f15724,plain,
( spl0_1701
<=> ! [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_1701])]) ).
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(f15722,plain,
spl0_1700,
inference(avatar_split_clause,[],[f1237,f15720]) ).
fof(f15720,plain,
( spl0_1700
<=> ! [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_1700])]) ).
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(f15718,plain,
spl0_1699,
inference(avatar_split_clause,[],[f1217,f15716]) ).
fof(f15716,plain,
( spl0_1699
<=> ! [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_1699])]) ).
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(f15714,plain,
spl0_1698,
inference(avatar_split_clause,[],[f127,f15712]) ).
fof(f15712,plain,
( spl0_1698
<=> ! [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_1698])]) ).
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(f15710,plain,
spl0_1697,
inference(avatar_split_clause,[],[f125,f15708]) ).
fof(f15708,plain,
( spl0_1697
<=> ! [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_1697])]) ).
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(f15706,plain,
spl0_1696,
inference(avatar_split_clause,[],[f80,f15704]) ).
fof(f15704,plain,
( spl0_1696
<=> ! [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_1696])]) ).
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(f15600,plain,
( ~ spl0_1695
| spl0_107
| ~ spl0_838
| ~ spl0_1179
| ~ spl0_1328 ),
inference(avatar_split_clause,[],[f12791,f10442,f9537,f7720,f3962,f15597]) ).
fof(f15597,plain,
( spl0_1695
<=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f7720,plain,
( spl0_838
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f9537,plain,
( spl0_1179
<=> ! [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_1179])]) ).
fof(f10442,plain,
( spl0_1328
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f12791,plain,
( c_0 = c_1
| ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| ~ spl0_838
| ~ spl0_1179
| ~ spl0_1328 ),
inference(forward_demodulation,[],[f12785,f7722]) ).
fof(f7722,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_838 ),
inference(avatar_component_clause,[],[f7720]) ).
fof(f12785,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_1179
| ~ spl0_1328 ),
inference(superposition,[],[f9538,f10444]) ).
fof(f10444,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_1328 ),
inference(avatar_component_clause,[],[f10442]) ).
fof(f9538,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_1179 ),
inference(avatar_component_clause,[],[f9537]) ).
fof(f15473,plain,
( spl0_1694
| ~ spl0_1048
| ~ spl0_1312 ),
inference(avatar_split_clause,[],[f12610,f10302,f8787,f15471]) ).
fof(f15471,plain,
( spl0_1694
<=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f10302,plain,
( spl0_1312
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f12610,plain,
( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1048
| ~ spl0_1312 ),
inference(superposition,[],[f8788,f10303]) ).
fof(f10303,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_1312 ),
inference(avatar_component_clause,[],[f10302]) ).
fof(f14650,plain,
spl0_1693,
inference(avatar_split_clause,[],[f3387,f14648]) ).
fof(f14648,plain,
( spl0_1693
<=> ! [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_1693])]) ).
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(f14646,plain,
spl0_1692,
inference(avatar_split_clause,[],[f3382,f14644]) ).
fof(f14644,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(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(f14641,plain,
spl0_1691,
inference(avatar_split_clause,[],[f3270,f14639]) ).
fof(f14639,plain,
( spl0_1691
<=> ! [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_1691])]) ).
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(f14637,plain,
spl0_1690,
inference(avatar_split_clause,[],[f3187,f14635]) ).
fof(f14635,plain,
( spl0_1690
<=> ! [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_1690])]) ).
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(f14628,plain,
( spl0_1689
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1688 ),
inference(avatar_split_clause,[],[f14624,f14621,f11328,f10972,f7083,f6138,f14626]) ).
fof(f14626,plain,
( spl0_1689
<=> ! [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_1689])]) ).
fof(f14621,plain,
( spl0_1688
<=> ! [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_1688])]) ).
fof(f14624,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1688 ),
inference(forward_demodulation,[],[f14622,f12329]) ).
fof(f14622,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_1688 ),
inference(avatar_component_clause,[],[f14621]) ).
fof(f14623,plain,
spl0_1688,
inference(avatar_split_clause,[],[f3151,f14621]) ).
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(f14619,plain,
spl0_1687,
inference(avatar_split_clause,[],[f3149,f14617]) ).
fof(f14617,plain,
( spl0_1687
<=> ! [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_1687])]) ).
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(f14615,plain,
spl0_1686,
inference(avatar_split_clause,[],[f3148,f14613]) ).
fof(f14613,plain,
( spl0_1686
<=> ! [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_1686])]) ).
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(f14611,plain,
spl0_1685,
inference(avatar_split_clause,[],[f3114,f14609]) ).
fof(f14609,plain,
( spl0_1685
<=> ! [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_1685])]) ).
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(f14607,plain,
spl0_1684,
inference(avatar_split_clause,[],[f3058,f14605]) ).
fof(f14605,plain,
( spl0_1684
<=> ! [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_1684])]) ).
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(f14603,plain,
spl0_1683,
inference(avatar_split_clause,[],[f2950,f14601]) ).
fof(f14601,plain,
( spl0_1683
<=> ! [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_1683])]) ).
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(f14599,plain,
( spl0_1682
| ~ spl0_720
| ~ spl0_721
| ~ spl0_723
| ~ spl0_801
| ~ spl0_1597 ),
inference(avatar_split_clause,[],[f14272,f12959,f7570,f7234,f7226,f7221,f14597]) ).
fof(f7226,plain,
( spl0_721
<=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f7234,plain,
( spl0_723
<=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f12959,plain,
( spl0_1597
<=> ! [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_1597])]) ).
fof(f14272,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_720
| ~ spl0_721
| ~ spl0_723
| ~ spl0_801
| ~ spl0_1597 ),
inference(forward_demodulation,[],[f14271,f7227]) ).
fof(f7227,plain,
( ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3
| ~ spl0_721 ),
inference(avatar_component_clause,[],[f7226]) ).
fof(f14271,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ spl0_720
| ~ spl0_723
| ~ spl0_801
| ~ spl0_1597 ),
inference(forward_demodulation,[],[f14270,f7572]) ).
fof(f14270,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_720
| ~ spl0_723
| ~ spl0_1597 ),
inference(forward_demodulation,[],[f14259,f7235]) ).
fof(f7235,plain,
( ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11)
| ~ spl0_723 ),
inference(avatar_component_clause,[],[f7234]) ).
fof(f14259,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_720
| ~ spl0_1597 ),
inference(superposition,[],[f12960,f7223]) ).
fof(f12960,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_1597 ),
inference(avatar_component_clause,[],[f12959]) ).
fof(f14595,plain,
spl0_1681,
inference(avatar_split_clause,[],[f2896,f14593]) ).
fof(f14593,plain,
( spl0_1681
<=> ! [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_1681])]) ).
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(f14591,plain,
spl0_1680,
inference(avatar_split_clause,[],[f2841,f14589]) ).
fof(f14589,plain,
( spl0_1680
<=> ! [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_1680])]) ).
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(f14587,plain,
spl0_1679,
inference(avatar_split_clause,[],[f2840,f14585]) ).
fof(f14585,plain,
( spl0_1679
<=> ! [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_1679])]) ).
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(f14583,plain,
spl0_1678,
inference(avatar_split_clause,[],[f2745,f14581]) ).
fof(f14581,plain,
( spl0_1678
<=> ! [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_1678])]) ).
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(f14579,plain,
spl0_1677,
inference(avatar_split_clause,[],[f2727,f14577]) ).
fof(f14577,plain,
( spl0_1677
<=> ! [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_1677])]) ).
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(f14575,plain,
spl0_1676,
inference(avatar_split_clause,[],[f2726,f14573]) ).
fof(f14573,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(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(f14571,plain,
spl0_1675,
inference(avatar_split_clause,[],[f2683,f14569]) ).
fof(f14569,plain,
( spl0_1675
<=> ! [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_1675])]) ).
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(f14567,plain,
spl0_1674,
inference(avatar_split_clause,[],[f2658,f14565]) ).
fof(f14565,plain,
( spl0_1674
<=> ! [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_1674])]) ).
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(f14563,plain,
spl0_1673,
inference(avatar_split_clause,[],[f2655,f14561]) ).
fof(f14561,plain,
( spl0_1673
<=> ! [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_1673])]) ).
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(f14559,plain,
spl0_1672,
inference(avatar_split_clause,[],[f2621,f14557]) ).
fof(f14557,plain,
( spl0_1672
<=> ! [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_1672])]) ).
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(f14555,plain,
( spl0_1671
| ~ spl0_719
| ~ spl0_721
| ~ spl0_746
| ~ spl0_801
| ~ spl0_915
| ~ spl0_1596 ),
inference(avatar_split_clause,[],[f14253,f12955,f8042,f7570,f7334,f7226,f7216,f14552]) ).
fof(f7216,plain,
( spl0_719
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f12955,plain,
( spl0_1596
<=> ! [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_1596])]) ).
fof(f14253,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_719
| ~ spl0_721
| ~ spl0_746
| ~ spl0_801
| ~ spl0_915
| ~ spl0_1596 ),
inference(forward_demodulation,[],[f14252,f7218]) ).
fof(f7218,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_719 ),
inference(avatar_component_clause,[],[f7216]) ).
fof(f14252,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_721
| ~ spl0_746
| ~ spl0_801
| ~ spl0_915
| ~ spl0_1596 ),
inference(forward_demodulation,[],[f14251,f7572]) ).
fof(f14251,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_721
| ~ spl0_746
| ~ spl0_915
| ~ spl0_1596 ),
inference(forward_demodulation,[],[f14250,f7227]) ).
fof(f14250,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_746
| ~ spl0_915
| ~ spl0_1596 ),
inference(forward_demodulation,[],[f14244,f8043]) ).
fof(f14244,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_746
| ~ spl0_1596 ),
inference(superposition,[],[f12956,f7336]) ).
fof(f12956,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_1596 ),
inference(avatar_component_clause,[],[f12955]) ).
fof(f14550,plain,
spl0_1670,
inference(avatar_split_clause,[],[f2488,f14548]) ).
fof(f14548,plain,
( spl0_1670
<=> ! [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_1670])]) ).
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(f14546,plain,
spl0_1669,
inference(avatar_split_clause,[],[f2472,f14544]) ).
fof(f14544,plain,
( spl0_1669
<=> ! [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_1669])]) ).
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(f14542,plain,
spl0_1668,
inference(avatar_split_clause,[],[f2468,f14540]) ).
fof(f14540,plain,
( spl0_1668
<=> ! [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_1668])]) ).
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(f14538,plain,
spl0_1667,
inference(avatar_split_clause,[],[f2363,f14536]) ).
fof(f14536,plain,
( spl0_1667
<=> ! [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_1667])]) ).
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(f14534,plain,
spl0_1666,
inference(avatar_split_clause,[],[f2362,f14532]) ).
fof(f14532,plain,
( spl0_1666
<=> ! [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_1666])]) ).
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(f14530,plain,
spl0_1665,
inference(avatar_split_clause,[],[f2349,f14528]) ).
fof(f14528,plain,
( spl0_1665
<=> ! [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_1665])]) ).
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(f14526,plain,
spl0_1664,
inference(avatar_split_clause,[],[f2348,f14524]) ).
fof(f14524,plain,
( spl0_1664
<=> ! [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_1664])]) ).
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(f14522,plain,
spl0_1663,
inference(avatar_split_clause,[],[f2268,f14520]) ).
fof(f14520,plain,
( spl0_1663
<=> ! [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_1663])]) ).
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(f14518,plain,
spl0_1662,
inference(avatar_split_clause,[],[f2263,f14516]) ).
fof(f14516,plain,
( spl0_1662
<=> ! [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_1662])]) ).
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(f14514,plain,
spl0_1661,
inference(avatar_split_clause,[],[f2246,f14512]) ).
fof(f14512,plain,
( spl0_1661
<=> ! [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_1661])]) ).
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(f14510,plain,
( spl0_1660
| ~ spl0_675
| ~ spl0_1578 ),
inference(avatar_split_clause,[],[f14192,f12830,f7019,f14508]) ).
fof(f14508,plain,
( spl0_1660
<=> ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f12830,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(f14192,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(X0),tc_set(tc_Message_Omsg))
| ~ spl0_675
| ~ spl0_1578 ),
inference(resolution,[],[f12831,f7020]) ).
fof(f12831,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_1578 ),
inference(avatar_component_clause,[],[f12830]) ).
fof(f14506,plain,
spl0_1659,
inference(avatar_split_clause,[],[f2242,f14504]) ).
fof(f14504,plain,
( spl0_1659
<=> ! [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_1659])]) ).
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(f14502,plain,
spl0_1658,
inference(avatar_split_clause,[],[f2236,f14500]) ).
fof(f14500,plain,
( spl0_1658
<=> ! [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_1658])]) ).
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(f14498,plain,
spl0_1657,
inference(avatar_split_clause,[],[f2235,f14496]) ).
fof(f14496,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(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(f14494,plain,
spl0_1656,
inference(avatar_split_clause,[],[f2232,f14492]) ).
fof(f14492,plain,
( spl0_1656
<=> ! [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_1656])]) ).
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(f14490,plain,
spl0_1655,
inference(avatar_split_clause,[],[f2231,f14488]) ).
fof(f14488,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(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(f14486,plain,
spl0_1654,
inference(avatar_split_clause,[],[f2195,f14484]) ).
fof(f14484,plain,
( spl0_1654
<=> ! [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_1654])]) ).
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(f14482,plain,
spl0_1653,
inference(avatar_split_clause,[],[f2190,f14480]) ).
fof(f14480,plain,
( spl0_1653
<=> ! [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_1653])]) ).
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(f14478,plain,
spl0_1652,
inference(avatar_split_clause,[],[f2111,f14476]) ).
fof(f14476,plain,
( spl0_1652
<=> ! [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_1652])]) ).
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(f14474,plain,
spl0_1651,
inference(avatar_split_clause,[],[f2085,f14472]) ).
fof(f14472,plain,
( spl0_1651
<=> ! [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_1651])]) ).
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(f14470,plain,
spl0_1650,
inference(avatar_split_clause,[],[f2084,f14468]) ).
fof(f14468,plain,
( spl0_1650
<=> ! [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_1650])]) ).
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(f14466,plain,
( spl0_1649
| ~ spl0_675
| ~ spl0_1576 ),
inference(avatar_split_clause,[],[f14167,f12822,f7019,f14464]) ).
fof(f14464,plain,
( spl0_1649
<=> ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f12822,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(f14167,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_675
| ~ spl0_1576 ),
inference(resolution,[],[f12823,f7020]) ).
fof(f12823,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_1576 ),
inference(avatar_component_clause,[],[f12822]) ).
fof(f14462,plain,
spl0_1648,
inference(avatar_split_clause,[],[f2083,f14460]) ).
fof(f14460,plain,
( spl0_1648
<=> ! [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_1648])]) ).
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(f14458,plain,
spl0_1647,
inference(avatar_split_clause,[],[f2082,f14456]) ).
fof(f14456,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(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(f14454,plain,
spl0_1646,
inference(avatar_split_clause,[],[f2076,f14452]) ).
fof(f14452,plain,
( spl0_1646
<=> ! [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_1646])]) ).
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(f14450,plain,
spl0_1645,
inference(avatar_split_clause,[],[f2075,f14448]) ).
fof(f14448,plain,
( spl0_1645
<=> ! [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_1645])]) ).
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(f14446,plain,
spl0_1644,
inference(avatar_split_clause,[],[f2073,f14444]) ).
fof(f14444,plain,
( spl0_1644
<=> ! [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_1644])]) ).
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(f14442,plain,
spl0_1643,
inference(avatar_split_clause,[],[f2072,f14440]) ).
fof(f14440,plain,
( spl0_1643
<=> ! [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_1643])]) ).
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(f14438,plain,
spl0_1642,
inference(avatar_split_clause,[],[f2071,f14436]) ).
fof(f14436,plain,
( spl0_1642
<=> ! [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_1642])]) ).
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(f14434,plain,
spl0_1641,
inference(avatar_split_clause,[],[f2070,f14432]) ).
fof(f14432,plain,
( spl0_1641
<=> ! [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_1641])]) ).
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(f14430,plain,
spl0_1640,
inference(avatar_split_clause,[],[f2068,f14428]) ).
fof(f14428,plain,
( spl0_1640
<=> ! [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_1640])]) ).
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(f14426,plain,
spl0_1639,
inference(avatar_split_clause,[],[f2067,f14424]) ).
fof(f14424,plain,
( spl0_1639
<=> ! [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_1639])]) ).
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(f14422,plain,
( spl0_1638
| ~ spl0_675
| ~ spl0_1568 ),
inference(avatar_split_clause,[],[f14043,f12779,f7019,f14420]) ).
fof(f14420,plain,
( spl0_1638
<=> ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f12779,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(f14043,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
| ~ spl0_675
| ~ spl0_1568 ),
inference(resolution,[],[f12780,f7020]) ).
fof(f12780,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_1568 ),
inference(avatar_component_clause,[],[f12779]) ).
fof(f14418,plain,
spl0_1637,
inference(avatar_split_clause,[],[f1927,f14416]) ).
fof(f14416,plain,
( spl0_1637
<=> ! [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_1637])]) ).
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(f14414,plain,
spl0_1636,
inference(avatar_split_clause,[],[f1868,f14412]) ).
fof(f14412,plain,
( spl0_1636
<=> ! [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_1636])]) ).
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(f14410,plain,
spl0_1635,
inference(avatar_split_clause,[],[f1820,f14408]) ).
fof(f14408,plain,
( spl0_1635
<=> ! [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_1635])]) ).
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(f14406,plain,
spl0_1634,
inference(avatar_split_clause,[],[f1819,f14404]) ).
fof(f14404,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(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(f14402,plain,
spl0_1633,
inference(avatar_split_clause,[],[f1817,f14400]) ).
fof(f14400,plain,
( spl0_1633
<=> ! [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_1633])]) ).
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(f14398,plain,
spl0_1632,
inference(avatar_split_clause,[],[f1816,f14396]) ).
fof(f14396,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(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(f14394,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1760,f14392]) ).
fof(f14392,plain,
( spl0_1631
<=> ! [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_1631])]) ).
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(f14390,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1756,f14388]) ).
fof(f14388,plain,
( spl0_1630
<=> ! [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_1630])]) ).
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(f14386,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1710,f14384]) ).
fof(f14384,plain,
( spl0_1629
<=> ! [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_1629])]) ).
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(f14382,plain,
spl0_1628,
inference(avatar_split_clause,[],[f1640,f14380]) ).
fof(f14380,plain,
( spl0_1628
<=> ! [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_1628])]) ).
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(f14378,plain,
( spl0_1627
| ~ spl0_783
| ~ spl0_1500 ),
inference(avatar_split_clause,[],[f13184,f12489,f7498,f14376]) ).
fof(f14376,plain,
( spl0_1627
<=> ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f7498,plain,
( spl0_783
<=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f13184,plain,
( ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_783
| ~ spl0_1500 ),
inference(superposition,[],[f7499,f12490]) ).
fof(f7499,plain,
( ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ spl0_783 ),
inference(avatar_component_clause,[],[f7498]) ).
fof(f14374,plain,
spl0_1626,
inference(avatar_split_clause,[],[f1632,f14372]) ).
fof(f14372,plain,
( spl0_1626
<=> ! [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_1626])]) ).
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(f14370,plain,
spl0_1625,
inference(avatar_split_clause,[],[f1612,f14368]) ).
fof(f14368,plain,
( spl0_1625
<=> ! [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_1625])]) ).
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(f14366,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1600,f14364]) ).
fof(f14364,plain,
( spl0_1624
<=> ! [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_1624])]) ).
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(f14362,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1596,f14360]) ).
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(f14358,plain,
spl0_1622,
inference(avatar_split_clause,[],[f1544,f14356]) ).
fof(f14356,plain,
( spl0_1622
<=> ! [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_1622])]) ).
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(f14354,plain,
spl0_1621,
inference(avatar_split_clause,[],[f1456,f14352]) ).
fof(f14352,plain,
( spl0_1621
<=> ! [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_1621])]) ).
fof(f14350,plain,
spl0_1620,
inference(avatar_split_clause,[],[f1431,f14348]) ).
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(f14346,plain,
spl0_1619,
inference(avatar_split_clause,[],[f1415,f14344]) ).
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(f14342,plain,
spl0_1618,
inference(avatar_split_clause,[],[f1414,f14340]) ).
fof(f14340,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(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(f14338,plain,
spl0_1617,
inference(avatar_split_clause,[],[f1411,f14336]) ).
fof(f14336,plain,
( spl0_1617
<=> ! [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_1617])]) ).
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(f14331,plain,
spl0_1616,
inference(avatar_split_clause,[],[f1410,f14329]) ).
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(f14327,plain,
spl0_1615,
inference(avatar_split_clause,[],[f1281,f14325]) ).
fof(f14325,plain,
( spl0_1615
<=> ! [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_1615])]) ).
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(f14323,plain,
spl0_1614,
inference(avatar_split_clause,[],[f1198,f14321]) ).
fof(f14321,plain,
( spl0_1614
<=> ! [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_1614])]) ).
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(f14319,plain,
spl0_1613,
inference(avatar_split_clause,[],[f1197,f14317]) ).
fof(f14317,plain,
( spl0_1613
<=> ! [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_1613])]) ).
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(f14315,plain,
spl0_1612,
inference(avatar_split_clause,[],[f99,f14313]) ).
fof(f14313,plain,
( spl0_1612
<=> ! [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_1612])]) ).
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(f14311,plain,
spl0_1611,
inference(avatar_split_clause,[],[f96,f14309]) ).
fof(f14309,plain,
( spl0_1611
<=> ! [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_1611])]) ).
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(f14307,plain,
spl0_1610,
inference(avatar_split_clause,[],[f59,f14305]) ).
fof(f14305,plain,
( spl0_1610
<=> ! [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_1610])]) ).
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(f14303,plain,
spl0_1609,
inference(avatar_split_clause,[],[f48,f14301]) ).
fof(f14301,plain,
( spl0_1609
<=> ! [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_1609])]) ).
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(f14299,plain,
spl0_1608,
inference(avatar_split_clause,[],[f43,f14297]) ).
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(f14295,plain,
spl0_1607,
inference(avatar_split_clause,[],[f27,f14293]) ).
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(f14149,plain,
( spl0_1606
| ~ spl0_123
| ~ spl0_1563 ),
inference(avatar_split_clause,[],[f13952,f12759,f4034,f14147]) ).
fof(f14147,plain,
( spl0_1606
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f12759,plain,
( spl0_1563
<=> ! [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_1563])]) ).
fof(f13952,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_123
| ~ spl0_1563 ),
inference(resolution,[],[f12760,f4035]) ).
fof(f12760,plain,
( ! [X18,X1,X5] :
( ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1))
| ~ c_Wellfounded__Recursion_Owf(X5,X1) )
| ~ spl0_1563 ),
inference(avatar_component_clause,[],[f12759]) ).
fof(f13982,plain,
( spl0_1605
| ~ spl0_1198
| ~ spl0_1563 ),
inference(avatar_split_clause,[],[f13946,f12759,f9614,f13980]) ).
fof(f13980,plain,
( spl0_1605
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f9614,plain,
( spl0_1198
<=> ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f13946,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1198
| ~ spl0_1563 ),
inference(resolution,[],[f12760,f9615]) ).
fof(f9615,plain,
( ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| ~ spl0_1198 ),
inference(avatar_component_clause,[],[f9614]) ).
fof(f13570,plain,
( ~ spl0_1603
| spl0_1604
| ~ spl0_121
| ~ spl0_1385 ),
inference(avatar_split_clause,[],[f11668,f10996,f4026,f13568,f13564]) ).
fof(f13564,plain,
( spl0_1603
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f13568,plain,
( spl0_1604
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f10996,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(f11668,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_121
| ~ spl0_1385 ),
inference(resolution,[],[f10997,f4027]) ).
fof(f10997,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,[],[f10996]) ).
fof(f13131,plain,
( ~ spl0_1601
| spl0_1602
| ~ spl0_121
| ~ spl0_1347 ),
inference(avatar_split_clause,[],[f11449,f10841,f4026,f13129,f13125]) ).
fof(f13125,plain,
( spl0_1601
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f13129,plain,
( spl0_1602
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f10841,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(f11449,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_121
| ~ spl0_1347 ),
inference(resolution,[],[f10842,f4027]) ).
fof(f10842,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_1347 ),
inference(avatar_component_clause,[],[f10841]) ).
fof(f12973,plain,
spl0_1600,
inference(avatar_split_clause,[],[f3339,f12971]) ).
fof(f12971,plain,
( spl0_1600
<=> ! [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_1600])]) ).
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(f12969,plain,
spl0_1599,
inference(avatar_split_clause,[],[f3327,f12967]) ).
fof(f12967,plain,
( spl0_1599
<=> ! [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_1599])]) ).
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(f12965,plain,
spl0_1598,
inference(avatar_split_clause,[],[f3274,f12963]) ).
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(f12961,plain,
spl0_1597,
inference(avatar_split_clause,[],[f3260,f12959]) ).
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(f12957,plain,
spl0_1596,
inference(avatar_split_clause,[],[f3256,f12955]) ).
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(f12949,plain,
spl0_1595,
inference(avatar_split_clause,[],[f3162,f12947]) ).
fof(f12947,plain,
( spl0_1595
<=> ! [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_1595])]) ).
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(f12945,plain,
spl0_1594,
inference(avatar_split_clause,[],[f3160,f12943]) ).
fof(f12943,plain,
( spl0_1594
<=> ! [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_1594])]) ).
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(f12913,plain,
( spl0_1593
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1592 ),
inference(avatar_split_clause,[],[f12909,f12906,f11328,f10972,f7083,f6138,f12911]) ).
fof(f12906,plain,
( spl0_1592
<=> ! [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_1592])]) ).
fof(f12909,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_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1592 ),
inference(forward_demodulation,[],[f12907,f12329]) ).
fof(f12907,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_1592 ),
inference(avatar_component_clause,[],[f12906]) ).
fof(f12908,plain,
spl0_1592,
inference(avatar_split_clause,[],[f3143,f12906]) ).
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(f12904,plain,
spl0_1591,
inference(avatar_split_clause,[],[f3104,f12902]) ).
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(f12896,plain,
( spl0_1590
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1589 ),
inference(avatar_split_clause,[],[f12892,f12889,f11328,f10972,f7083,f6138,f12894]) ).
fof(f12889,plain,
( spl0_1589
<=> ! [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_1589])]) ).
fof(f12892,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1589 ),
inference(forward_demodulation,[],[f12890,f12329]) ).
fof(f12890,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_1589 ),
inference(avatar_component_clause,[],[f12889]) ).
fof(f12891,plain,
spl0_1589,
inference(avatar_split_clause,[],[f3044,f12889]) ).
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(f12887,plain,
spl0_1588,
inference(avatar_split_clause,[],[f3040,f12885]) ).
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(f12878,plain,
spl0_1587,
inference(avatar_split_clause,[],[f3027,f12876]) ).
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(f12874,plain,
spl0_1586,
inference(avatar_split_clause,[],[f3026,f12872]) ).
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(f12867,plain,
( spl0_1585
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1584 ),
inference(avatar_split_clause,[],[f12863,f12860,f11328,f10972,f7083,f6138,f12865]) ).
fof(f12865,plain,
( spl0_1585
<=> ! [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_1585])]) ).
fof(f12860,plain,
( spl0_1584
<=> ! [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_1584])]) ).
fof(f12863,plain,
( ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21)
| ~ spl0_649
| ~ spl0_690
| ~ spl0_1379
| ~ spl0_1466
| ~ spl0_1584 ),
inference(forward_demodulation,[],[f12861,f12329]) ).
fof(f12861,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_1584 ),
inference(avatar_component_clause,[],[f12860]) ).
fof(f12862,plain,
spl0_1584,
inference(avatar_split_clause,[],[f3021,f12860]) ).
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(f12858,plain,
spl0_1583,
inference(avatar_split_clause,[],[f2946,f12856]) ).
fof(f12856,plain,
( spl0_1583
<=> ! [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_1583])]) ).
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(f12854,plain,
spl0_1582,
inference(avatar_split_clause,[],[f2945,f12852]) ).
fof(f12852,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(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(f12850,plain,
spl0_1581,
inference(avatar_split_clause,[],[f2944,f12848]) ).
fof(f12848,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_OGets(X12,X86),X102,tc_Event_Oevent)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
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(f12846,plain,
spl0_1580,
inference(avatar_split_clause,[],[f2943,f12844]) ).
fof(f12844,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(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(f12842,plain,
spl0_1579,
inference(avatar_split_clause,[],[f2889,f12840]) ).
fof(f12840,plain,
( spl0_1579
<=> ! [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_1579])]) ).
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(f12832,plain,
spl0_1578,
inference(avatar_split_clause,[],[f2888,f12830]) ).
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(f12828,plain,
spl0_1577,
inference(avatar_split_clause,[],[f2882,f12826]) ).
fof(f12826,plain,
( spl0_1577
<=> ! [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_1577])]) ).
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(f12824,plain,
spl0_1576,
inference(avatar_split_clause,[],[f2881,f12822]) ).
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(f12820,plain,
spl0_1575,
inference(avatar_split_clause,[],[f2879,f12818]) ).
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(f12816,plain,
spl0_1574,
inference(avatar_split_clause,[],[f2878,f12814]) ).
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(f12812,plain,
spl0_1573,
inference(avatar_split_clause,[],[f2876,f12810]) ).
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(f12808,plain,
spl0_1572,
inference(avatar_split_clause,[],[f2875,f12806]) ).
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(f12804,plain,
spl0_1571,
inference(avatar_split_clause,[],[f2872,f12802]) ).
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(f12800,plain,
spl0_1570,
inference(avatar_split_clause,[],[f2870,f12798]) ).
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(f12796,plain,
spl0_1569,
inference(avatar_split_clause,[],[f2864,f12794]) ).
fof(f12794,plain,
( spl0_1569
<=> ! [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_1569])]) ).
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(f12781,plain,
spl0_1568,
inference(avatar_split_clause,[],[f2863,f12779]) ).
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(f12777,plain,
spl0_1567,
inference(avatar_split_clause,[],[f2861,f12775]) ).
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(f12773,plain,
spl0_1566,
inference(avatar_split_clause,[],[f2860,f12771]) ).
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(f12769,plain,
spl0_1565,
inference(avatar_split_clause,[],[f2857,f12767]) ).
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(f12765,plain,
spl0_1564,
inference(avatar_split_clause,[],[f2855,f12763]) ).
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(f12761,plain,
spl0_1563,
inference(avatar_split_clause,[],[f2725,f12759]) ).
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(f12757,plain,
spl0_1562,
inference(avatar_split_clause,[],[f2689,f12755]) ).
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(f12753,plain,
spl0_1561,
inference(avatar_split_clause,[],[f2669,f12751]) ).
fof(f12751,plain,
( spl0_1561
<=> ! [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_1561])]) ).
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(f12749,plain,
spl0_1560,
inference(avatar_split_clause,[],[f2656,f12747]) ).
fof(f12747,plain,
( spl0_1560
<=> ! [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_1560])]) ).
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(f12745,plain,
spl0_1559,
inference(avatar_split_clause,[],[f2646,f12743]) ).
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(f12740,plain,
spl0_1558,
inference(avatar_split_clause,[],[f2645,f12738]) ).
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(f12736,plain,
spl0_1557,
inference(avatar_split_clause,[],[f2631,f12734]) ).
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(f12732,plain,
spl0_1556,
inference(avatar_split_clause,[],[f2630,f12730]) ).
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(f12728,plain,
spl0_1555,
inference(avatar_split_clause,[],[f2622,f12726]) ).
fof(f12726,plain,
( spl0_1555
<=> ! [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_1555])]) ).
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(f12724,plain,
spl0_1554,
inference(avatar_split_clause,[],[f2616,f12722]) ).
fof(f12722,plain,
( spl0_1554
<=> ! [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_1554])]) ).
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(f12720,plain,
spl0_1553,
inference(avatar_split_clause,[],[f2555,f12718]) ).
fof(f12718,plain,
( spl0_1553
<=> ! [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_1553])]) ).
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(f12716,plain,
spl0_1552,
inference(avatar_split_clause,[],[f2554,f12714]) ).
fof(f12714,plain,
( spl0_1552
<=> ! [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_1552])]) ).
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(f12712,plain,
spl0_1551,
inference(avatar_split_clause,[],[f2552,f12710]) ).
fof(f12710,plain,
( spl0_1551
<=> ! [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_1551])]) ).
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(f12708,plain,
spl0_1550,
inference(avatar_split_clause,[],[f2551,f12706]) ).
fof(f12706,plain,
( spl0_1550
<=> ! [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_1550])]) ).
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(f12704,plain,
spl0_1549,
inference(avatar_split_clause,[],[f2525,f12702]) ).
fof(f12702,plain,
( spl0_1549
<=> ! [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_1549])]) ).
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(f12695,plain,
spl0_1548,
inference(avatar_split_clause,[],[f2524,f12693]) ).
fof(f12693,plain,
( spl0_1548
<=> ! [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_1548])]) ).
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(f12691,plain,
spl0_1547,
inference(avatar_split_clause,[],[f2520,f12689]) ).
fof(f12689,plain,
( spl0_1547
<=> ! [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_1547])]) ).
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(f12687,plain,
spl0_1546,
inference(avatar_split_clause,[],[f2519,f12685]) ).
fof(f12685,plain,
( spl0_1546
<=> ! [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_1546])]) ).
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(f12683,plain,
spl0_1545,
inference(avatar_split_clause,[],[f2387,f12681]) ).
fof(f12681,plain,
( spl0_1545
<=> ! [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_1545])]) ).
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(f12679,plain,
spl0_1544,
inference(avatar_split_clause,[],[f2367,f12677]) ).
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(f12675,plain,
spl0_1543,
inference(avatar_split_clause,[],[f2365,f12673]) ).
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(f12671,plain,
spl0_1542,
inference(avatar_split_clause,[],[f2361,f12669]) ).
fof(f12669,plain,
( spl0_1542
<=> ! [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_1542])]) ).
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(f12667,plain,
spl0_1541,
inference(avatar_split_clause,[],[f2358,f12665]) ).
fof(f12665,plain,
( spl0_1541
<=> ! [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_1541])]) ).
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(f12663,plain,
spl0_1540,
inference(avatar_split_clause,[],[f2347,f12661]) ).
fof(f12661,plain,
( spl0_1540
<=> ! [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_1540])]) ).
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(f12659,plain,
spl0_1539,
inference(avatar_split_clause,[],[f2339,f12657]) ).
fof(f12657,plain,
( spl0_1539
<=> ! [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_1539])]) ).
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(f12655,plain,
( ~ spl0_1538
| ~ spl0_650
| ~ spl0_1206
| ~ spl0_1317 ),
inference(avatar_split_clause,[],[f10329,f10323,f9646,f6143,f12652]) ).
fof(f10329,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_1206
| ~ spl0_1317 ),
inference(forward_demodulation,[],[f10328,f9647]) ).
fof(f10328,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_1317 ),
inference(superposition,[],[f10324,f6145]) ).
fof(f12650,plain,
spl0_1537,
inference(avatar_split_clause,[],[f2295,f12648]) ).
fof(f12648,plain,
( spl0_1537
<=> ! [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_1537])]) ).
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(f12646,plain,
spl0_1536,
inference(avatar_split_clause,[],[f2282,f12644]) ).
fof(f12644,plain,
( spl0_1536
<=> ! [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_1536])]) ).
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(f12642,plain,
spl0_1535,
inference(avatar_split_clause,[],[f2265,f12640]) ).
fof(f12640,plain,
( spl0_1535
<=> ! [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_1535])]) ).
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(f12638,plain,
spl0_1534,
inference(avatar_split_clause,[],[f2264,f12636]) ).
fof(f12636,plain,
( spl0_1534
<=> ! [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_1534])]) ).
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(f12634,plain,
spl0_1533,
inference(avatar_split_clause,[],[f2260,f12632]) ).
fof(f12632,plain,
( spl0_1533
<=> ! [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_1533])]) ).
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(f12630,plain,
spl0_1532,
inference(avatar_split_clause,[],[f2259,f12628]) ).
fof(f12628,plain,
( spl0_1532
<=> ! [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_1532])]) ).
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(f12626,plain,
spl0_1531,
inference(avatar_split_clause,[],[f2257,f12624]) ).
fof(f12624,plain,
( spl0_1531
<=> ! [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_1531])]) ).
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(f12622,plain,
spl0_1530,
inference(avatar_split_clause,[],[f2256,f12620]) ).
fof(f12620,plain,
( spl0_1530
<=> ! [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_1530])]) ).
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(f12618,plain,
spl0_1529,
inference(avatar_split_clause,[],[f2254,f12616]) ).
fof(f12616,plain,
( spl0_1529
<=> ! [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_1529])]) ).
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(f12614,plain,
spl0_1528,
inference(avatar_split_clause,[],[f2253,f12612]) ).
fof(f12612,plain,
( spl0_1528
<=> ! [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_1528])]) ).
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(f12605,plain,
spl0_1527,
inference(avatar_split_clause,[],[f2249,f12603]) ).
fof(f12603,plain,
( spl0_1527
<=> ! [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_1527])]) ).
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(f12601,plain,
spl0_1526,
inference(avatar_split_clause,[],[f2248,f12599]) ).
fof(f12599,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(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(f12597,plain,
spl0_1525,
inference(avatar_split_clause,[],[f2215,f12595]) ).
fof(f12595,plain,
( spl0_1525
<=> ! [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_1525])]) ).
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(f12593,plain,
spl0_1524,
inference(avatar_split_clause,[],[f2212,f12591]) ).
fof(f12591,plain,
( spl0_1524
<=> ! [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_1524])]) ).
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(f12589,plain,
spl0_1523,
inference(avatar_split_clause,[],[f2210,f12587]) ).
fof(f12587,plain,
( spl0_1523
<=> ! [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_1523])]) ).
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(f12585,plain,
spl0_1522,
inference(avatar_split_clause,[],[f2207,f12583]) ).
fof(f12583,plain,
( spl0_1522
<=> ! [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_1522])]) ).
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(f12581,plain,
spl0_1521,
inference(avatar_split_clause,[],[f2206,f12579]) ).
fof(f12579,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(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(f12577,plain,
spl0_1520,
inference(avatar_split_clause,[],[f2204,f12575]) ).
fof(f12575,plain,
( spl0_1520
<=> ! [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_1520])]) ).
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(f12573,plain,
spl0_1519,
inference(avatar_split_clause,[],[f2203,f12571]) ).
fof(f12571,plain,
( spl0_1519
<=> ! [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_1519])]) ).
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(f12569,plain,
spl0_1518,
inference(avatar_split_clause,[],[f2202,f12567]) ).
fof(f12567,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(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(f12561,plain,
spl0_1517,
inference(avatar_split_clause,[],[f2201,f12559]) ).
fof(f12559,plain,
( spl0_1517
<=> ! [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_1517])]) ).
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(f12557,plain,
spl0_1516,
inference(avatar_split_clause,[],[f2200,f12555]) ).
fof(f12555,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(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(f12553,plain,
spl0_1515,
inference(avatar_split_clause,[],[f2184,f12551]) ).
fof(f12551,plain,
( spl0_1515
<=> ! [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_1515])]) ).
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(f12549,plain,
spl0_1514,
inference(avatar_split_clause,[],[f2110,f12547]) ).
fof(f12547,plain,
( spl0_1514
<=> ! [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_1514])]) ).
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(f12545,plain,
spl0_1513,
inference(avatar_split_clause,[],[f2109,f12543]) ).
fof(f12543,plain,
( spl0_1513
<=> ! [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_1513])]) ).
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(f12541,plain,
spl0_1512,
inference(avatar_split_clause,[],[f2045,f12539]) ).
fof(f12539,plain,
( spl0_1512
<=> ! [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_1512])]) ).
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(f12537,plain,
spl0_1511,
inference(avatar_split_clause,[],[f2044,f12535]) ).
fof(f12535,plain,
( spl0_1511
<=> ! [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_1511])]) ).
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(f12533,plain,
spl0_1510,
inference(avatar_split_clause,[],[f1852,f12531]) ).
fof(f12531,plain,
( spl0_1510
<=> ! [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_1510])]) ).
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(f12529,plain,
spl0_1509,
inference(avatar_split_clause,[],[f1799,f12527]) ).
fof(f12527,plain,
( spl0_1509
<=> ! [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_1509])]) ).
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(f12525,plain,
spl0_1508,
inference(avatar_split_clause,[],[f1765,f12523]) ).
fof(f12523,plain,
( spl0_1508
<=> ! [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_1508])]) ).
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(f12519,plain,
spl0_1507,
inference(avatar_split_clause,[],[f1748,f12517]) ).
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(f12515,plain,
spl0_1506,
inference(avatar_split_clause,[],[f1742,f12513]) ).
fof(f12513,plain,
( spl0_1506
<=> ! [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_1506])]) ).
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(f12511,plain,
spl0_1505,
inference(avatar_split_clause,[],[f1702,f12509]) ).
fof(f12509,plain,
( spl0_1505
<=> ! [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_1505])]) ).
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(f12507,plain,
spl0_1504,
inference(avatar_split_clause,[],[f1604,f12505]) ).
fof(f12505,plain,
( spl0_1504
<=> ! [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_1504])]) ).
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(f12503,plain,
spl0_1503,
inference(avatar_split_clause,[],[f1591,f12501]) ).
fof(f12501,plain,
( spl0_1503
<=> ! [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_1503])]) ).
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(f12499,plain,
spl0_1502,
inference(avatar_split_clause,[],[f1589,f12497]) ).
fof(f12497,plain,
( spl0_1502
<=> ! [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_1502])]) ).
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(f12495,plain,
spl0_1501,
inference(avatar_split_clause,[],[f1581,f12493]) ).
fof(f12493,plain,
( spl0_1501
<=> ! [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_1501])]) ).
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(f12491,plain,
spl0_1500,
inference(avatar_split_clause,[],[f1580,f12489]) ).
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(f12487,plain,
spl0_1499,
inference(avatar_split_clause,[],[f1578,f12485]) ).
fof(f12485,plain,
( spl0_1499
<=> ! [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_1499])]) ).
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(f12483,plain,
spl0_1498,
inference(avatar_split_clause,[],[f1576,f12481]) ).
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(f12479,plain,
spl0_1497,
inference(avatar_split_clause,[],[f1575,f12477]) ).
fof(f12477,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(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(f12475,plain,
spl0_1496,
inference(avatar_split_clause,[],[f1475,f12473]) ).
fof(f12473,plain,
( spl0_1496
<=> ! [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_1496])]) ).
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(f12471,plain,
spl0_1495,
inference(avatar_split_clause,[],[f1416,f12469]) ).
fof(f12469,plain,
( spl0_1495
<=> ! [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_1495])]) ).
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(f12467,plain,
spl0_1494,
inference(avatar_split_clause,[],[f1305,f12465]) ).
fof(f12465,plain,
( spl0_1494
<=> ! [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_1494])]) ).
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(f12463,plain,
spl0_1493,
inference(avatar_split_clause,[],[f1304,f12461]) ).
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(f12459,plain,
spl0_1492,
inference(avatar_split_clause,[],[f1291,f12457]) ).
fof(f12457,plain,
( spl0_1492
<=> ! [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_1492])]) ).
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(f12455,plain,
spl0_1491,
inference(avatar_split_clause,[],[f1287,f12453]) ).
fof(f12453,plain,
( spl0_1491
<=> ! [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_1491])]) ).
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(f12451,plain,
spl0_1490,
inference(avatar_split_clause,[],[f1286,f12449]) ).
fof(f12449,plain,
( spl0_1490
<=> ! [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_1490])]) ).
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(f12447,plain,
spl0_1489,
inference(avatar_split_clause,[],[f1285,f12445]) ).
fof(f12445,plain,
( spl0_1489
<=> ! [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_1489])]) ).
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(f12443,plain,
spl0_1488,
inference(avatar_split_clause,[],[f1284,f12441]) ).
fof(f12441,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(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(f12439,plain,
spl0_1487,
inference(avatar_split_clause,[],[f1276,f12437]) ).
fof(f12437,plain,
( spl0_1487
<=> ! [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_1487])]) ).
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(f12435,plain,
spl0_1486,
inference(avatar_split_clause,[],[f1223,f12433]) ).
fof(f12433,plain,
( spl0_1486
<=> ! [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_1486])]) ).
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(f12431,plain,
spl0_1485,
inference(avatar_split_clause,[],[f1221,f12429]) ).
fof(f12429,plain,
( spl0_1485
<=> ! [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_1485])]) ).
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(f12427,plain,
spl0_1484,
inference(avatar_split_clause,[],[f111,f12425]) ).
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(f12423,plain,
spl0_1483,
inference(avatar_split_clause,[],[f108,f12421]) ).
fof(f12421,plain,
( spl0_1483
<=> ! [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_1483])]) ).
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(f12419,plain,
spl0_1482,
inference(avatar_split_clause,[],[f104,f12417]) ).
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(f12415,plain,
spl0_1481,
inference(avatar_split_clause,[],[f100,f12413]) ).
fof(f12413,plain,
( spl0_1481
<=> ! [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_1481])]) ).
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(f12411,plain,
spl0_1480,
inference(avatar_split_clause,[],[f97,f12409]) ).
fof(f12409,plain,
( spl0_1480
<=> ! [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_1480])]) ).
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(f12407,plain,
spl0_1479,
inference(avatar_split_clause,[],[f29,f12405]) ).
fof(f12405,plain,
( spl0_1479
<=> ! [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_1479])]) ).
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_1478
| ~ spl0_1027
| ~ spl0_1454 ),
inference(avatar_split_clause,[],[f12232,f11280,f8698,f12268]) ).
fof(f11280,plain,
( spl0_1454
<=> ! [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_1454])]) ).
fof(f12232,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_1027
| ~ spl0_1454 ),
inference(superposition,[],[f11281,f8700]) ).
fof(f11281,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_1454 ),
inference(avatar_component_clause,[],[f11280]) ).
fof(f11949,plain,
( spl0_1477
| ~ spl0_662
| ~ spl0_818
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f9998,f9686,f7639,f6196,f11946]) ).
fof(f11946,plain,
( spl0_1477
<=> c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f6196,plain,
( spl0_662
<=> c_emptyset = c_Message_Oparts(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f7639,plain,
( spl0_818
<=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f9998,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_662
| ~ spl0_818
| ~ spl0_1216 ),
inference(forward_demodulation,[],[f9993,f7640]) ).
fof(f7640,plain,
( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
| ~ spl0_818 ),
inference(avatar_component_clause,[],[f7639]) ).
fof(f9993,plain,
( c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg) = c_Message_Oparts(c_Message_Osynth(c_emptyset))
| ~ spl0_662
| ~ spl0_1216 ),
inference(superposition,[],[f9687,f6198]) ).
fof(f6198,plain,
( c_emptyset = c_Message_Oparts(c_emptyset)
| ~ spl0_662 ),
inference(avatar_component_clause,[],[f6196]) ).
fof(f11862,plain,
( spl0_1476
| ~ spl0_665
| ~ spl0_818
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f9992,f9682,f7639,f6211,f11859]) ).
fof(f11859,plain,
( spl0_1476
<=> c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f6211,plain,
( spl0_665
<=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f9992,plain,
( c_Message_Osynth(c_emptyset) = c_Message_Oanalz(c_Message_Osynth(c_emptyset))
| ~ spl0_665
| ~ spl0_818
| ~ spl0_1215 ),
inference(forward_demodulation,[],[f9987,f7640]) ).
fof(f9987,plain,
( c_Message_Oanalz(c_Message_Osynth(c_emptyset)) = c_union(c_emptyset,c_Message_Osynth(c_emptyset),tc_Message_Omsg)
| ~ spl0_665
| ~ spl0_1215 ),
inference(superposition,[],[f9683,f6213]) ).
fof(f6213,plain,
( c_emptyset = c_Message_Oanalz(c_emptyset)
| ~ spl0_665 ),
inference(avatar_component_clause,[],[f6211]) ).
fof(f11649,plain,
( spl0_1475
| ~ spl0_729
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f9959,f9610,f7260,f11647]) ).
fof(f11647,plain,
( spl0_1475
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f7260,plain,
( spl0_729
<=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f9610,plain,
( spl0_1197
<=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f9959,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_729
| ~ spl0_1197 ),
inference(superposition,[],[f9611,f7261]) ).
fof(f7261,plain,
( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
| ~ spl0_729 ),
inference(avatar_component_clause,[],[f7260]) ).
fof(f9611,plain,
( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f9610]) ).
fof(f11444,plain,
( spl0_1474
| ~ spl0_1129
| ~ spl0_1336 ),
inference(avatar_split_clause,[],[f11388,f10797,f9163,f11442]) ).
fof(f9163,plain,
( spl0_1129
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f10797,plain,
( spl0_1336
<=> ! [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_1336])]) ).
fof(f11388,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1129
| ~ spl0_1336 ),
inference(resolution,[],[f10798,f9164]) ).
fof(f9164,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1129 ),
inference(avatar_component_clause,[],[f9163]) ).
fof(f10798,plain,
( ! [X1,X12,X13] :
( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1336 ),
inference(avatar_component_clause,[],[f10797]) ).
fof(f11358,plain,
spl0_1473,
inference(avatar_split_clause,[],[f3386,f11356]) ).
fof(f11356,plain,
( spl0_1473
<=> ! [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_1473])]) ).
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(f11354,plain,
spl0_1472,
inference(avatar_split_clause,[],[f3314,f11352]) ).
fof(f11352,plain,
( spl0_1472
<=> ! [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_1472])]) ).
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(f11350,plain,
spl0_1471,
inference(avatar_split_clause,[],[f3307,f11348]) ).
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(f11346,plain,
spl0_1470,
inference(avatar_split_clause,[],[f3120,f11344]) ).
fof(f11344,plain,
( spl0_1470
<=> ! [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_1470])]) ).
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(f11342,plain,
spl0_1469,
inference(avatar_split_clause,[],[f3119,f11340]) ).
fof(f11340,plain,
( spl0_1469
<=> ! [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_1469])]) ).
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(f11338,plain,
spl0_1468,
inference(avatar_split_clause,[],[f3110,f11336]) ).
fof(f11336,plain,
( spl0_1468
<=> ! [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_1468])]) ).
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(f11334,plain,
( spl0_1467
| ~ spl0_653
| ~ spl0_1167 ),
inference(avatar_split_clause,[],[f9876,f9489,f6157,f11332]) ).
fof(f11332,plain,
( spl0_1467
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f6157,plain,
( spl0_653
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f9876,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_653
| ~ spl0_1167 ),
inference(resolution,[],[f9490,f6158]) ).
fof(f6158,plain,
( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
| ~ spl0_653 ),
inference(avatar_component_clause,[],[f6157]) ).
fof(f11330,plain,
spl0_1466,
inference(avatar_split_clause,[],[f3034,f11328]) ).
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(f11326,plain,
spl0_1465,
inference(avatar_split_clause,[],[f3031,f11324]) ).
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(f11322,plain,
spl0_1464,
inference(avatar_split_clause,[],[f3030,f11320]) ).
fof(f11320,plain,
( spl0_1464
<=> ! [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_1464])]) ).
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(f11318,plain,
spl0_1463,
inference(avatar_split_clause,[],[f2935,f11316]) ).
fof(f11316,plain,
( spl0_1463
<=> ! [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_1463])]) ).
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(f11314,plain,
spl0_1462,
inference(avatar_split_clause,[],[f2897,f11312]) ).
fof(f11312,plain,
( spl0_1462
<=> ! [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_1462])]) ).
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(f11310,plain,
spl0_1461,
inference(avatar_split_clause,[],[f2893,f11308]) ).
fof(f11308,plain,
( spl0_1461
<=> ! [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_1461])]) ).
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(f11306,plain,
spl0_1460,
inference(avatar_split_clause,[],[f2892,f11304]) ).
fof(f11304,plain,
( spl0_1460
<=> ! [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_1460])]) ).
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(f11302,plain,
spl0_1459,
inference(avatar_split_clause,[],[f2851,f11300]) ).
fof(f11300,plain,
( spl0_1459
<=> ! [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_1459])]) ).
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(f11298,plain,
spl0_1458,
inference(avatar_split_clause,[],[f2834,f11296]) ).
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(f11294,plain,
spl0_1457,
inference(avatar_split_clause,[],[f2833,f11292]) ).
fof(f11292,plain,
( spl0_1457
<=> ! [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_1457])]) ).
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(f11290,plain,
( spl0_1456
| ~ spl0_653
| ~ spl0_1164 ),
inference(avatar_split_clause,[],[f9866,f9476,f6157,f11288]) ).
fof(f11288,plain,
( spl0_1456
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f9476,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(f9866,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_653
| ~ spl0_1164 ),
inference(resolution,[],[f9477,f6158]) ).
fof(f9477,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,[],[f9476]) ).
fof(f11286,plain,
spl0_1455,
inference(avatar_split_clause,[],[f2796,f11284]) ).
fof(f11284,plain,
( spl0_1455
<=> ! [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_1455])]) ).
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(f11282,plain,
spl0_1454,
inference(avatar_split_clause,[],[f2794,f11280]) ).
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(f11278,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2783,f11276]) ).
fof(f11276,plain,
( spl0_1453
<=> ! [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_1453])]) ).
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(f11274,plain,
spl0_1452,
inference(avatar_split_clause,[],[f2782,f11272]) ).
fof(f11272,plain,
( spl0_1452
<=> ! [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_1452])]) ).
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(f11270,plain,
spl0_1451,
inference(avatar_split_clause,[],[f2781,f11268]) ).
fof(f11268,plain,
( spl0_1451
<=> ! [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_1451])]) ).
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(f11266,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2774,f11264]) ).
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(f11262,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2771,f11260]) ).
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(f11258,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2768,f11256]) ).
fof(f11256,plain,
( spl0_1448
<=> ! [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_1448])]) ).
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(f11254,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2742,f11252]) ).
fof(f11252,plain,
( spl0_1447
<=> ! [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_1447])]) ).
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(f11250,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2729,f11248]) ).
fof(f11248,plain,
( spl0_1446
<=> ! [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_1446])]) ).
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(f11245,plain,
spl0_1445,
inference(avatar_split_clause,[],[f2728,f11243]) ).
fof(f11243,plain,
( spl0_1445
<=> ! [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_1445])]) ).
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(f11241,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2703,f11239]) ).
fof(f11239,plain,
( spl0_1444
<=> ! [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_1444])]) ).
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(f11237,plain,
spl0_1443,
inference(avatar_split_clause,[],[f2701,f11235]) ).
fof(f11235,plain,
( spl0_1443
<=> ! [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_1443])]) ).
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(f11233,plain,
spl0_1442,
inference(avatar_split_clause,[],[f2692,f11231]) ).
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(f11229,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2688,f11227]) ).
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(f11225,plain,
spl0_1440,
inference(avatar_split_clause,[],[f2676,f11223]) ).
fof(f11223,plain,
( spl0_1440
<=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
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(f11221,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2670,f11219]) ).
fof(f11219,plain,
( spl0_1439
<=> ! [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_1439])]) ).
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(f11217,plain,
spl0_1438,
inference(avatar_split_clause,[],[f2653,f11215]) ).
fof(f11215,plain,
( spl0_1438
<=> ! [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_1438])]) ).
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(f11213,plain,
spl0_1437,
inference(avatar_split_clause,[],[f2628,f11211]) ).
fof(f11211,plain,
( spl0_1437
<=> ! [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_1437])]) ).
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(f11209,plain,
spl0_1436,
inference(avatar_split_clause,[],[f2627,f11207]) ).
fof(f11207,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(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(f11201,plain,
spl0_1435,
inference(avatar_split_clause,[],[f2617,f11199]) ).
fof(f11199,plain,
( spl0_1435
<=> ! [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_1435])]) ).
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(f11197,plain,
spl0_1434,
inference(avatar_split_clause,[],[f2614,f11195]) ).
fof(f11195,plain,
( spl0_1434
<=> ! [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_1434])]) ).
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(f11193,plain,
spl0_1433,
inference(avatar_split_clause,[],[f2595,f11191]) ).
fof(f11191,plain,
( spl0_1433
<=> ! [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_1433])]) ).
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(f11189,plain,
spl0_1432,
inference(avatar_split_clause,[],[f2594,f11187]) ).
fof(f11187,plain,
( spl0_1432
<=> ! [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_1432])]) ).
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(f11185,plain,
spl0_1431,
inference(avatar_split_clause,[],[f2592,f11183]) ).
fof(f11183,plain,
( spl0_1431
<=> ! [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_1431])]) ).
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(f11181,plain,
spl0_1430,
inference(avatar_split_clause,[],[f2591,f11179]) ).
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(f11177,plain,
spl0_1429,
inference(avatar_split_clause,[],[f2581,f11175]) ).
fof(f11175,plain,
( spl0_1429
<=> ! [X13,X12,X1] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
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(f11173,plain,
spl0_1428,
inference(avatar_split_clause,[],[f2570,f11171]) ).
fof(f11171,plain,
( spl0_1428
<=> ! [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_1428])]) ).
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(f11169,plain,
spl0_1427,
inference(avatar_split_clause,[],[f2569,f11167]) ).
fof(f11167,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(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(f11165,plain,
spl0_1426,
inference(avatar_split_clause,[],[f2568,f11163]) ).
fof(f11163,plain,
( spl0_1426
<=> ! [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_1426])]) ).
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(f11161,plain,
spl0_1425,
inference(avatar_split_clause,[],[f2559,f11159]) ).
fof(f11159,plain,
( spl0_1425
<=> ! [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_1425])]) ).
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(f11157,plain,
spl0_1424,
inference(avatar_split_clause,[],[f2558,f11155]) ).
fof(f11155,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(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(f11153,plain,
spl0_1423,
inference(avatar_split_clause,[],[f2557,f11151]) ).
fof(f11151,plain,
( spl0_1423
<=> ! [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_1423])]) ).
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(f11149,plain,
spl0_1422,
inference(avatar_split_clause,[],[f2550,f11147]) ).
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(f11145,plain,
spl0_1421,
inference(avatar_split_clause,[],[f2546,f11143]) ).
fof(f11143,plain,
( spl0_1421
<=> ! [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_1421])]) ).
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(f11141,plain,
spl0_1420,
inference(avatar_split_clause,[],[f2543,f11139]) ).
fof(f11139,plain,
( spl0_1420
<=> ! [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_1420])]) ).
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(f11137,plain,
spl0_1419,
inference(avatar_split_clause,[],[f2537,f11135]) ).
fof(f11135,plain,
( spl0_1419
<=> ! [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_1419])]) ).
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(f11133,plain,
spl0_1418,
inference(avatar_split_clause,[],[f2536,f11131]) ).
fof(f11131,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(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(f11129,plain,
spl0_1417,
inference(avatar_split_clause,[],[f2535,f11127]) ).
fof(f11127,plain,
( spl0_1417
<=> ! [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_1417])]) ).
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(f11125,plain,
spl0_1416,
inference(avatar_split_clause,[],[f2531,f11123]) ).
fof(f11123,plain,
( spl0_1416
<=> ! [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_1416])]) ).
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(f11118,plain,
spl0_1415,
inference(avatar_split_clause,[],[f2530,f11116]) ).
fof(f11116,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(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(f11114,plain,
spl0_1414,
inference(avatar_split_clause,[],[f2529,f11112]) ).
fof(f11112,plain,
( spl0_1414
<=> ! [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_1414])]) ).
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(f11110,plain,
spl0_1413,
inference(avatar_split_clause,[],[f2523,f11108]) ).
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(f11106,plain,
spl0_1412,
inference(avatar_split_clause,[],[f2518,f11104]) ).
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(f11102,plain,
spl0_1411,
inference(avatar_split_clause,[],[f2517,f11100]) ).
fof(f11100,plain,
( spl0_1411
<=> ! [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_1411])]) ).
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(f11098,plain,
spl0_1410,
inference(avatar_split_clause,[],[f2516,f11096]) ).
fof(f11096,plain,
( spl0_1410
<=> ! [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_1410])]) ).
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(f11094,plain,
spl0_1409,
inference(avatar_split_clause,[],[f2515,f11092]) ).
fof(f11092,plain,
( spl0_1409
<=> ! [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_1409])]) ).
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(f11090,plain,
spl0_1408,
inference(avatar_split_clause,[],[f2514,f11088]) ).
fof(f11088,plain,
( spl0_1408
<=> ! [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_1408])]) ).
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(f11086,plain,
spl0_1407,
inference(avatar_split_clause,[],[f2302,f11084]) ).
fof(f11084,plain,
( spl0_1407
<=> ! [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_1407])]) ).
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(f11082,plain,
spl0_1406,
inference(avatar_split_clause,[],[f2301,f11080]) ).
fof(f11080,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(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(f11078,plain,
spl0_1405,
inference(avatar_split_clause,[],[f2300,f11076]) ).
fof(f11076,plain,
( spl0_1405
<=> ! [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_1405])]) ).
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(f11074,plain,
spl0_1404,
inference(avatar_split_clause,[],[f2299,f11072]) ).
fof(f11072,plain,
( spl0_1404
<=> ! [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_1404])]) ).
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(f11070,plain,
spl0_1403,
inference(avatar_split_clause,[],[f2296,f11068]) ).
fof(f11068,plain,
( spl0_1403
<=> ! [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_1403])]) ).
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(f11066,plain,
spl0_1402,
inference(avatar_split_clause,[],[f2289,f11064]) ).
fof(f11064,plain,
( spl0_1402
<=> ! [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_1402])]) ).
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(f11062,plain,
spl0_1401,
inference(avatar_split_clause,[],[f2288,f11060]) ).
fof(f11060,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(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(f11058,plain,
spl0_1400,
inference(avatar_split_clause,[],[f2287,f11056]) ).
fof(f11056,plain,
( spl0_1400
<=> ! [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_1400])]) ).
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(f11054,plain,
spl0_1399,
inference(avatar_split_clause,[],[f2286,f11052]) ).
fof(f11052,plain,
( spl0_1399
<=> ! [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_1399])]) ).
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(f11050,plain,
spl0_1398,
inference(avatar_split_clause,[],[f2283,f11048]) ).
fof(f11048,plain,
( spl0_1398
<=> ! [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_1398])]) ).
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(f11046,plain,
spl0_1397,
inference(avatar_split_clause,[],[f2277,f11044]) ).
fof(f11044,plain,
( spl0_1397
<=> ! [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_1397])]) ).
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(f11042,plain,
spl0_1396,
inference(avatar_split_clause,[],[f2276,f11040]) ).
fof(f11040,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(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(f11038,plain,
spl0_1395,
inference(avatar_split_clause,[],[f2275,f11036]) ).
fof(f11036,plain,
( spl0_1395
<=> ! [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_1395])]) ).
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(f11034,plain,
spl0_1394,
inference(avatar_split_clause,[],[f2274,f11032]) ).
fof(f11032,plain,
( spl0_1394
<=> ! [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_1394])]) ).
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(f11030,plain,
spl0_1393,
inference(avatar_split_clause,[],[f2234,f11028]) ).
fof(f11028,plain,
( spl0_1393
<=> ! [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_1393])]) ).
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(f11026,plain,
spl0_1392,
inference(avatar_split_clause,[],[f2233,f11024]) ).
fof(f11024,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(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(f11022,plain,
spl0_1391,
inference(avatar_split_clause,[],[f2230,f11020]) ).
fof(f11020,plain,
( spl0_1391
<=> ! [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_1391])]) ).
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(f11018,plain,
spl0_1390,
inference(avatar_split_clause,[],[f2229,f11016]) ).
fof(f11016,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(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(f11014,plain,
spl0_1389,
inference(avatar_split_clause,[],[f2227,f11012]) ).
fof(f11012,plain,
( spl0_1389
<=> ! [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_1389])]) ).
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(f11010,plain,
spl0_1388,
inference(avatar_split_clause,[],[f2224,f11008]) ).
fof(f11008,plain,
( spl0_1388
<=> ! [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_1388])]) ).
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(f11006,plain,
spl0_1387,
inference(avatar_split_clause,[],[f2223,f11004]) ).
fof(f11004,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(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(f11002,plain,
spl0_1386,
inference(avatar_split_clause,[],[f2222,f11000]) ).
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(f10998,plain,
spl0_1385,
inference(avatar_split_clause,[],[f2221,f10996]) ).
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(f10994,plain,
spl0_1384,
inference(avatar_split_clause,[],[f2167,f10992]) ).
fof(f10992,plain,
( spl0_1384
<=> ! [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_1384])]) ).
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(f10990,plain,
spl0_1383,
inference(avatar_split_clause,[],[f2166,f10988]) ).
fof(f10988,plain,
( spl0_1383
<=> ! [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_1383])]) ).
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(f10986,plain,
spl0_1382,
inference(avatar_split_clause,[],[f2086,f10984]) ).
fof(f10984,plain,
( spl0_1382
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
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(f10982,plain,
spl0_1381,
inference(avatar_split_clause,[],[f2081,f10980]) ).
fof(f10980,plain,
( spl0_1381
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
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(f10978,plain,
spl0_1380,
inference(avatar_split_clause,[],[f2065,f10976]) ).
fof(f10976,plain,
( spl0_1380
<=> ! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
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(f10974,plain,
spl0_1379,
inference(avatar_split_clause,[],[f1850,f10972]) ).
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(f10970,plain,
spl0_1378,
inference(avatar_split_clause,[],[f1813,f10968]) ).
fof(f10968,plain,
( spl0_1378
<=> ! [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_1378])]) ).
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(f10966,plain,
spl0_1377,
inference(avatar_split_clause,[],[f1807,f10964]) ).
fof(f10964,plain,
( spl0_1377
<=> ! [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_1377])]) ).
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(f10962,plain,
spl0_1376,
inference(avatar_split_clause,[],[f1806,f10960]) ).
fof(f10960,plain,
( spl0_1376
<=> ! [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_1376])]) ).
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(f10958,plain,
( spl0_1375
| ~ spl0_720
| ~ spl0_801
| ~ spl0_1122 ),
inference(avatar_split_clause,[],[f9338,f9089,f7570,f7221,f10955]) ).
fof(f9338,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_720
| ~ spl0_801
| ~ spl0_1122 ),
inference(forward_demodulation,[],[f9335,f7223]) ).
fof(f9335,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_801
| ~ spl0_1122 ),
inference(superposition,[],[f9090,f7572]) ).
fof(f10953,plain,
spl0_1374,
inference(avatar_split_clause,[],[f1784,f10951]) ).
fof(f10951,plain,
( spl0_1374
<=> ! [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_1374])]) ).
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(f10949,plain,
spl0_1373,
inference(avatar_split_clause,[],[f1743,f10947]) ).
fof(f10947,plain,
( spl0_1373
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
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(f10945,plain,
spl0_1372,
inference(avatar_split_clause,[],[f1737,f10943]) ).
fof(f10943,plain,
( spl0_1372
<=> ! [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_1372])]) ).
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(f10941,plain,
spl0_1371,
inference(avatar_split_clause,[],[f1626,f10939]) ).
fof(f10939,plain,
( spl0_1371
<=> ! [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_1371])]) ).
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(f10937,plain,
spl0_1370,
inference(avatar_split_clause,[],[f1625,f10935]) ).
fof(f10935,plain,
( spl0_1370
<=> ! [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_1370])]) ).
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(f10933,plain,
spl0_1369,
inference(avatar_split_clause,[],[f1610,f10931]) ).
fof(f10931,plain,
( spl0_1369
<=> ! [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_1369])]) ).
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(f10929,plain,
spl0_1368,
inference(avatar_split_clause,[],[f1552,f10927]) ).
fof(f10927,plain,
( spl0_1368
<=> ! [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_1368])]) ).
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(f10925,plain,
spl0_1367,
inference(avatar_split_clause,[],[f1530,f10923]) ).
fof(f10923,plain,
( spl0_1367
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
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(f10921,plain,
spl0_1366,
inference(avatar_split_clause,[],[f1493,f10919]) ).
fof(f10919,plain,
( spl0_1366
<=> ! [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_1366])]) ).
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(f10917,plain,
spl0_1365,
inference(avatar_split_clause,[],[f1492,f10915]) ).
fof(f10915,plain,
( spl0_1365
<=> ! [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_1365])]) ).
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(f10913,plain,
spl0_1364,
inference(avatar_split_clause,[],[f1485,f10911]) ).
fof(f10911,plain,
( spl0_1364
<=> ! [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_1364])]) ).
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(f10908,plain,
( spl0_1363
| ~ spl0_920
| ~ spl0_1362 ),
inference(avatar_split_clause,[],[f10904,f10901,f8118,f10906]) ).
fof(f10906,plain,
( spl0_1363
<=> ! [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_1363])]) ).
fof(f8118,plain,
( spl0_920
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f10901,plain,
( spl0_1362
<=> ! [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_1362])]) ).
fof(f10904,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_920
| ~ spl0_1362 ),
inference(forward_demodulation,[],[f10902,f8120]) ).
fof(f8120,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_920 ),
inference(avatar_component_clause,[],[f8118]) ).
fof(f10902,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_1362 ),
inference(avatar_component_clause,[],[f10901]) ).
fof(f10903,plain,
spl0_1362,
inference(avatar_split_clause,[],[f1484,f10901]) ).
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(f10899,plain,
spl0_1361,
inference(avatar_split_clause,[],[f1477,f10897]) ).
fof(f10897,plain,
( spl0_1361
<=> ! [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_1361])]) ).
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(f10895,plain,
spl0_1360,
inference(avatar_split_clause,[],[f1476,f10893]) ).
fof(f10893,plain,
( spl0_1360
<=> ! [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_1360])]) ).
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(f10891,plain,
spl0_1359,
inference(avatar_split_clause,[],[f1457,f10889]) ).
fof(f10889,plain,
( spl0_1359
<=> ! [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_1359])]) ).
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(f10887,plain,
spl0_1358,
inference(avatar_split_clause,[],[f1442,f10885]) ).
fof(f10885,plain,
( spl0_1358
<=> ! [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_1358])]) ).
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(f10883,plain,
spl0_1357,
inference(avatar_split_clause,[],[f1413,f10881]) ).
fof(f10881,plain,
( spl0_1357
<=> ! [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_1357])]) ).
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(f10879,plain,
spl0_1356,
inference(avatar_split_clause,[],[f1412,f10877]) ).
fof(f10877,plain,
( spl0_1356
<=> ! [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_1356])]) ).
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(f10875,plain,
( spl0_1354
| ~ spl0_1355
| ~ spl0_803
| ~ spl0_1081 ),
inference(avatar_split_clause,[],[f9275,f8923,f7579,f10872,f10869]) ).
fof(f10869,plain,
( spl0_1354
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f10872,plain,
( spl0_1355
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f7579,plain,
( spl0_803
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f8923,plain,
( spl0_1081
<=> ! [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_1081])]) ).
fof(f9275,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_803
| ~ spl0_1081 ),
inference(superposition,[],[f8924,f7580]) ).
fof(f7580,plain,
( ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat)
| ~ spl0_803 ),
inference(avatar_component_clause,[],[f7579]) ).
fof(f8924,plain,
( ! [X3,X0] :
( ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_1081 ),
inference(avatar_component_clause,[],[f8923]) ).
fof(f10867,plain,
spl0_1353,
inference(avatar_split_clause,[],[f1409,f10865]) ).
fof(f10865,plain,
( spl0_1353
<=> ! [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_1353])]) ).
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(f10863,plain,
spl0_1352,
inference(avatar_split_clause,[],[f1408,f10861]) ).
fof(f10861,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(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(f10859,plain,
spl0_1351,
inference(avatar_split_clause,[],[f1406,f10857]) ).
fof(f10857,plain,
( spl0_1351
<=> ! [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_1351])]) ).
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(f10855,plain,
spl0_1350,
inference(avatar_split_clause,[],[f1400,f10853]) ).
fof(f10853,plain,
( spl0_1350
<=> ! [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_1350])]) ).
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(f10851,plain,
spl0_1349,
inference(avatar_split_clause,[],[f1399,f10849]) ).
fof(f10849,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(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(f10847,plain,
spl0_1348,
inference(avatar_split_clause,[],[f1398,f10845]) ).
fof(f10845,plain,
( spl0_1348
<=> ! [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_1348])]) ).
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(f10843,plain,
spl0_1347,
inference(avatar_split_clause,[],[f1397,f10841]) ).
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(f10839,plain,
spl0_1346,
inference(avatar_split_clause,[],[f1361,f10837]) ).
fof(f10837,plain,
( spl0_1346
<=> ! [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_1346])]) ).
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(f10835,plain,
spl0_1345,
inference(avatar_split_clause,[],[f1356,f10833]) ).
fof(f10833,plain,
( spl0_1345
<=> ! [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_1345])]) ).
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(f10831,plain,
spl0_1344,
inference(avatar_split_clause,[],[f1342,f10829]) ).
fof(f10829,plain,
( spl0_1344
<=> ! [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_1344])]) ).
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(f10827,plain,
spl0_1343,
inference(avatar_split_clause,[],[f1341,f10825]) ).
fof(f10825,plain,
( spl0_1343
<=> ! [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_1343])]) ).
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(f10823,plain,
spl0_1342,
inference(avatar_split_clause,[],[f1243,f10821]) ).
fof(f10821,plain,
( spl0_1342
<=> ! [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_1342])]) ).
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(f10819,plain,
spl0_1341,
inference(avatar_split_clause,[],[f1233,f10817]) ).
fof(f10817,plain,
( spl0_1341
<=> ! [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_1341])]) ).
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(f10815,plain,
spl0_1340,
inference(avatar_split_clause,[],[f1232,f10813]) ).
fof(f10813,plain,
( spl0_1340
<=> ! [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_1340])]) ).
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(f10811,plain,
spl0_1339,
inference(avatar_split_clause,[],[f1191,f10809]) ).
fof(f10809,plain,
( spl0_1339
<=> ! [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_1339])]) ).
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(f10807,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1189,f10805]) ).
fof(f10805,plain,
( spl0_1338
<=> ! [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_1338])]) ).
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(f10803,plain,
spl0_1337,
inference(avatar_split_clause,[],[f1185,f10801]) ).
fof(f10801,plain,
( spl0_1337
<=> ! [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_1337])]) ).
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(f10799,plain,
spl0_1336,
inference(avatar_split_clause,[],[f110,f10797]) ).
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(f10795,plain,
spl0_1335,
inference(avatar_split_clause,[],[f109,f10793]) ).
fof(f10793,plain,
( spl0_1335
<=> ! [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_1335])]) ).
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(f10791,plain,
spl0_1334,
inference(avatar_split_clause,[],[f49,f10789]) ).
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(f10787,plain,
( spl0_1333
| ~ spl0_769
| ~ spl0_1046 ),
inference(avatar_split_clause,[],[f9186,f8779,f7442,f10785]) ).
fof(f10785,plain,
( spl0_1333
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f7442,plain,
( spl0_769
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f8779,plain,
( spl0_1046
<=> ! [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_1046])]) ).
fof(f9186,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_769
| ~ spl0_1046 ),
inference(superposition,[],[f8780,f7443]) ).
fof(f7443,plain,
( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f7442]) ).
fof(f8780,plain,
( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
| ~ spl0_1046 ),
inference(avatar_component_clause,[],[f8779]) ).
fof(f10783,plain,
spl0_1332,
inference(avatar_split_clause,[],[f2,f10781]) ).
fof(f10781,plain,
( spl0_1332
<=> ! [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_1332])]) ).
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(f10779,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1,f10777]) ).
fof(f10777,plain,
( spl0_1331
<=> ! [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_1331])]) ).
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(f10632,plain,
( ~ spl0_1329
| spl0_1330
| ~ spl0_791
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f10590,f10218,f7530,f10630,f10626]) ).
fof(f10626,plain,
( spl0_1329
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f10630,plain,
( spl0_1330
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f10590,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_791
| ~ spl0_1291 ),
inference(trivial_inequality_removal,[],[f10583]) ).
fof(f10583,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_791
| ~ spl0_1291 ),
inference(superposition,[],[f10219,f7531]) ).
fof(f10445,plain,
( spl0_1328
| ~ spl0_60
| ~ spl0_1025 ),
inference(avatar_split_clause,[],[f8702,f8561,f3730,f10442]) ).
fof(f8561,plain,
( spl0_1025
<=> ! [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_1025])]) ).
fof(f8702,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1025 ),
inference(resolution,[],[f8562,f3732]) ).
fof(f8562,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
| ~ spl0_1025 ),
inference(avatar_component_clause,[],[f8561]) ).
fof(f10400,plain,
( spl0_1327
| ~ spl0_898
| ~ spl0_1000 ),
inference(avatar_split_clause,[],[f8670,f8458,f7972,f10397]) ).
fof(f10397,plain,
( spl0_1327
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f8670,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_898
| ~ spl0_1000 ),
inference(superposition,[],[f7973,f8460]) ).
fof(f10395,plain,
( spl0_1326
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_1249 ),
inference(avatar_split_clause,[],[f10052,f10049,f8902,f3730,f10393]) ).
fof(f10049,plain,
( spl0_1249
<=> ! [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_1249])]) ).
fof(f10052,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_60
| ~ spl0_1076
| ~ spl0_1249 ),
inference(forward_demodulation,[],[f10050,f9266]) ).
fof(f10050,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_1249 ),
inference(avatar_component_clause,[],[f10049]) ).
fof(f10361,plain,
spl0_1325,
inference(avatar_split_clause,[],[f3331,f10359]) ).
fof(f10359,plain,
( spl0_1325
<=> ! [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_1325])]) ).
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(f10357,plain,
spl0_1324,
inference(avatar_split_clause,[],[f3330,f10355]) ).
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(f10353,plain,
spl0_1323,
inference(avatar_split_clause,[],[f3324,f10351]) ).
fof(f10351,plain,
( spl0_1323
<=> ! [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_1323])]) ).
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(f10349,plain,
( spl0_1322
| ~ spl0_95
| ~ spl0_988 ),
inference(avatar_split_clause,[],[f8656,f8409,f3905,f10347]) ).
fof(f10347,plain,
( spl0_1322
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f3905,plain,
( spl0_95
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f8409,plain,
( spl0_988
<=> ! [X1,X3] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f8656,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_95
| ~ spl0_988 ),
inference(resolution,[],[f8410,f3907]) ).
fof(f3907,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f3905]) ).
fof(f8410,plain,
( ! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 )
| ~ spl0_988 ),
inference(avatar_component_clause,[],[f8409]) ).
fof(f10345,plain,
spl0_1321,
inference(avatar_split_clause,[],[f3259,f10343]) ).
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(f10341,plain,
spl0_1320,
inference(avatar_split_clause,[],[f3255,f10339]) ).
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(f10337,plain,
spl0_1319,
inference(avatar_split_clause,[],[f3251,f10335]) ).
fof(f10335,plain,
( spl0_1319
<=> ! [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_1319])]) ).
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(f10333,plain,
spl0_1318,
inference(avatar_split_clause,[],[f3037,f10331]) ).
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(f10325,plain,
( spl0_1317
| ~ spl0_1316 ),
inference(avatar_split_clause,[],[f10321,f10318,f10323]) ).
fof(f10318,plain,
( spl0_1316
<=> ! [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_1316])]) ).
fof(f10321,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(forward_demodulation,[],[f10319,f3034]) ).
fof(f10319,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_1316 ),
inference(avatar_component_clause,[],[f10318]) ).
fof(f10320,plain,
spl0_1316,
inference(avatar_split_clause,[],[f3025,f10318]) ).
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(f10316,plain,
spl0_1315,
inference(avatar_split_clause,[],[f2890,f10314]) ).
fof(f10314,plain,
( spl0_1315
<=> ! [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_1315])]) ).
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(f10312,plain,
spl0_1314,
inference(avatar_split_clause,[],[f2885,f10310]) ).
fof(f10310,plain,
( spl0_1314
<=> ! [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_1314])]) ).
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(f10308,plain,
spl0_1313,
inference(avatar_split_clause,[],[f2843,f10306]) ).
fof(f10306,plain,
( spl0_1313
<=> ! [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_1313])]) ).
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(f10304,plain,
( spl0_1312
| ~ spl0_61
| ~ spl0_988 ),
inference(avatar_split_clause,[],[f8655,f8409,f3735,f10302]) ).
fof(f3735,plain,
( spl0_61
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f8655,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_61
| ~ spl0_988 ),
inference(resolution,[],[f8410,f3737]) ).
fof(f3737,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f3735]) ).
fof(f10300,plain,
spl0_1311,
inference(avatar_split_clause,[],[f2831,f10298]) ).
fof(f10298,plain,
( spl0_1311
<=> ! [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_1311])]) ).
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(f10296,plain,
spl0_1310,
inference(avatar_split_clause,[],[f2793,f10294]) ).
fof(f10294,plain,
( spl0_1310
<=> ! [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_1310])]) ).
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(f10292,plain,
spl0_1309,
inference(avatar_split_clause,[],[f2715,f10290]) ).
fof(f10290,plain,
( spl0_1309
<=> ! [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_1309])]) ).
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(f10288,plain,
spl0_1308,
inference(avatar_split_clause,[],[f2713,f10286]) ).
fof(f10286,plain,
( spl0_1308
<=> ! [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_1308])]) ).
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(f10284,plain,
spl0_1307,
inference(avatar_split_clause,[],[f2685,f10282]) ).
fof(f10282,plain,
( spl0_1307
<=> ! [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_1307])]) ).
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(f10280,plain,
spl0_1306,
inference(avatar_split_clause,[],[f2642,f10278]) ).
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(f10276,plain,
spl0_1305,
inference(avatar_split_clause,[],[f2641,f10274]) ).
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(f10272,plain,
spl0_1304,
inference(avatar_split_clause,[],[f2583,f10270]) ).
fof(f10270,plain,
( spl0_1304
<=> ! [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_1304])]) ).
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(f10268,plain,
spl0_1303,
inference(avatar_split_clause,[],[f2582,f10266]) ).
fof(f10266,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(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(f10264,plain,
spl0_1302,
inference(avatar_split_clause,[],[f2545,f10262]) ).
fof(f10262,plain,
( spl0_1302
<=> ! [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_1302])]) ).
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(f10260,plain,
( spl0_1301
| ~ spl0_95
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f8654,f8405,f3905,f10258]) ).
fof(f10258,plain,
( spl0_1301
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f8405,plain,
( spl0_987
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f8654,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_95
| ~ spl0_987 ),
inference(resolution,[],[f8406,f3907]) ).
fof(f8406,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) )
| ~ spl0_987 ),
inference(avatar_component_clause,[],[f8405]) ).
fof(f10256,plain,
spl0_1300,
inference(avatar_split_clause,[],[f2542,f10254]) ).
fof(f10254,plain,
( spl0_1300
<=> ! [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_1300])]) ).
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(f10252,plain,
spl0_1299,
inference(avatar_split_clause,[],[f2522,f10250]) ).
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(f10248,plain,
spl0_1298,
inference(avatar_split_clause,[],[f2271,f10246]) ).
fof(f10246,plain,
( spl0_1298
<=> ! [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_1298])]) ).
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(f10244,plain,
spl0_1297,
inference(avatar_split_clause,[],[f2270,f10242]) ).
fof(f10242,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(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(f10240,plain,
spl0_1296,
inference(avatar_split_clause,[],[f2252,f10238]) ).
fof(f10238,plain,
( spl0_1296
<=> ! [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_1296])]) ).
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(f10236,plain,
spl0_1295,
inference(avatar_split_clause,[],[f2245,f10234]) ).
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(f10232,plain,
spl0_1294,
inference(avatar_split_clause,[],[f2244,f10230]) ).
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(f10228,plain,
spl0_1293,
inference(avatar_split_clause,[],[f2240,f10226]) ).
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(f10224,plain,
spl0_1292,
inference(avatar_split_clause,[],[f2239,f10222]) ).
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(f10220,plain,
spl0_1291,
inference(avatar_split_clause,[],[f2199,f10218]) ).
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(f10216,plain,
( spl0_1290
| ~ spl0_61
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f8653,f8405,f3735,f10214]) ).
fof(f10214,plain,
( spl0_1290
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f8653,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_61
| ~ spl0_987 ),
inference(resolution,[],[f8406,f3737]) ).
fof(f10212,plain,
spl0_1289,
inference(avatar_split_clause,[],[f2183,f10210]) ).
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(f10208,plain,
spl0_1288,
inference(avatar_split_clause,[],[f2181,f10206]) ).
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(f10204,plain,
spl0_1287,
inference(avatar_split_clause,[],[f2179,f10202]) ).
fof(f10202,plain,
( spl0_1287
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f2179,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f10200,plain,
spl0_1286,
inference(avatar_split_clause,[],[f2178,f10198]) ).
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(f10196,plain,
spl0_1285,
inference(avatar_split_clause,[],[f2147,f10194]) ).
fof(f10194,plain,
( spl0_1285
<=> ! [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_1285])]) ).
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(f10192,plain,
spl0_1284,
inference(avatar_split_clause,[],[f2127,f10190]) ).
fof(f10188,plain,
spl0_1283,
inference(avatar_split_clause,[],[f2104,f10186]) ).
fof(f10186,plain,
( spl0_1283
<=> ! [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_1283])]) ).
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(f10184,plain,
spl0_1282,
inference(avatar_split_clause,[],[f2103,f10182]) ).
fof(f10182,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(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(f10180,plain,
spl0_1281,
inference(avatar_split_clause,[],[f2079,f10178]) ).
fof(f10178,plain,
( spl0_1281
<=> ! [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_1281])]) ).
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(f10176,plain,
spl0_1280,
inference(avatar_split_clause,[],[f2078,f10174]) ).
fof(f10174,plain,
( spl0_1280
<=> ! [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_1280])]) ).
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(f10172,plain,
( spl0_1279
| ~ spl0_99
| ~ spl0_983 ),
inference(avatar_split_clause,[],[f8649,f8388,f3925,f10170]) ).
fof(f10170,plain,
( spl0_1279
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f8388,plain,
( spl0_983
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f8649,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_99
| ~ spl0_983 ),
inference(resolution,[],[f8389,f3927]) ).
fof(f8389,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 )
| ~ spl0_983 ),
inference(avatar_component_clause,[],[f8388]) ).
fof(f10168,plain,
spl0_1278,
inference(avatar_split_clause,[],[f2030,f10166]) ).
fof(f10166,plain,
( spl0_1278
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f2030,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f10164,plain,
spl0_1277,
inference(avatar_split_clause,[],[f2029,f10162]) ).
fof(f10162,plain,
( spl0_1277
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f2029,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f10160,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1851,f10158]) ).
fof(f10158,plain,
( spl0_1276
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1851,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f10156,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1814,f10154]) ).
fof(f10154,plain,
( spl0_1275
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1814,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f10152,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1761,f10150]) ).
fof(f10150,plain,
( spl0_1274
<=> ! [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_1274])]) ).
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(f10148,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1731,f10146]) ).
fof(f10146,plain,
( spl0_1273
<=> ! [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_1273])]) ).
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(f10144,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1712,f10142]) ).
fof(f10142,plain,
( spl0_1272
<=> ! [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_1272])]) ).
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(f10140,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1613,f10138]) ).
fof(f10138,plain,
( spl0_1271
<=> ! [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_1271])]) ).
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(f10136,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1609,f10134]) ).
fof(f10134,plain,
( spl0_1270
<=> ! [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_1270])]) ).
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(f10132,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1608,f10130]) ).
fof(f10130,plain,
( spl0_1269
<=> ! [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_1269])]) ).
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(f10128,plain,
( spl0_1268
| ~ spl0_35
| ~ spl0_983 ),
inference(avatar_split_clause,[],[f8648,f8388,f3605,f10126]) ).
fof(f10126,plain,
( spl0_1268
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f8648,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_35
| ~ spl0_983 ),
inference(resolution,[],[f8389,f3607]) ).
fof(f10124,plain,
spl0_1267,
inference(avatar_split_clause,[],[f1595,f10122]) ).
fof(f10122,plain,
( spl0_1267
<=> ! [X1,X23,X3] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f1595,axiom,
! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f10120,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1594,f10118]) ).
fof(f10118,plain,
( spl0_1266
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f1594,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f10116,plain,
spl0_1265,
inference(avatar_split_clause,[],[f1593,f10114]) ).
fof(f10114,plain,
( spl0_1265
<=> ! [X60,X1] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f1593,axiom,
! [X1,X60] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f10112,plain,
spl0_1264,
inference(avatar_split_clause,[],[f1584,f10110]) ).
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(f10108,plain,
spl0_1263,
inference(avatar_split_clause,[],[f1583,f10106]) ).
fof(f10106,plain,
( spl0_1263
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
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(f10104,plain,
spl0_1262,
inference(avatar_split_clause,[],[f1582,f10102]) ).
fof(f10102,plain,
( spl0_1262
<=> ! [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_1262])]) ).
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(f10100,plain,
spl0_1261,
inference(avatar_split_clause,[],[f1539,f10098]) ).
fof(f10098,plain,
( spl0_1261
<=> ! [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_1261])]) ).
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(f10096,plain,
spl0_1260,
inference(avatar_split_clause,[],[f1463,f10094]) ).
fof(f10094,plain,
( spl0_1260
<=> ! [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_1260])]) ).
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(f10092,plain,
spl0_1259,
inference(avatar_split_clause,[],[f1462,f10090]) ).
fof(f10090,plain,
( spl0_1259
<=> ! [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_1259])]) ).
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(f10088,plain,
spl0_1258,
inference(avatar_split_clause,[],[f1455,f10086]) ).
fof(f10086,plain,
( spl0_1258
<=> ! [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_1258])]) ).
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(f10084,plain,
( spl0_1257
| ~ spl0_99
| ~ spl0_982 ),
inference(avatar_split_clause,[],[f8647,f8384,f3925,f10082]) ).
fof(f10082,plain,
( spl0_1257
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f8384,plain,
( spl0_982
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f8647,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_99
| ~ spl0_982 ),
inference(resolution,[],[f8385,f3927]) ).
fof(f8385,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 )
| ~ spl0_982 ),
inference(avatar_component_clause,[],[f8384]) ).
fof(f10080,plain,
spl0_1256,
inference(avatar_split_clause,[],[f1454,f10078]) ).
fof(f10078,plain,
( spl0_1256
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f1454,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f10076,plain,
spl0_1255,
inference(avatar_split_clause,[],[f1418,f10074]) ).
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(f10072,plain,
spl0_1254,
inference(avatar_split_clause,[],[f1354,f10070]) ).
fof(f10070,plain,
( spl0_1254
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f1354,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f10068,plain,
spl0_1253,
inference(avatar_split_clause,[],[f1353,f10066]) ).
fof(f10066,plain,
( spl0_1253
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f1353,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f10064,plain,
spl0_1252,
inference(avatar_split_clause,[],[f1352,f10062]) ).
fof(f10062,plain,
( spl0_1252
<=> ! [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_1252])]) ).
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(f10060,plain,
spl0_1251,
inference(avatar_split_clause,[],[f1351,f10058]) ).
fof(f10058,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(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(f10056,plain,
spl0_1250,
inference(avatar_split_clause,[],[f1348,f10054]) ).
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(f10051,plain,
spl0_1249,
inference(avatar_split_clause,[],[f1345,f10049]) ).
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(f10047,plain,
spl0_1248,
inference(avatar_split_clause,[],[f1310,f10045]) ).
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(f10043,plain,
spl0_1247,
inference(avatar_split_clause,[],[f1307,f10041]) ).
fof(f10041,plain,
( spl0_1247
<=> ! [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_1247])]) ).
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(f10039,plain,
( spl0_1246
| ~ spl0_35
| ~ spl0_982 ),
inference(avatar_split_clause,[],[f8646,f8384,f3605,f10037]) ).
fof(f10037,plain,
( spl0_1246
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f8646,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_35
| ~ spl0_982 ),
inference(resolution,[],[f8385,f3607]) ).
fof(f10035,plain,
spl0_1245,
inference(avatar_split_clause,[],[f1236,f10033]) ).
fof(f10033,plain,
( spl0_1245
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f1236,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f10031,plain,
spl0_1244,
inference(avatar_split_clause,[],[f1234,f10029]) ).
fof(f10029,plain,
( spl0_1244
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f1234,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f10027,plain,
spl0_1243,
inference(avatar_split_clause,[],[f1178,f10025]) ).
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(f10023,plain,
spl0_1242,
inference(avatar_split_clause,[],[f1166,f10021]) ).
fof(f10021,plain,
( spl0_1242
<=> ! [X0,X1,X40] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f1166,axiom,
! [X40,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f10006,plain,
( spl0_1241
| ~ spl0_72
| ~ spl0_978 ),
inference(avatar_split_clause,[],[f8640,f8368,f3790,f10004]) ).
fof(f10004,plain,
( spl0_1241
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f3790,plain,
( spl0_72
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f8368,plain,
( spl0_978
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f8640,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_72
| ~ spl0_978 ),
inference(resolution,[],[f8369,f3792]) ).
fof(f3792,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f3790]) ).
fof(f8369,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 )
| ~ spl0_978 ),
inference(avatar_component_clause,[],[f8368]) ).
fof(f9978,plain,
( spl0_1240
| ~ spl0_23
| ~ spl0_978 ),
inference(avatar_split_clause,[],[f8639,f8368,f3545,f9976]) ).
fof(f9976,plain,
( spl0_1240
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f3545,plain,
( spl0_23
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f8639,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_23
| ~ spl0_978 ),
inference(resolution,[],[f8369,f3547]) ).
fof(f3547,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f3545]) ).
fof(f9966,plain,
( spl0_1239
| ~ spl0_72
| ~ spl0_977 ),
inference(avatar_split_clause,[],[f8638,f8364,f3790,f9964]) ).
fof(f9964,plain,
( spl0_1239
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f8364,plain,
( spl0_977
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f8638,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_72
| ~ spl0_977 ),
inference(resolution,[],[f8365,f3792]) ).
fof(f8365,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 )
| ~ spl0_977 ),
inference(avatar_component_clause,[],[f8364]) ).
fof(f9950,plain,
( spl0_1238
| ~ spl0_23
| ~ spl0_977 ),
inference(avatar_split_clause,[],[f8637,f8364,f3545,f9948]) ).
fof(f9948,plain,
( spl0_1238
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f8637,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_23
| ~ spl0_977 ),
inference(resolution,[],[f8365,f3547]) ).
fof(f9909,plain,
( spl0_1237
| ~ spl0_17
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f8636,f8360,f3515,f9907]) ).
fof(f9907,plain,
( spl0_1237
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f8360,plain,
( spl0_976
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f8636,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_17
| ~ spl0_976 ),
inference(resolution,[],[f8361,f3517]) ).
fof(f8361,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) )
| ~ spl0_976 ),
inference(avatar_component_clause,[],[f8360]) ).
fof(f9875,plain,
( spl0_1236
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_1166 ),
inference(avatar_split_clause,[],[f9487,f9484,f8902,f3730,f9873]) ).
fof(f9873,plain,
( spl0_1236
<=> ! [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_1236])]) ).
fof(f9484,plain,
( spl0_1166
<=> ! [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_1166])]) ).
fof(f9487,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_1076
| ~ spl0_1166 ),
inference(forward_demodulation,[],[f9485,f9266]) ).
fof(f9485,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_1166 ),
inference(avatar_component_clause,[],[f9484]) ).
fof(f9830,plain,
( spl0_1235
| spl0_688
| ~ spl0_1152 ),
inference(avatar_split_clause,[],[f9812,f9428,f7074,f9827]) ).
fof(f9827,plain,
( spl0_1235
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f7074,plain,
( spl0_688
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f9428,plain,
( spl0_1152
<=> ! [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_1152])]) ).
fof(f9812,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_688
| ~ spl0_1152 ),
inference(resolution,[],[f9429,f7076]) ).
fof(f7076,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_688 ),
inference(avatar_component_clause,[],[f7074]) ).
fof(f9429,plain,
( ! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_0 = c_Finite__Set_Ocard(X12,X1) )
| ~ spl0_1152 ),
inference(avatar_component_clause,[],[f9428]) ).
fof(f9794,plain,
( spl0_1234
| ~ spl0_17
| ~ spl0_975 ),
inference(avatar_split_clause,[],[f8635,f8356,f3515,f9792]) ).
fof(f9792,plain,
( spl0_1234
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f8356,plain,
( spl0_975
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f8635,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_17
| ~ spl0_975 ),
inference(resolution,[],[f8357,f3517]) ).
fof(f8357,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 )
| ~ spl0_975 ),
inference(avatar_component_clause,[],[f8356]) ).
fof(f9762,plain,
spl0_1233,
inference(avatar_split_clause,[],[f3381,f9760]) ).
fof(f9760,plain,
( spl0_1233
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(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(f9758,plain,
spl0_1232,
inference(avatar_split_clause,[],[f3262,f9756]) ).
fof(f9756,plain,
( spl0_1232
<=> ! [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_1232])]) ).
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(f9754,plain,
spl0_1231,
inference(avatar_split_clause,[],[f3258,f9752]) ).
fof(f9752,plain,
( spl0_1231
<=> ! [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_1231])]) ).
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(f9750,plain,
spl0_1230,
inference(avatar_split_clause,[],[f3257,f9748]) ).
fof(f9748,plain,
( spl0_1230
<=> ! [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_1230])]) ).
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(f9746,plain,
spl0_1229,
inference(avatar_split_clause,[],[f3126,f9744]) ).
fof(f9744,plain,
( spl0_1229
<=> ! [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_1229])]) ).
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(f9742,plain,
spl0_1228,
inference(avatar_split_clause,[],[f3112,f9740]) ).
fof(f9740,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(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(f9738,plain,
spl0_1227,
inference(avatar_split_clause,[],[f3039,f9736]) ).
fof(f9736,plain,
( spl0_1227
<=> ! [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_1227])]) ).
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(f9734,plain,
( spl0_1226
| ~ spl0_650
| ~ spl0_1206
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f9729,f9724,f9646,f6143,f9731]) ).
fof(f9731,plain,
( spl0_1226
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f9729,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_1206
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f9728,f9647]) ).
fof(f9728,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_1225 ),
inference(superposition,[],[f9725,f6145]) ).
fof(f9726,plain,
( spl0_1225
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f9722,f9719,f9724]) ).
fof(f9719,plain,
( spl0_1224
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f9722,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1224 ),
inference(forward_demodulation,[],[f9720,f3034]) ).
fof(f9720,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1224 ),
inference(avatar_component_clause,[],[f9719]) ).
fof(f9721,plain,
spl0_1224,
inference(avatar_split_clause,[],[f3023,f9719]) ).
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(f9717,plain,
spl0_1223,
inference(avatar_split_clause,[],[f3015,f9715]) ).
fof(f9715,plain,
( spl0_1223
<=> ! [X86,X107,X87,X91] : c_Message_Omsg_OCrypt(X91,X107) != c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X86,X87)),X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(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(f9713,plain,
( spl0_1222
| ~ spl0_818
| ~ spl0_1221 ),
inference(avatar_split_clause,[],[f9709,f9706,f7639,f9711]) ).
fof(f9711,plain,
( spl0_1222
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f9706,plain,
( spl0_1221
<=> ! [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_1221])]) ).
fof(f9709,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1)
| ~ spl0_818
| ~ spl0_1221 ),
inference(forward_demodulation,[],[f9707,f7640]) ).
fof(f9707,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1)
| ~ spl0_1221 ),
inference(avatar_component_clause,[],[f9706]) ).
fof(f9708,plain,
spl0_1221,
inference(avatar_split_clause,[],[f2983,f9706]) ).
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(f9704,plain,
spl0_1220,
inference(avatar_split_clause,[],[f2920,f9702]) ).
fof(f9702,plain,
( spl0_1220
<=> ! [X4,X27,X12,X111] :
( X12 = X111
| c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
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(f9700,plain,
spl0_1219,
inference(avatar_split_clause,[],[f2919,f9698]) ).
fof(f9698,plain,
( spl0_1219
<=> ! [X4,X111,X12,X27] :
( X4 = X27
| c_Public_OpublicKey(X27,X12) != c_Public_OpublicKey(X4,X111) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
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(f9696,plain,
spl0_1218,
inference(avatar_split_clause,[],[f2898,f9694]) ).
fof(f9694,plain,
( spl0_1218
<=> ! [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_1218])]) ).
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(f9692,plain,
( spl0_1217
| ~ spl0_12
| ~ spl0_974 ),
inference(avatar_split_clause,[],[f8633,f8352,f3490,f9690]) ).
fof(f9690,plain,
( spl0_1217
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f3490,plain,
( spl0_12
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f8352,plain,
( spl0_974
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f8633,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_12
| ~ spl0_974 ),
inference(resolution,[],[f8353,f3492]) ).
fof(f3492,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f3490]) ).
fof(f8353,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 )
| ~ spl0_974 ),
inference(avatar_component_clause,[],[f8352]) ).
fof(f9688,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2883,f9686]) ).
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(f9684,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2865,f9682]) ).
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(f9680,plain,
spl0_1214,
inference(avatar_split_clause,[],[f2852,f9678]) ).
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(f9676,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2800,f9674]) ).
fof(f9674,plain,
( spl0_1213
<=> ! [X102,X86,X12] : c_Event_Oused(X102) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f2800,axiom,
! [X86,X102,X12] : c_Event_Oused(X102) = c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(X12,X86),X102,tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Gets_0) ).
fof(f9672,plain,
spl0_1212,
inference(avatar_split_clause,[],[f2787,f9670]) ).
fof(f9670,plain,
( spl0_1212
<=> ! [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_1212])]) ).
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(f9668,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2786,f9666]) ).
fof(f9666,plain,
( spl0_1211
<=> ! [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_1211])]) ).
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(f9664,plain,
spl0_1210,
inference(avatar_split_clause,[],[f2785,f9662]) ).
fof(f9662,plain,
( spl0_1210
<=> ! [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_1210])]) ).
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(f9660,plain,
spl0_1209,
inference(avatar_split_clause,[],[f2784,f9658]) ).
fof(f9658,plain,
( spl0_1209
<=> ! [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_1209])]) ).
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(f9656,plain,
spl0_1208,
inference(avatar_split_clause,[],[f2759,f9654]) ).
fof(f9654,plain,
( spl0_1208
<=> ! [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_1208])]) ).
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(f9652,plain,
spl0_1207,
inference(avatar_split_clause,[],[f2758,f9650]) ).
fof(f9650,plain,
( spl0_1207
<=> ! [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_1207])]) ).
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(f9648,plain,
( spl0_1206
| ~ spl0_12
| ~ spl0_973 ),
inference(avatar_split_clause,[],[f8631,f8348,f3490,f9646]) ).
fof(f8348,plain,
( spl0_973
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f8631,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_12
| ~ spl0_973 ),
inference(resolution,[],[f8349,f3492]) ).
fof(f8349,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 )
| ~ spl0_973 ),
inference(avatar_component_clause,[],[f8348]) ).
fof(f9644,plain,
spl0_1205,
inference(avatar_split_clause,[],[f2757,f9642]) ).
fof(f9642,plain,
( spl0_1205
<=> ! [X100,X101,X98,X99] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f2757,axiom,
! [X101,X98,X99,X100] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
fof(f9640,plain,
spl0_1204,
inference(avatar_split_clause,[],[f2756,f9638]) ).
fof(f9638,plain,
( spl0_1204
<=> ! [X101,X98,X100,X99] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f2756,axiom,
! [X101,X98,X99,X100] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
fof(f9636,plain,
spl0_1203,
inference(avatar_split_clause,[],[f2748,f9634]) ).
fof(f9634,plain,
( spl0_1203
<=> ! [X87,X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f2748,axiom,
! [X88,X86,X87] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
fof(f9632,plain,
spl0_1202,
inference(avatar_split_clause,[],[f2671,f9630]) ).
fof(f9630,plain,
( spl0_1202
<=> ! [X12,X1] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f2671,axiom,
! [X1,X12] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f9628,plain,
spl0_1201,
inference(avatar_split_clause,[],[f2654,f9626]) ).
fof(f9626,plain,
( spl0_1201
<=> ! [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_1201])]) ).
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(f9624,plain,
spl0_1200,
inference(avatar_split_clause,[],[f2618,f9622]) ).
fof(f9622,plain,
( spl0_1200
<=> ! [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_1200])]) ).
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(f9620,plain,
spl0_1199,
inference(avatar_split_clause,[],[f2615,f9618]) ).
fof(f9618,plain,
( spl0_1199
<=> ! [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_1199])]) ).
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(f9616,plain,
spl0_1198,
inference(avatar_split_clause,[],[f2388,f9614]) ).
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(f9612,plain,
spl0_1197,
inference(avatar_split_clause,[],[f2383,f9610]) ).
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(f9608,plain,
spl0_1196,
inference(avatar_split_clause,[],[f2366,f9606]) ).
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(f9604,plain,
( spl0_1195
| ~ spl0_719
| ~ spl0_914
| ~ spl0_969 ),
inference(avatar_split_clause,[],[f8617,f8332,f8037,f7216,f9601]) ).
fof(f9601,plain,
( spl0_1195
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f8332,plain,
( spl0_969
<=> ! [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_969])]) ).
fof(f8617,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_719
| ~ spl0_914
| ~ spl0_969 ),
inference(forward_demodulation,[],[f8615,f7218]) ).
fof(f8615,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_914
| ~ spl0_969 ),
inference(superposition,[],[f8333,f8039]) ).
fof(f8333,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
| ~ spl0_969 ),
inference(avatar_component_clause,[],[f8332]) ).
fof(f9599,plain,
spl0_1194,
inference(avatar_split_clause,[],[f2364,f9597]) ).
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(f9595,plain,
spl0_1193,
inference(avatar_split_clause,[],[f2342,f9593]) ).
fof(f9593,plain,
( spl0_1193
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f2342,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f9591,plain,
spl0_1192,
inference(avatar_split_clause,[],[f2341,f9589]) ).
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(f9587,plain,
spl0_1191,
inference(avatar_split_clause,[],[f2294,f9585]) ).
fof(f9585,plain,
( spl0_1191
<=> ! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f2294,axiom,
! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f9583,plain,
spl0_1190,
inference(avatar_split_clause,[],[f2281,f9581]) ).
fof(f9581,plain,
( spl0_1190
<=> ! [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_1190])]) ).
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(f9579,plain,
spl0_1189,
inference(avatar_split_clause,[],[f2247,f9577]) ).
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(f9575,plain,
spl0_1188,
inference(avatar_split_clause,[],[f2225,f9573]) ).
fof(f9573,plain,
( spl0_1188
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
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(f9571,plain,
spl0_1187,
inference(avatar_split_clause,[],[f2213,f9569]) ).
fof(f9569,plain,
( spl0_1187
<=> ! [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_1187])]) ).
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(f9567,plain,
spl0_1186,
inference(avatar_split_clause,[],[f2211,f9565]) ).
fof(f9565,plain,
( spl0_1186
<=> ! [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_1186])]) ).
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(f9563,plain,
spl0_1185,
inference(avatar_split_clause,[],[f2197,f9561]) ).
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(f9559,plain,
( spl0_1184
| ~ spl0_90
| ~ spl0_950 ),
inference(avatar_split_clause,[],[f8589,f8255,f3880,f9557]) ).
fof(f9557,plain,
( spl0_1184
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f3880,plain,
( spl0_90
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f8255,plain,
( spl0_950
<=> ! [X1,X3] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f8589,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_90
| ~ spl0_950 ),
inference(resolution,[],[f8256,f3882]) ).
fof(f3882,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f3880]) ).
fof(f8256,plain,
( ! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 )
| ~ spl0_950 ),
inference(avatar_component_clause,[],[f8255]) ).
fof(f9555,plain,
spl0_1183,
inference(avatar_split_clause,[],[f2172,f9553]) ).
fof(f9553,plain,
( spl0_1183
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(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(f9551,plain,
spl0_1182,
inference(avatar_split_clause,[],[f2171,f9549]) ).
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(f9547,plain,
spl0_1181,
inference(avatar_split_clause,[],[f2039,f9545]) ).
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(f9543,plain,
spl0_1180,
inference(avatar_split_clause,[],[f2038,f9541]) ).
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(f9539,plain,
spl0_1179,
inference(avatar_split_clause,[],[f1849,f9537]) ).
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(f9535,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1832,f9533]) ).
fof(f9533,plain,
( spl0_1178
<=> ! [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_1178])]) ).
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(f9531,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1803,f9529]) ).
fof(f9529,plain,
( spl0_1177
<=> ! [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_1177])]) ).
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(f9527,plain,
spl0_1176,
inference(avatar_split_clause,[],[f1759,f9525]) ).
fof(f9525,plain,
( spl0_1176
<=> ! [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_1176])]) ).
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(f9523,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1730,f9521]) ).
fof(f9521,plain,
( spl0_1175
<=> ! [X25,X1,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
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(f9519,plain,
spl0_1174,
inference(avatar_split_clause,[],[f1603,f9517]) ).
fof(f9517,plain,
( spl0_1174
<=> ! [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_1174])]) ).
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(f9515,plain,
( spl0_1173
| ~ spl0_32
| ~ spl0_950 ),
inference(avatar_split_clause,[],[f8588,f8255,f3590,f9513]) ).
fof(f9513,plain,
( spl0_1173
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f3590,plain,
( spl0_32
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f8588,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_32
| ~ spl0_950 ),
inference(resolution,[],[f8256,f3592]) ).
fof(f3592,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f3590]) ).
fof(f9511,plain,
spl0_1172,
inference(avatar_split_clause,[],[f1548,f9509]) ).
fof(f9509,plain,
( spl0_1172
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f1548,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f9507,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1541,f9505]) ).
fof(f9505,plain,
( spl0_1171
<=> ! [X54,X57,X55,X56] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1541,axiom,
! [X56,X54,X57,X55] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f9503,plain,
spl0_1170,
inference(avatar_split_clause,[],[f1540,f9501]) ).
fof(f9501,plain,
( spl0_1170
<=> ! [X55,X54,X56,X57] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f1540,axiom,
! [X56,X54,X57,X55] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f9499,plain,
spl0_1169,
inference(avatar_split_clause,[],[f1509,f9497]) ).
fof(f9497,plain,
( spl0_1169
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f1509,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f9495,plain,
spl0_1168,
inference(avatar_split_clause,[],[f1488,f9493]) ).
fof(f9493,plain,
( spl0_1168
<=> ! [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_1168])]) ).
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(f9491,plain,
spl0_1167,
inference(avatar_split_clause,[],[f1487,f9489]) ).
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(f9486,plain,
spl0_1166,
inference(avatar_split_clause,[],[f1467,f9484]) ).
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(f9482,plain,
spl0_1165,
inference(avatar_split_clause,[],[f1440,f9480]) ).
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(f9478,plain,
spl0_1164,
inference(avatar_split_clause,[],[f1439,f9476]) ).
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(f9474,plain,
spl0_1163,
inference(avatar_split_clause,[],[f1430,f9472]) ).
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(f9470,plain,
( spl0_1162
| ~ spl0_97
| ~ spl0_949 ),
inference(avatar_split_clause,[],[f8587,f8251,f3915,f9468]) ).
fof(f9468,plain,
( spl0_1162
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f3915,plain,
( spl0_97
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f8251,plain,
( spl0_949
<=> ! [X1,X3] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f8587,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_97
| ~ spl0_949 ),
inference(resolution,[],[f8252,f3917]) ).
fof(f3917,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f3915]) ).
fof(f8252,plain,
( ! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 )
| ~ spl0_949 ),
inference(avatar_component_clause,[],[f8251]) ).
fof(f9466,plain,
spl0_1161,
inference(avatar_split_clause,[],[f1429,f9464]) ).
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(f9462,plain,
spl0_1160,
inference(avatar_split_clause,[],[f1428,f9460]) ).
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(f9458,plain,
spl0_1159,
inference(avatar_split_clause,[],[f1427,f9456]) ).
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(f9454,plain,
spl0_1158,
inference(avatar_split_clause,[],[f1426,f9452]) ).
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(f9450,plain,
spl0_1157,
inference(avatar_split_clause,[],[f1425,f9448]) ).
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(f9446,plain,
spl0_1156,
inference(avatar_split_clause,[],[f1407,f9444]) ).
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(f9442,plain,
spl0_1155,
inference(avatar_split_clause,[],[f1404,f9440]) ).
fof(f9440,plain,
( spl0_1155
<=> ! [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_1155])]) ).
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(f9438,plain,
spl0_1154,
inference(avatar_split_clause,[],[f1390,f9436]) ).
fof(f9436,plain,
( spl0_1154
<=> ! [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_1154])]) ).
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(f9434,plain,
spl0_1153,
inference(avatar_split_clause,[],[f1389,f9432]) ).
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(f9430,plain,
spl0_1152,
inference(avatar_split_clause,[],[f1279,f9428]) ).
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(f9425,plain,
spl0_1151,
inference(avatar_split_clause,[],[f1275,f9423]) ).
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(f9421,plain,
spl0_1150,
inference(avatar_split_clause,[],[f1265,f9419]) ).
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(f9417,plain,
spl0_1149,
inference(avatar_split_clause,[],[f1235,f9415]) ).
fof(f9415,plain,
( spl0_1149
<=> ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
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(f9413,plain,
spl0_1148,
inference(avatar_split_clause,[],[f1224,f9411]) ).
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(f9409,plain,
spl0_1147,
inference(avatar_split_clause,[],[f1216,f9407]) ).
fof(f9407,plain,
( spl0_1147
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
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(f9405,plain,
spl0_1146,
inference(avatar_split_clause,[],[f1200,f9403]) ).
fof(f9403,plain,
( spl0_1146
<=> ! [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_1146])]) ).
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(f9401,plain,
spl0_1145,
inference(avatar_split_clause,[],[f1199,f9399]) ).
fof(f9399,plain,
( spl0_1145
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f1199,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom_0) ).
fof(f9397,plain,
spl0_1144,
inference(avatar_split_clause,[],[f1196,f9395]) ).
fof(f9395,plain,
( spl0_1144
<=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f1196,axiom,
! [X2,X1,X9,X7,X16] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons_0) ).
fof(f9393,plain,
spl0_1143,
inference(avatar_split_clause,[],[f1180,f9391]) ).
fof(f9391,plain,
( spl0_1143
<=> ! [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_1143])]) ).
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(f9389,plain,
spl0_1142,
inference(avatar_split_clause,[],[f1179,f9387]) ).
fof(f9387,plain,
( spl0_1142
<=> ! [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_1142])]) ).
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(f9385,plain,
( spl0_1141
| ~ spl0_918
| ~ spl0_1073 ),
inference(avatar_split_clause,[],[f9249,f8890,f8070,f9383]) ).
fof(f9383,plain,
( spl0_1141
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f8070,plain,
( spl0_918
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f9249,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_918
| ~ spl0_1073 ),
inference(resolution,[],[f8891,f8071]) ).
fof(f8071,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f8070]) ).
fof(f9381,plain,
spl0_1140,
inference(avatar_split_clause,[],[f1175,f9379]) ).
fof(f9379,plain,
( spl0_1140
<=> ! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f1175,axiom,
! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f9377,plain,
spl0_1139,
inference(avatar_split_clause,[],[f1170,f9375]) ).
fof(f9375,plain,
( spl0_1139
<=> ! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f1170,axiom,
! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f9373,plain,
spl0_1138,
inference(avatar_split_clause,[],[f1169,f9371]) ).
fof(f9371,plain,
( spl0_1138
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f1169,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f9369,plain,
spl0_1137,
inference(avatar_split_clause,[],[f1168,f9367]) ).
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(f9365,plain,
spl0_1136,
inference(avatar_split_clause,[],[f105,f9363]) ).
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(f9361,plain,
spl0_1135,
inference(avatar_split_clause,[],[f103,f9359]) ).
fof(f9359,plain,
( spl0_1135
<=> ! [X13,X12,X1] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f103,axiom,
! [X1,X12,X13] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f9357,plain,
spl0_1134,
inference(avatar_split_clause,[],[f102,f9355]) ).
fof(f9355,plain,
( spl0_1134
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f102,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f9330,plain,
( ~ spl0_1133
| spl0_8
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f9312,f9020,f3470,f9327]) ).
fof(f9327,plain,
( spl0_1133
<=> 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_1133])]) ).
fof(f9020,plain,
( spl0_1105
<=> ! [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_1105])]) ).
fof(f9312,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)
| spl0_8
| ~ spl0_1105 ),
inference(resolution,[],[f9021,f3472]) ).
fof(f9021,plain,
( ! [X88,X86] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(X86,X88,tc_Message_Omsg) )
| ~ spl0_1105 ),
inference(avatar_component_clause,[],[f9020]) ).
fof(f9293,plain,
( spl0_1132
| ~ spl0_820
| ~ spl0_1091 ),
inference(avatar_split_clause,[],[f9284,f8964,f7647,f9291]) ).
fof(f9291,plain,
( spl0_1132
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f9284,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_820
| ~ spl0_1091 ),
inference(superposition,[],[f7648,f8965]) ).
fof(f9246,plain,
( spl0_1131
| ~ spl0_820
| ~ spl0_1063 ),
inference(avatar_split_clause,[],[f9231,f8850,f7647,f9244]) ).
fof(f9244,plain,
( spl0_1131
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f9231,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_820
| ~ spl0_1063 ),
inference(superposition,[],[f7648,f8851]) ).
fof(f9225,plain,
( spl0_1130
| ~ spl0_33
| ~ spl0_949 ),
inference(avatar_split_clause,[],[f8586,f8251,f3595,f9223]) ).
fof(f9223,plain,
( spl0_1130
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f3595,plain,
( spl0_33
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f8586,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_33
| ~ spl0_949 ),
inference(resolution,[],[f8252,f3597]) ).
fof(f3597,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f3595]) ).
fof(f9165,plain,
( ~ spl0_82
| spl0_1129
| ~ spl0_686
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8584,f8243,f7066,f9163,f3840]) ).
fof(f3840,plain,
( spl0_82
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f7066,plain,
( spl0_686
<=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f8243,plain,
( spl0_947
<=> ! [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_947])]) ).
fof(f8584,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_686
| ~ spl0_947 ),
inference(superposition,[],[f8244,f7067]) ).
fof(f7067,plain,
( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
| ~ spl0_686 ),
inference(avatar_component_clause,[],[f7066]) ).
fof(f8244,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_947 ),
inference(avatar_component_clause,[],[f8243]) ).
fof(f9127,plain,
( spl0_1128
| ~ spl0_845
| ~ spl0_863 ),
inference(avatar_split_clause,[],[f8085,f7832,f7760,f9125]) ).
fof(f9125,plain,
( spl0_1128
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f8085,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_845
| ~ spl0_863 ),
inference(resolution,[],[f7833,f7761]) ).
fof(f9111,plain,
spl0_1127,
inference(avatar_split_clause,[],[f3332,f9109]) ).
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(f9107,plain,
spl0_1126,
inference(avatar_split_clause,[],[f3325,f9105]) ).
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(f9103,plain,
spl0_1125,
inference(avatar_split_clause,[],[f3317,f9101]) ).
fof(f9101,plain,
( spl0_1125
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
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(f9099,plain,
spl0_1124,
inference(avatar_split_clause,[],[f3315,f9097]) ).
fof(f9097,plain,
( spl0_1124
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
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(f9095,plain,
spl0_1123,
inference(avatar_split_clause,[],[f3029,f9093]) ).
fof(f9093,plain,
( spl0_1123
<=> ! [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_1123])]) ).
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(f9091,plain,
spl0_1122,
inference(avatar_split_clause,[],[f3028,f9089]) ).
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(f9087,plain,
spl0_1121,
inference(avatar_split_clause,[],[f3013,f9085]) ).
fof(f9085,plain,
( spl0_1121
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
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(f9083,plain,
spl0_1120,
inference(avatar_split_clause,[],[f3012,f9081]) ).
fof(f9081,plain,
( spl0_1120
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
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(f9079,plain,
( spl0_1119
| ~ spl0_844
| ~ spl0_863 ),
inference(avatar_split_clause,[],[f8084,f7832,f7756,f9077]) ).
fof(f9077,plain,
( spl0_1119
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f8084,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_844
| ~ spl0_863 ),
inference(resolution,[],[f7833,f7757]) ).
fof(f9075,plain,
spl0_1118,
inference(avatar_split_clause,[],[f3011,f9073]) ).
fof(f9073,plain,
( spl0_1118
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
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(f9071,plain,
spl0_1117,
inference(avatar_split_clause,[],[f3005,f9069]) ).
fof(f9069,plain,
( spl0_1117
<=> ! [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_1117])]) ).
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(f9067,plain,
spl0_1116,
inference(avatar_split_clause,[],[f2997,f9065]) ).
fof(f9065,plain,
( spl0_1116
<=> ! [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_1116])]) ).
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(f9063,plain,
spl0_1115,
inference(avatar_split_clause,[],[f2995,f9061]) ).
fof(f9061,plain,
( spl0_1115
<=> ! [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_1115])]) ).
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(f9059,plain,
spl0_1114,
inference(avatar_split_clause,[],[f2993,f9057]) ).
fof(f9057,plain,
( spl0_1114
<=> ! [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_1114])]) ).
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(f9055,plain,
spl0_1113,
inference(avatar_split_clause,[],[f2991,f9053]) ).
fof(f9053,plain,
( spl0_1113
<=> ! [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_1113])]) ).
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(f9051,plain,
spl0_1112,
inference(avatar_split_clause,[],[f2989,f9049]) ).
fof(f9049,plain,
( spl0_1112
<=> ! [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_1112])]) ).
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(f9047,plain,
spl0_1111,
inference(avatar_split_clause,[],[f2932,f9045]) ).
fof(f9045,plain,
( spl0_1111
<=> ! [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_1111])]) ).
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(f9043,plain,
spl0_1110,
inference(avatar_split_clause,[],[f2931,f9041]) ).
fof(f9041,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(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(f9039,plain,
spl0_1109,
inference(avatar_split_clause,[],[f2930,f9037]) ).
fof(f9037,plain,
( spl0_1109
<=> ! [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_1109])]) ).
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(f9035,plain,
( spl0_1108
| ~ spl0_649
| ~ spl0_860 ),
inference(avatar_split_clause,[],[f8077,f7820,f6138,f9032]) ).
fof(f9032,plain,
( spl0_1108
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f7820,plain,
( spl0_860
<=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f8077,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_649
| ~ spl0_860 ),
inference(superposition,[],[f7821,f6140]) ).
fof(f7821,plain,
( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
| ~ spl0_860 ),
inference(avatar_component_clause,[],[f7820]) ).
fof(f9030,plain,
spl0_1107,
inference(avatar_split_clause,[],[f2916,f9028]) ).
fof(f9028,plain,
( spl0_1107
<=> ! [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_1107])]) ).
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(f9026,plain,
spl0_1106,
inference(avatar_split_clause,[],[f2886,f9024]) ).
fof(f9024,plain,
( spl0_1106
<=> ! [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_1106])]) ).
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(f9022,plain,
spl0_1105,
inference(avatar_split_clause,[],[f2847,f9020]) ).
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(f9018,plain,
spl0_1104,
inference(avatar_split_clause,[],[f2767,f9016]) ).
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(f9014,plain,
spl0_1103,
inference(avatar_split_clause,[],[f2750,f9012]) ).
fof(f9012,plain,
( spl0_1103
<=> ! [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_1103])]) ).
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(f9010,plain,
spl0_1102,
inference(avatar_split_clause,[],[f2749,f9008]) ).
fof(f9008,plain,
( spl0_1102
<=> ! [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_1102])]) ).
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(f9006,plain,
spl0_1101,
inference(avatar_split_clause,[],[f2747,f9004]) ).
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(f9002,plain,
spl0_1100,
inference(avatar_split_clause,[],[f2746,f9000]) ).
fof(f9000,plain,
( spl0_1100
<=> ! [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_1100])]) ).
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(f8998,plain,
spl0_1099,
inference(avatar_split_clause,[],[f2744,f8996]) ).
fof(f8996,plain,
( spl0_1099
<=> ! [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_1099])]) ).
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(f8994,plain,
spl0_1098,
inference(avatar_split_clause,[],[f2718,f8992]) ).
fof(f8992,plain,
( spl0_1098
<=> ! [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_1098])]) ).
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(f8990,plain,
spl0_1097,
inference(avatar_split_clause,[],[f2717,f8988]) ).
fof(f8988,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(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(f8986,plain,
spl0_1096,
inference(avatar_split_clause,[],[f2704,f8984]) ).
fof(f8984,plain,
( spl0_1096
<=> ! [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_1096])]) ).
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(f8982,plain,
spl0_1095,
inference(avatar_split_clause,[],[f2667,f8980]) ).
fof(f8980,plain,
( spl0_1095
<=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
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(f8978,plain,
spl0_1094,
inference(avatar_split_clause,[],[f2659,f8976]) ).
fof(f8976,plain,
( spl0_1094
<=> ! [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_1094])]) ).
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(f8974,plain,
spl0_1093,
inference(avatar_split_clause,[],[f2636,f8972]) ).
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(f8970,plain,
spl0_1092,
inference(avatar_split_clause,[],[f2635,f8968]) ).
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(f8966,plain,
spl0_1091,
inference(avatar_split_clause,[],[f2626,f8964]) ).
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(f8962,plain,
spl0_1090,
inference(avatar_split_clause,[],[f2390,f8960]) ).
fof(f8960,plain,
( spl0_1090
<=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
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(f8958,plain,
spl0_1089,
inference(avatar_split_clause,[],[f2389,f8956]) ).
fof(f8956,plain,
( spl0_1089
<=> ! [X1,X3] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
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(f8954,plain,
spl0_1088,
inference(avatar_split_clause,[],[f2382,f8952]) ).
fof(f8952,plain,
( spl0_1088
<=> ! [X2,X1,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
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(f8950,plain,
( ~ spl0_60
| spl0_1087
| ~ spl0_878
| ~ spl0_985 ),
inference(avatar_split_clause,[],[f8619,f8396,f7892,f8947,f3730]) ).
fof(f8947,plain,
( spl0_1087
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f7892,plain,
( spl0_878
<=> ! [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_878])]) ).
fof(f8396,plain,
( spl0_985
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f8619,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_878
| ~ spl0_985 ),
inference(superposition,[],[f7893,f8398]) ).
fof(f8398,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_985 ),
inference(avatar_component_clause,[],[f8396]) ).
fof(f7893,plain,
( ! [X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_878 ),
inference(avatar_component_clause,[],[f7892]) ).
fof(f8945,plain,
spl0_1086,
inference(avatar_split_clause,[],[f2298,f8943]) ).
fof(f8943,plain,
( spl0_1086
<=> ! [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_1086])]) ).
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(f8941,plain,
spl0_1085,
inference(avatar_split_clause,[],[f2297,f8939]) ).
fof(f8939,plain,
( spl0_1085
<=> ! [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_1085])]) ).
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(f8937,plain,
spl0_1084,
inference(avatar_split_clause,[],[f2293,f8935]) ).
fof(f8935,plain,
( spl0_1084
<=> ! [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_1084])]) ).
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(f8933,plain,
spl0_1083,
inference(avatar_split_clause,[],[f2285,f8931]) ).
fof(f8931,plain,
( spl0_1083
<=> ! [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_1083])]) ).
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(f8929,plain,
spl0_1082,
inference(avatar_split_clause,[],[f2284,f8927]) ).
fof(f8927,plain,
( spl0_1082
<=> ! [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_1082])]) ).
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(f8925,plain,
spl0_1081,
inference(avatar_split_clause,[],[f2280,f8923]) ).
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(f8921,plain,
spl0_1080,
inference(avatar_split_clause,[],[f2216,f8919]) ).
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(f8917,plain,
spl0_1079,
inference(avatar_split_clause,[],[f2154,f8915]) ).
fof(f8913,plain,
spl0_1078,
inference(avatar_split_clause,[],[f2150,f8911]) ).
fof(f8911,plain,
( spl0_1078
<=> ! [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_1078])]) ).
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(f8909,plain,
spl0_1077,
inference(avatar_split_clause,[],[f2136,f8907]) ).
fof(f8907,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_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
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(f8904,plain,
spl0_1076,
inference(avatar_split_clause,[],[f2118,f8902]) ).
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(f8900,plain,
spl0_1075,
inference(avatar_split_clause,[],[f2032,f8898]) ).
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(f8896,plain,
spl0_1074,
inference(avatar_split_clause,[],[f2031,f8894]) ).
fof(f8894,plain,
( spl0_1074
<=> ! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
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(f8892,plain,
spl0_1073,
inference(avatar_split_clause,[],[f1786,f8890]) ).
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(f8888,plain,
spl0_1072,
inference(avatar_split_clause,[],[f1758,f8886]) ).
fof(f8886,plain,
( spl0_1072
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
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(f8884,plain,
spl0_1071,
inference(avatar_split_clause,[],[f1757,f8882]) ).
fof(f8882,plain,
( spl0_1071
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
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(f8880,plain,
spl0_1070,
inference(avatar_split_clause,[],[f1754,f8878]) ).
fof(f8878,plain,
( spl0_1070
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
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(f8876,plain,
spl0_1069,
inference(avatar_split_clause,[],[f1746,f8874]) ).
fof(f8874,plain,
( spl0_1069
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
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(f8872,plain,
spl0_1068,
inference(avatar_split_clause,[],[f1744,f8870]) ).
fof(f8870,plain,
( spl0_1068
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
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(f8868,plain,
spl0_1067,
inference(avatar_split_clause,[],[f1740,f8866]) ).
fof(f8866,plain,
( spl0_1067
<=> ! [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_1067])]) ).
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(f8864,plain,
( spl0_1066
| ~ spl0_742
| ~ spl0_1045 ),
inference(avatar_split_clause,[],[f8818,f8775,f7316,f8862]) ).
fof(f8862,plain,
( spl0_1066
<=> ! [X0] :
( v_KAB != X0
| v_KAB = c_Message_OinvKey(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f8775,plain,
( spl0_1045
<=> ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_KAB = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f8818,plain,
( ! [X0] :
( v_KAB != X0
| v_KAB = c_Message_OinvKey(X0) )
| ~ spl0_742
| ~ spl0_1045 ),
inference(superposition,[],[f8776,f7317]) ).
fof(f8776,plain,
( ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_KAB = X0 )
| ~ spl0_1045 ),
inference(avatar_component_clause,[],[f8775]) ).
fof(f8860,plain,
spl0_1065,
inference(avatar_split_clause,[],[f1720,f8858]) ).
fof(f8858,plain,
( spl0_1065
<=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
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(f8856,plain,
spl0_1064,
inference(avatar_split_clause,[],[f1692,f8854]) ).
fof(f8854,plain,
( spl0_1064
<=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
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(f8852,plain,
spl0_1063,
inference(avatar_split_clause,[],[f1639,f8850]) ).
fof(f8848,plain,
spl0_1062,
inference(avatar_split_clause,[],[f1607,f8846]) ).
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(f8844,plain,
spl0_1061,
inference(avatar_split_clause,[],[f1597,f8842]) ).
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(f8840,plain,
spl0_1060,
inference(avatar_split_clause,[],[f1565,f8838]) ).
fof(f8838,plain,
( spl0_1060
<=> ! [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_1060])]) ).
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(f8836,plain,
spl0_1059,
inference(avatar_split_clause,[],[f1564,f8834]) ).
fof(f8834,plain,
( spl0_1059
<=> ! [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_1059])]) ).
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(f8832,plain,
spl0_1058,
inference(avatar_split_clause,[],[f1563,f8830]) ).
fof(f8830,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(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(f8828,plain,
spl0_1057,
inference(avatar_split_clause,[],[f1560,f8826]) ).
fof(f8826,plain,
( spl0_1057
<=> ! [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_1057])]) ).
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(f8824,plain,
spl0_1056,
inference(avatar_split_clause,[],[f1559,f8822]) ).
fof(f8822,plain,
( spl0_1056
<=> ! [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_1056])]) ).
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(f8817,plain,
spl0_1055,
inference(avatar_split_clause,[],[f1556,f8815]) ).
fof(f8815,plain,
( spl0_1055
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
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(f8813,plain,
spl0_1054,
inference(avatar_split_clause,[],[f1555,f8811]) ).
fof(f8811,plain,
( spl0_1054
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
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(f8809,plain,
spl0_1053,
inference(avatar_split_clause,[],[f1553,f8807]) ).
fof(f8807,plain,
( spl0_1053
<=> ! [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_1053])]) ).
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(f8805,plain,
spl0_1052,
inference(avatar_split_clause,[],[f1528,f8803]) ).
fof(f8803,plain,
( spl0_1052
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
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(f8801,plain,
spl0_1051,
inference(avatar_split_clause,[],[f1527,f8799]) ).
fof(f8799,plain,
( spl0_1051
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
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(f8797,plain,
spl0_1050,
inference(avatar_split_clause,[],[f1497,f8795]) ).
fof(f8795,plain,
( spl0_1050
<=> ! [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_1050])]) ).
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(f8793,plain,
spl0_1049,
inference(avatar_split_clause,[],[f1496,f8791]) ).
fof(f8791,plain,
( spl0_1049
<=> ! [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_1049])]) ).
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(f8789,plain,
spl0_1048,
inference(avatar_split_clause,[],[f1483,f8787]) ).
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(f8785,plain,
spl0_1047,
inference(avatar_split_clause,[],[f1471,f8783]) ).
fof(f8783,plain,
( spl0_1047
<=> ! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
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(f8781,plain,
spl0_1046,
inference(avatar_split_clause,[],[f1441,f8779]) ).
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(f8777,plain,
( spl0_1045
| ~ spl0_1004
| ~ spl0_1027 ),
inference(avatar_split_clause,[],[f8731,f8698,f8475,f8775]) ).
fof(f8731,plain,
( ! [X0] :
( v_KAB != c_Message_OinvKey(X0)
| v_KAB = X0 )
| ~ spl0_1004
| ~ spl0_1027 ),
inference(superposition,[],[f8476,f8700]) ).
fof(f8773,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1423,f8771]) ).
fof(f8771,plain,
( spl0_1044
<=> ! [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_1044])]) ).
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(f8769,plain,
spl0_1043,
inference(avatar_split_clause,[],[f1422,f8767]) ).
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(f8765,plain,
spl0_1042,
inference(avatar_split_clause,[],[f1421,f8763]) ).
fof(f8763,plain,
( spl0_1042
<=> ! [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_1042])]) ).
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(f8761,plain,
spl0_1041,
inference(avatar_split_clause,[],[f1420,f8759]) ).
fof(f8759,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(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(f8757,plain,
spl0_1040,
inference(avatar_split_clause,[],[f1380,f8755]) ).
fof(f8755,plain,
( spl0_1040
<=> ! [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_1040])]) ).
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(f8753,plain,
spl0_1039,
inference(avatar_split_clause,[],[f1379,f8751]) ).
fof(f8751,plain,
( spl0_1039
<=> ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
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(f8749,plain,
spl0_1038,
inference(avatar_split_clause,[],[f1349,f8747]) ).
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(f8745,plain,
spl0_1037,
inference(avatar_split_clause,[],[f1244,f8743]) ).
fof(f8743,plain,
( spl0_1037
<=> ! [X5,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
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(f8741,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1242,f8739]) ).
fof(f8739,plain,
( spl0_1036
<=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
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(f8737,plain,
spl0_1035,
inference(avatar_split_clause,[],[f1240,f8735]) ).
fof(f8735,plain,
( spl0_1035
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
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(f8730,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1238,f8728]) ).
fof(f8728,plain,
( spl0_1034
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
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(f8726,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1195,f8724]) ).
fof(f8724,plain,
( spl0_1033
<=> ! [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_1033])]) ).
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(f8722,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1192,f8720]) ).
fof(f8720,plain,
( spl0_1032
<=> ! [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_1032])]) ).
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(f8718,plain,
spl0_1031,
inference(avatar_split_clause,[],[f63,f8716]) ).
fof(f8716,plain,
( spl0_1031
<=> ! [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_1031])]) ).
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(f8714,plain,
spl0_1030,
inference(avatar_split_clause,[],[f62,f8712]) ).
fof(f8712,plain,
( spl0_1030
<=> ! [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_1030])]) ).
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(f8710,plain,
spl0_1029,
inference(avatar_split_clause,[],[f35,f8708]) ).
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(f8706,plain,
spl0_1028,
inference(avatar_split_clause,[],[f34,f8704]) ).
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(f8701,plain,
( spl0_1027
| ~ spl0_4
| ~ spl0_1014 ),
inference(avatar_split_clause,[],[f8693,f8516,f3450,f8698]) ).
fof(f8516,plain,
( spl0_1014
<=> ! [X3] :
( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f8693,plain,
( v_KAB = c_Message_OinvKey(v_KAB)
| ~ spl0_4
| ~ spl0_1014 ),
inference(resolution,[],[f8517,f3452]) ).
fof(f8517,plain,
( ! [X3] :
( ~ c_in(X3,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(X3) = X3 )
| ~ spl0_1014 ),
inference(avatar_component_clause,[],[f8516]) ).
fof(f8676,plain,
( ~ spl0_1026
| ~ spl0_820
| ~ spl0_1000 ),
inference(avatar_split_clause,[],[f8671,f8458,f7647,f8673]) ).
fof(f8673,plain,
( spl0_1026
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f8671,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_820
| ~ spl0_1000 ),
inference(superposition,[],[f7648,f8460]) ).
fof(f8563,plain,
spl0_1025,
inference(avatar_split_clause,[],[f3304,f8561]) ).
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(f8559,plain,
spl0_1024,
inference(avatar_split_clause,[],[f3250,f8557]) ).
fof(f8557,plain,
( spl0_1024
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
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(f8555,plain,
spl0_1023,
inference(avatar_split_clause,[],[f3249,f8553]) ).
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(f8551,plain,
spl0_1022,
inference(avatar_split_clause,[],[f3017,f8549]) ).
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(f8547,plain,
spl0_1021,
inference(avatar_split_clause,[],[f2988,f8545]) ).
fof(f8545,plain,
( spl0_1021
<=> ! [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_1021])]) ).
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(f8543,plain,
spl0_1020,
inference(avatar_split_clause,[],[f2986,f8541]) ).
fof(f8541,plain,
( spl0_1020
<=> ! [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_1020])]) ).
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(f8539,plain,
spl0_1019,
inference(avatar_split_clause,[],[f2927,f8537]) ).
fof(f8537,plain,
( spl0_1019
<=> ! [X0,X3] :
( X0 = X3
| c_Public_OshrK(X0) != c_Public_OshrK(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
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(f8535,plain,
spl0_1018,
inference(avatar_split_clause,[],[f2925,f8533]) ).
fof(f8533,plain,
( spl0_1018
<=> ! [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_1018])]) ).
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(f8531,plain,
( spl0_1017
| ~ spl0_48
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f8124,f7932,f3670,f8528]) ).
fof(f8528,plain,
( spl0_1017
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f7932,plain,
( spl0_888
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f8124,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_48
| ~ spl0_888 ),
inference(resolution,[],[f7933,f3672]) ).
fof(f3672,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f3670]) ).
fof(f7933,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) )
| ~ spl0_888 ),
inference(avatar_component_clause,[],[f7932]) ).
fof(f8526,plain,
spl0_1016,
inference(avatar_split_clause,[],[f2922,f8524]) ).
fof(f8524,plain,
( spl0_1016
<=> ! [X4,X27,X12,X111] : c_Message_OinvKey(c_Public_OpublicKey(X27,X12)) != c_Public_OpublicKey(X4,X111) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
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(f8522,plain,
spl0_1015,
inference(avatar_split_clause,[],[f2921,f8520]) ).
fof(f8520,plain,
( spl0_1015
<=> ! [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_1015])]) ).
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(f8518,plain,
spl0_1014,
inference(avatar_split_clause,[],[f2899,f8516]) ).
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(f8514,plain,
spl0_1013,
inference(avatar_split_clause,[],[f2788,f8512]) ).
fof(f8512,plain,
( spl0_1013
<=> ! [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_1013])]) ).
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(f8510,plain,
spl0_1012,
inference(avatar_split_clause,[],[f2778,f8508]) ).
fof(f8508,plain,
( spl0_1012
<=> ! [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_1012])]) ).
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(f8506,plain,
spl0_1011,
inference(avatar_split_clause,[],[f2775,f8504]) ).
fof(f8504,plain,
( spl0_1011
<=> ! [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_1011])]) ).
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(f8502,plain,
spl0_1010,
inference(avatar_split_clause,[],[f2755,f8500]) ).
fof(f8500,plain,
( spl0_1010
<=> ! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
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(f8498,plain,
spl0_1009,
inference(avatar_split_clause,[],[f2754,f8496]) ).
fof(f8496,plain,
( spl0_1009
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
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(f8494,plain,
spl0_1008,
inference(avatar_split_clause,[],[f2753,f8492]) ).
fof(f8492,plain,
( spl0_1008
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
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(f8490,plain,
spl0_1007,
inference(avatar_split_clause,[],[f2752,f8488]) ).
fof(f8488,plain,
( spl0_1007
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
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(f8486,plain,
( spl0_1006
| ~ spl0_48
| ~ spl0_887 ),
inference(avatar_split_clause,[],[f8123,f7928,f3670,f8483]) ).
fof(f8483,plain,
( spl0_1006
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f7928,plain,
( spl0_887
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f8123,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_48
| ~ spl0_887 ),
inference(resolution,[],[f7929,f3672]) ).
fof(f7929,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) )
| ~ spl0_887 ),
inference(avatar_component_clause,[],[f7928]) ).
fof(f8481,plain,
spl0_1005,
inference(avatar_split_clause,[],[f2751,f8479]) ).
fof(f8479,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(f8477,plain,
spl0_1004,
inference(avatar_split_clause,[],[f2741,f8475]) ).
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(f8473,plain,
spl0_1003,
inference(avatar_split_clause,[],[f2736,f8471]) ).
fof(f8471,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(f8469,plain,
spl0_1002,
inference(avatar_split_clause,[],[f2699,f8467]) ).
fof(f8467,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(f8465,plain,
spl0_1001,
inference(avatar_split_clause,[],[f2660,f8463]) ).
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(f8461,plain,
spl0_1000,
inference(avatar_split_clause,[],[f2534,f8458]) ).
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(f8456,plain,
spl0_999,
inference(avatar_split_clause,[],[f2492,f8454]) ).
fof(f8454,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(f8452,plain,
spl0_998,
inference(avatar_split_clause,[],[f2491,f8450]) ).
fof(f8450,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(f8448,plain,
spl0_997,
inference(avatar_split_clause,[],[f2474,f8446]) ).
fof(f8446,plain,
( spl0_997
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
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(f8444,plain,
spl0_996,
inference(avatar_split_clause,[],[f2473,f8442]) ).
fof(f8442,plain,
( spl0_996
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
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(f8439,plain,
spl0_995,
inference(avatar_split_clause,[],[f2470,f8437]) ).
fof(f8437,plain,
( spl0_995
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
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(f8435,plain,
spl0_994,
inference(avatar_split_clause,[],[f2469,f8433]) ).
fof(f8433,plain,
( spl0_994
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
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(f8431,plain,
spl0_993,
inference(avatar_split_clause,[],[f2379,f8429]) ).
fof(f8429,plain,
( spl0_993
<=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
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(f8427,plain,
spl0_992,
inference(avatar_split_clause,[],[f2377,f8425]) ).
fof(f8425,plain,
( spl0_992
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
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(f8423,plain,
spl0_991,
inference(avatar_split_clause,[],[f2371,f8421]) ).
fof(f8421,plain,
( spl0_991
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
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(f8419,plain,
spl0_990,
inference(avatar_split_clause,[],[f2369,f8417]) ).
fof(f8417,plain,
( spl0_990
<=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
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(f8415,plain,
spl0_989,
inference(avatar_split_clause,[],[f2357,f8413]) ).
fof(f8413,plain,
( spl0_989
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
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(f8411,plain,
spl0_988,
inference(avatar_split_clause,[],[f2354,f8409]) ).
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(f8407,plain,
spl0_987,
inference(avatar_split_clause,[],[f2353,f8405]) ).
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(f8403,plain,
spl0_986,
inference(avatar_split_clause,[],[f2292,f8401]) ).
fof(f8401,plain,
( spl0_986
<=> ! [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_986])]) ).
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(f8399,plain,
( spl0_985
| ~ spl0_60
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f8115,f7916,f3730,f8396]) ).
fof(f7916,plain,
( spl0_884
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f8115,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_60
| ~ spl0_884 ),
inference(resolution,[],[f7917,f3732]) ).
fof(f7917,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f7916]) ).
fof(f8394,plain,
spl0_984,
inference(avatar_split_clause,[],[f2291,f8392]) ).
fof(f8392,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(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(f8390,plain,
spl0_983,
inference(avatar_split_clause,[],[f2267,f8388]) ).
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(f8386,plain,
spl0_982,
inference(avatar_split_clause,[],[f2262,f8384]) ).
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(f8382,plain,
spl0_981,
inference(avatar_split_clause,[],[f2251,f8380]) ).
fof(f8380,plain,
( spl0_981
<=> ! [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_981])]) ).
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(f8378,plain,
spl0_980,
inference(avatar_split_clause,[],[f2250,f8376]) ).
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(f8374,plain,
spl0_979,
inference(avatar_split_clause,[],[f2241,f8372]) ).
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(f8370,plain,
spl0_978,
inference(avatar_split_clause,[],[f2218,f8368]) ).
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(f8366,plain,
spl0_977,
inference(avatar_split_clause,[],[f2217,f8364]) ).
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(f8362,plain,
spl0_976,
inference(avatar_split_clause,[],[f2205,f8360]) ).
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(f8358,plain,
spl0_975,
inference(avatar_split_clause,[],[f2198,f8356]) ).
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(f8354,plain,
spl0_974,
inference(avatar_split_clause,[],[f2196,f8352]) ).
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(f8350,plain,
spl0_973,
inference(avatar_split_clause,[],[f2185,f8348]) ).
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(f8346,plain,
spl0_972,
inference(avatar_split_clause,[],[f2182,f8344]) ).
fof(f8344,plain,
( spl0_972
<=> ! [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_972])]) ).
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(f8342,plain,
spl0_971,
inference(avatar_split_clause,[],[f2180,f8340]) ).
fof(f8340,plain,
( spl0_971
<=> ! [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_971])]) ).
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(f8338,plain,
spl0_970,
inference(avatar_split_clause,[],[f2177,f8336]) ).
fof(f8336,plain,
( spl0_970
<=> ! [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_970])]) ).
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(f8334,plain,
spl0_969,
inference(avatar_split_clause,[],[f2153,f8332]) ).
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(f8330,plain,
spl0_968,
inference(avatar_split_clause,[],[f1865,f8328]) ).
fof(f8328,plain,
( spl0_968
<=> ! [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_968])]) ).
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(f8326,plain,
spl0_967,
inference(avatar_split_clause,[],[f1818,f8324]) ).
fof(f8324,plain,
( spl0_967
<=> ! [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_967])]) ).
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(f8322,plain,
spl0_966,
inference(avatar_split_clause,[],[f1815,f8320]) ).
fof(f8320,plain,
( spl0_966
<=> ! [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_966])]) ).
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(f8318,plain,
spl0_965,
inference(avatar_split_clause,[],[f1805,f8316]) ).
fof(f8316,plain,
( spl0_965
<=> ! [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_965])]) ).
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(f8314,plain,
spl0_964,
inference(avatar_split_clause,[],[f1779,f8312]) ).
fof(f8312,plain,
( spl0_964
<=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
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(f8310,plain,
spl0_963,
inference(avatar_split_clause,[],[f1752,f8308]) ).
fof(f8308,plain,
( spl0_963
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
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(f8306,plain,
spl0_962,
inference(avatar_split_clause,[],[f1735,f8304]) ).
fof(f8304,plain,
( spl0_962
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
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(f8302,plain,
spl0_961,
inference(avatar_split_clause,[],[f1717,f8300]) ).
fof(f8300,plain,
( spl0_961
<=> ! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
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(f8298,plain,
spl0_960,
inference(avatar_split_clause,[],[f1588,f8296]) ).
fof(f8296,plain,
( spl0_960
<=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
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(f8294,plain,
spl0_959,
inference(avatar_split_clause,[],[f1579,f8292]) ).
fof(f8292,plain,
( spl0_959
<=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
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(f8290,plain,
spl0_958,
inference(avatar_split_clause,[],[f1562,f8288]) ).
fof(f8288,plain,
( spl0_958
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
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(f8286,plain,
spl0_957,
inference(avatar_split_clause,[],[f1561,f8284]) ).
fof(f8284,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(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(f8282,plain,
spl0_956,
inference(avatar_split_clause,[],[f1550,f8280]) ).
fof(f8280,plain,
( spl0_956
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
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(f8278,plain,
spl0_955,
inference(avatar_split_clause,[],[f1549,f8276]) ).
fof(f8276,plain,
( spl0_955
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
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(f8274,plain,
( ~ spl0_953
| spl0_954
| ~ spl0_718
| ~ spl0_878 ),
inference(avatar_split_clause,[],[f8114,f7892,f7211,f8271,f8267]) ).
fof(f8267,plain,
( spl0_953
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f8271,plain,
( spl0_954
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f8114,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_718
| ~ spl0_878 ),
inference(superposition,[],[f7893,f7213]) ).
fof(f8265,plain,
spl0_952,
inference(avatar_split_clause,[],[f1537,f8263]) ).
fof(f8263,plain,
( spl0_952
<=> ! [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_952])]) ).
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(f8261,plain,
spl0_951,
inference(avatar_split_clause,[],[f1513,f8259]) ).
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(f8257,plain,
spl0_950,
inference(avatar_split_clause,[],[f1499,f8255]) ).
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(f8253,plain,
spl0_949,
inference(avatar_split_clause,[],[f1498,f8251]) ).
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(f8249,plain,
spl0_948,
inference(avatar_split_clause,[],[f1490,f8247]) ).
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(f8245,plain,
spl0_947,
inference(avatar_split_clause,[],[f1419,f8243]) ).
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(f8241,plain,
spl0_946,
inference(avatar_split_clause,[],[f1392,f8239]) ).
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(f8237,plain,
spl0_945,
inference(avatar_split_clause,[],[f1385,f8235]) ).
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(f8233,plain,
spl0_944,
inference(avatar_split_clause,[],[f1376,f8231]) ).
fof(f8231,plain,
( spl0_944
<=> ! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
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(f8229,plain,
spl0_943,
inference(avatar_split_clause,[],[f1375,f8227]) ).
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(f8225,plain,
spl0_942,
inference(avatar_split_clause,[],[f1308,f8223]) ).
fof(f8223,plain,
( spl0_942
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
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(f8221,plain,
spl0_941,
inference(avatar_split_clause,[],[f1298,f8219]) ).
fof(f8219,plain,
( spl0_941
<=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
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(f8217,plain,
spl0_940,
inference(avatar_split_clause,[],[f1297,f8215]) ).
fof(f8215,plain,
( spl0_940
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
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(f8213,plain,
spl0_939,
inference(avatar_split_clause,[],[f1177,f8211]) ).
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(f8209,plain,
spl0_938,
inference(avatar_split_clause,[],[f1171,f8207]) ).
fof(f8207,plain,
( spl0_938
<=> ! [X1,X40] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
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(f8204,plain,
spl0_937,
inference(avatar_split_clause,[],[f1167,f8202]) ).
fof(f8202,plain,
( spl0_937
<=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
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(f8200,plain,
spl0_936,
inference(avatar_split_clause,[],[f252,f8198]) ).
fof(f8198,plain,
( spl0_936
<=> ! [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_936])]) ).
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(f8196,plain,
spl0_935,
inference(avatar_split_clause,[],[f246,f8194]) ).
fof(f8194,plain,
( spl0_935
<=> ! [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_935])]) ).
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(f8192,plain,
spl0_934,
inference(avatar_split_clause,[],[f196,f8190]) ).
fof(f8190,plain,
( spl0_934
<=> ! [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_934])]) ).
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(f8188,plain,
spl0_933,
inference(avatar_split_clause,[],[f94,f8186]) ).
fof(f8186,plain,
( spl0_933
<=> ! [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_933])]) ).
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(f8184,plain,
( spl0_932
| ~ spl0_56
| ~ spl0_871 ),
inference(avatar_split_clause,[],[f8089,f7864,f3710,f8181]) ).
fof(f8181,plain,
( spl0_932
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f3710,plain,
( spl0_56
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f7864,plain,
( spl0_871
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f8089,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_871 ),
inference(resolution,[],[f7865,f3712]) ).
fof(f3712,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f3710]) ).
fof(f7865,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) )
| ~ spl0_871 ),
inference(avatar_component_clause,[],[f7864]) ).
fof(f8179,plain,
spl0_931,
inference(avatar_split_clause,[],[f93,f8177]) ).
fof(f8177,plain,
( spl0_931
<=> ! [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_931])]) ).
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(f8175,plain,
spl0_930,
inference(avatar_split_clause,[],[f92,f8173]) ).
fof(f8173,plain,
( spl0_930
<=> ! [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_930])]) ).
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(f8171,plain,
spl0_929,
inference(avatar_split_clause,[],[f91,f8169]) ).
fof(f8169,plain,
( spl0_929
<=> ! [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_929])]) ).
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(f8167,plain,
spl0_928,
inference(avatar_split_clause,[],[f89,f8165]) ).
fof(f8165,plain,
( spl0_928
<=> ! [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_928])]) ).
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(f8163,plain,
spl0_927,
inference(avatar_split_clause,[],[f88,f8161]) ).
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(f8159,plain,
spl0_926,
inference(avatar_split_clause,[],[f87,f8157]) ).
fof(f8157,plain,
( spl0_926
<=> ! [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_926])]) ).
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(f8155,plain,
spl0_925,
inference(avatar_split_clause,[],[f86,f8153]) ).
fof(f8153,plain,
( spl0_925
<=> ! [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_925])]) ).
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(f8151,plain,
spl0_924,
inference(avatar_split_clause,[],[f37,f8149]) ).
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(f8145,plain,
( spl0_923
| ~ spl0_29
| ~ spl0_870 ),
inference(avatar_split_clause,[],[f8087,f7860,f3575,f8142]) ).
fof(f8142,plain,
( spl0_923
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f3575,plain,
( spl0_29
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f7860,plain,
( spl0_870
<=> ! [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_870])]) ).
fof(f8087,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_29
| ~ spl0_870 ),
inference(resolution,[],[f7861,f3577]) ).
fof(f3577,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f3575]) ).
fof(f7861,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) )
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f7860]) ).
fof(f8137,plain,
( spl0_922
| ~ spl0_30
| ~ spl0_862 ),
inference(avatar_split_clause,[],[f8081,f7828,f3580,f8134]) ).
fof(f8134,plain,
( spl0_922
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f7828,plain,
( spl0_862
<=> ! [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_862])]) ).
fof(f8081,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_30
| ~ spl0_862 ),
inference(resolution,[],[f7829,f3582]) ).
fof(f7829,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) )
| ~ spl0_862 ),
inference(avatar_component_clause,[],[f7828]) ).
fof(f8131,plain,
( spl0_921
| ~ spl0_58
| ~ spl0_861 ),
inference(avatar_split_clause,[],[f8080,f7824,f3720,f8128]) ).
fof(f8128,plain,
( spl0_921
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f7824,plain,
( spl0_861
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f8080,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_861 ),
inference(resolution,[],[f7825,f3722]) ).
fof(f7825,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) )
| ~ spl0_861 ),
inference(avatar_component_clause,[],[f7824]) ).
fof(f8121,plain,
( spl0_920
| ~ spl0_650
| ~ spl0_858 ),
inference(avatar_split_clause,[],[f8074,f7812,f6143,f8118]) ).
fof(f8074,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_858 ),
inference(superposition,[],[f7813,f6145]) ).
fof(f8107,plain,
( spl0_919
| ~ spl0_649
| ~ spl0_858 ),
inference(avatar_split_clause,[],[f8073,f7812,f6138,f8104]) ).
fof(f8104,plain,
( spl0_919
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f8073,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_858 ),
inference(superposition,[],[f7813,f6140]) ).
fof(f8072,plain,
( spl0_918
| ~ spl0_841
| ~ spl0_852 ),
inference(avatar_split_clause,[],[f8063,f7788,f7734,f8070]) ).
fof(f7734,plain,
( spl0_841
<=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f8063,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_841
| ~ spl0_852 ),
inference(superposition,[],[f7789,f7735]) ).
fof(f7735,plain,
( ! [X3] : c_div(X3,c_1,tc_nat) = X3
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f7734]) ).
fof(f8052,plain,
spl0_917,
inference(avatar_split_clause,[],[f3329,f8050]) ).
fof(f8050,plain,
( spl0_917
<=> ! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
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(f8048,plain,
spl0_916,
inference(avatar_split_clause,[],[f3237,f8046]) ).
fof(f8046,plain,
( spl0_916
<=> ! [X13,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
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(f8044,plain,
spl0_915,
inference(avatar_split_clause,[],[f3008,f8042]) ).
fof(f8040,plain,
spl0_914,
inference(avatar_split_clause,[],[f3006,f8037]) ).
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(f8035,plain,
spl0_913,
inference(avatar_split_clause,[],[f3002,f8033]) ).
fof(f8033,plain,
( spl0_913
<=> ! [X32] : c_emptyset = c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(X32,c_List_Olist_ONil))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
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(f8031,plain,
spl0_912,
inference(avatar_split_clause,[],[f2982,f8028]) ).
fof(f8028,plain,
( spl0_912
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f8026,plain,
spl0_911,
inference(avatar_split_clause,[],[f2978,f8024]) ).
fof(f8024,plain,
( spl0_911
<=> ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
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(f8022,plain,
spl0_910,
inference(avatar_split_clause,[],[f2928,f8020]) ).
fof(f8020,plain,
( spl0_910
<=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Message_OinvKey(c_Public_OpublicKey(X27,X32)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
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(f8018,plain,
spl0_909,
inference(avatar_split_clause,[],[f2926,f8016]) ).
fof(f8016,plain,
( spl0_909
<=> ! [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_909])]) ).
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(f8014,plain,
spl0_908,
inference(avatar_split_clause,[],[f2910,f8012]) ).
fof(f8012,plain,
( spl0_908
<=> ! [X27,X12] : ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(X27,X12)),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
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(f8010,plain,
spl0_907,
inference(avatar_split_clause,[],[f2906,f8008]) ).
fof(f8008,plain,
( spl0_907
<=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__rec(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
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(f8006,plain,
spl0_906,
inference(avatar_split_clause,[],[f2905,f8004]) ).
fof(f8004,plain,
( spl0_906
<=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__rec(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
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(f8002,plain,
spl0_905,
inference(avatar_split_clause,[],[f2902,f8000]) ).
fof(f8000,plain,
( spl0_905
<=> ! [X45,X1,X3] : c_Public_Okeymode_Okeymode__case(X45,X3,c_Public_Okeymode_OEncryption,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
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(f7998,plain,
spl0_904,
inference(avatar_split_clause,[],[f2901,f7996]) ).
fof(f7996,plain,
( spl0_904
<=> ! [X44,X1,X3] : c_Public_Okeymode_Okeymode__case(X3,X44,c_Public_Okeymode_OSignature,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
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(f7994,plain,
spl0_903,
inference(avatar_split_clause,[],[f2891,f7992]) ).
fof(f7992,plain,
( spl0_903
<=> ! [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_903])]) ).
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(f7990,plain,
spl0_902,
inference(avatar_split_clause,[],[f2790,f7988]) ).
fof(f7988,plain,
( spl0_902
<=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_ONotes(X94,X96),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
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(f7986,plain,
spl0_901,
inference(avatar_split_clause,[],[f2789,f7984]) ).
fof(f7984,plain,
( spl0_901
<=> ! [X96,X94] : c_0 = c_Nat_Osize(c_Event_Oevent_OGets(X94,X96),tc_Event_Oevent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
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(f7982,plain,
spl0_900,
inference(avatar_split_clause,[],[f2780,f7980]) ).
fof(f7980,plain,
( spl0_900
<=> ! [X96,X97,X94,X95] : c_Event_Oevent_ONotes(X95,X97) != c_Event_Oevent_OGets(X94,X96) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
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(f7978,plain,
spl0_899,
inference(avatar_split_clause,[],[f2705,f7976]) ).
fof(f7976,plain,
( spl0_899
<=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
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(f7974,plain,
spl0_898,
inference(avatar_split_clause,[],[f2684,f7972]) ).
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(f7970,plain,
spl0_897,
inference(avatar_split_clause,[],[f2668,f7968]) ).
fof(f7968,plain,
( spl0_897
<=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
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(f7966,plain,
spl0_896,
inference(avatar_split_clause,[],[f2648,f7964]) ).
fof(f7964,plain,
( spl0_896
<=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
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(f7962,plain,
spl0_895,
inference(avatar_split_clause,[],[f2590,f7960]) ).
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(f7958,plain,
spl0_894,
inference(avatar_split_clause,[],[f2588,f7956]) ).
fof(f7956,plain,
( spl0_894
<=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
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(f7954,plain,
spl0_893,
inference(avatar_split_clause,[],[f2587,f7952]) ).
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(f7950,plain,
spl0_892,
inference(avatar_split_clause,[],[f2549,f7948]) ).
fof(f7948,plain,
( spl0_892
<=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
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(f7946,plain,
spl0_891,
inference(avatar_split_clause,[],[f2394,f7944]) ).
fof(f7944,plain,
( spl0_891
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
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(f7942,plain,
spl0_890,
inference(avatar_split_clause,[],[f2374,f7940]) ).
fof(f7940,plain,
( spl0_890
<=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
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(f7938,plain,
spl0_889,
inference(avatar_split_clause,[],[f2372,f7936]) ).
fof(f7936,plain,
( spl0_889
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
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(f7934,plain,
spl0_888,
inference(avatar_split_clause,[],[f2243,f7932]) ).
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(f7930,plain,
spl0_887,
inference(avatar_split_clause,[],[f2238,f7928]) ).
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(f7926,plain,
spl0_886,
inference(avatar_split_clause,[],[f2220,f7924]) ).
fof(f7924,plain,
( spl0_886
<=> ! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
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(f7922,plain,
spl0_885,
inference(avatar_split_clause,[],[f2176,f7920]) ).
fof(f7920,plain,
( spl0_885
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
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(f7918,plain,
spl0_884,
inference(avatar_split_clause,[],[f2169,f7916]) ).
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(f7914,plain,
spl0_883,
inference(avatar_split_clause,[],[f2162,f7912]) ).
fof(f7912,plain,
( spl0_883
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
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(f7910,plain,
spl0_882,
inference(avatar_split_clause,[],[f2161,f7908]) ).
fof(f7908,plain,
( spl0_882
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
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(f7906,plain,
spl0_881,
inference(avatar_split_clause,[],[f2158,f7904]) ).
fof(f7904,plain,
( spl0_881
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
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(f7902,plain,
spl0_880,
inference(avatar_split_clause,[],[f2157,f7900]) ).
fof(f7900,plain,
( spl0_880
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
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(f7898,plain,
spl0_879,
inference(avatar_split_clause,[],[f2144,f7896]) ).
fof(f7896,plain,
( spl0_879
<=> ! [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_879])]) ).
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(f7894,plain,
spl0_878,
inference(avatar_split_clause,[],[f2143,f7892]) ).
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(f7890,plain,
spl0_877,
inference(avatar_split_clause,[],[f2089,f7888]) ).
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(f7886,plain,
spl0_876,
inference(avatar_split_clause,[],[f2088,f7884]) ).
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(f7882,plain,
spl0_875,
inference(avatar_split_clause,[],[f2087,f7880]) ).
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(f7878,plain,
spl0_874,
inference(avatar_split_clause,[],[f2048,f7876]) ).
fof(f7876,plain,
( spl0_874
<=> ! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
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(f7874,plain,
spl0_873,
inference(avatar_split_clause,[],[f2042,f7872]) ).
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(f7870,plain,
spl0_872,
inference(avatar_split_clause,[],[f2040,f7868]) ).
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(f7866,plain,
spl0_871,
inference(avatar_split_clause,[],[f1812,f7864]) ).
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(f7862,plain,
spl0_870,
inference(avatar_split_clause,[],[f1808,f7860]) ).
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(f7858,plain,
spl0_869,
inference(avatar_split_clause,[],[f1790,f7856]) ).
fof(f7856,plain,
( spl0_869
<=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
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(f7854,plain,
spl0_868,
inference(avatar_split_clause,[],[f1788,f7852]) ).
fof(f7852,plain,
( spl0_868
<=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
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(f7850,plain,
spl0_867,
inference(avatar_split_clause,[],[f1732,f7848]) ).
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(f7846,plain,
spl0_866,
inference(avatar_split_clause,[],[f1711,f7844]) ).
fof(f7844,plain,
( spl0_866
<=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
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(f7842,plain,
spl0_865,
inference(avatar_split_clause,[],[f1631,f7840]) ).
fof(f7840,plain,
( spl0_865
<=> ! [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_865])]) ).
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(f7838,plain,
spl0_864,
inference(avatar_split_clause,[],[f1542,f7836]) ).
fof(f7836,plain,
( spl0_864
<=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
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(f7834,plain,
spl0_863,
inference(avatar_split_clause,[],[f1478,f7832]) ).
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(f7830,plain,
spl0_862,
inference(avatar_split_clause,[],[f1401,f7828]) ).
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(f7826,plain,
spl0_861,
inference(avatar_split_clause,[],[f1396,f7824]) ).
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(f7822,plain,
spl0_860,
inference(avatar_split_clause,[],[f1387,f7820]) ).
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(f7818,plain,
spl0_859,
inference(avatar_split_clause,[],[f1373,f7816]) ).
fof(f7816,plain,
( spl0_859
<=> ! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
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(f7814,plain,
spl0_858,
inference(avatar_split_clause,[],[f1367,f7812]) ).
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(f7810,plain,
spl0_857,
inference(avatar_split_clause,[],[f1253,f7808]) ).
fof(f7808,plain,
( spl0_857
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
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(f7806,plain,
spl0_856,
inference(avatar_split_clause,[],[f1252,f7804]) ).
fof(f7804,plain,
( spl0_856
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
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(f7802,plain,
spl0_855,
inference(avatar_split_clause,[],[f1249,f7800]) ).
fof(f7800,plain,
( spl0_855
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
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(f7798,plain,
spl0_854,
inference(avatar_split_clause,[],[f1248,f7796]) ).
fof(f7796,plain,
( spl0_854
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
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(f7794,plain,
spl0_853,
inference(avatar_split_clause,[],[f1225,f7792]) ).
fof(f7792,plain,
( spl0_853
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
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(f7790,plain,
spl0_852,
inference(avatar_split_clause,[],[f1215,f7788]) ).
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(f7786,plain,
spl0_851,
inference(avatar_split_clause,[],[f1202,f7784]) ).
fof(f7784,plain,
( spl0_851
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
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(f7782,plain,
spl0_850,
inference(avatar_split_clause,[],[f1181,f7780]) ).
fof(f7780,plain,
( spl0_850
<=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
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(f7778,plain,
spl0_849,
inference(avatar_split_clause,[],[f95,f7776]) ).
fof(f7776,plain,
( spl0_849
<=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
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(f7774,plain,
spl0_848,
inference(avatar_split_clause,[],[f90,f7772]) ).
fof(f7772,plain,
( spl0_848
<=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
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(f7770,plain,
spl0_847,
inference(avatar_split_clause,[],[f61,f7768]) ).
fof(f7768,plain,
( spl0_847
<=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
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(f7766,plain,
spl0_846,
inference(avatar_split_clause,[],[f45,f7764]) ).
fof(f7764,plain,
( spl0_846
<=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
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(f7762,plain,
spl0_845,
inference(avatar_split_clause,[],[f42,f7760]) ).
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(f7758,plain,
spl0_844,
inference(avatar_split_clause,[],[f41,f7756]) ).
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(f7754,plain,
spl0_843,
inference(avatar_split_clause,[],[f26,f7752]) ).
fof(f7752,plain,
( spl0_843
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
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(f7750,plain,
spl0_842,
inference(avatar_split_clause,[],[f25,f7748]) ).
fof(f7748,plain,
( spl0_842
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
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(f7736,plain,
spl0_841,
inference(avatar_split_clause,[],[f3247,f7734]) ).
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(f7732,plain,
spl0_840,
inference(avatar_split_clause,[],[f3245,f7729]) ).
fof(f7729,plain,
( spl0_840
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
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(f7727,plain,
spl0_839,
inference(avatar_split_clause,[],[f3243,f7725]) ).
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(f7723,plain,
spl0_838,
inference(avatar_split_clause,[],[f3242,f7720]) ).
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(f7718,plain,
spl0_837,
inference(avatar_split_clause,[],[f3240,f7716]) ).
fof(f7716,plain,
( spl0_837
<=> ! [X41,X3] : c_append(c_List_Olist_ONil,X3,X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
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(f7714,plain,
spl0_836,
inference(avatar_split_clause,[],[f3238,f7711]) ).
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(f7709,plain,
spl0_835,
inference(avatar_split_clause,[],[f2929,f7707]) ).
fof(f7707,plain,
( spl0_835
<=> ! [X12,X32,X27] : c_Public_OshrK(X12) != c_Public_OpublicKey(X27,X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
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(f7705,plain,
spl0_834,
inference(avatar_split_clause,[],[f2911,f7703]) ).
fof(f7703,plain,
( spl0_834
<=> ! [X27,X12] : ~ c_in(c_Public_OpublicKey(X27,X12),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
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(f7701,plain,
spl0_833,
inference(avatar_split_clause,[],[f2900,f7699]) ).
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(f7697,plain,
spl0_832,
inference(avatar_split_clause,[],[f2895,f7695]) ).
fof(f7695,plain,
( spl0_832
<=> ! [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_832])]) ).
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(f7693,plain,
spl0_831,
inference(avatar_split_clause,[],[f2871,f7691]) ).
fof(f7691,plain,
( spl0_831
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
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(f7689,plain,
spl0_830,
inference(avatar_split_clause,[],[f2869,f7687]) ).
fof(f7687,plain,
( spl0_830
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
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(f7685,plain,
spl0_829,
inference(avatar_split_clause,[],[f2862,f7683]) ).
fof(f7683,plain,
( spl0_829
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
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(f7681,plain,
spl0_828,
inference(avatar_split_clause,[],[f2854,f7679]) ).
fof(f7679,plain,
( spl0_828
<=> ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
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(f7677,plain,
spl0_827,
inference(avatar_split_clause,[],[f2845,f7675]) ).
fof(f7675,plain,
( spl0_827
<=> ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
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(f7673,plain,
spl0_826,
inference(avatar_split_clause,[],[f2803,f7671]) ).
fof(f7671,plain,
( spl0_826
<=> ! [X12,X88] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
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(f7669,plain,
spl0_825,
inference(avatar_split_clause,[],[f2763,f7667]) ).
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(f7665,plain,
spl0_824,
inference(avatar_split_clause,[],[f2762,f7663]) ).
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(f7661,plain,
spl0_823,
inference(avatar_split_clause,[],[f2761,f7659]) ).
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(f7657,plain,
spl0_822,
inference(avatar_split_clause,[],[f2760,f7655]) ).
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(f7653,plain,
spl0_821,
inference(avatar_split_clause,[],[f2738,f7651]) ).
fof(f7651,plain,
( spl0_821
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
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(f7649,plain,
spl0_820,
inference(avatar_split_clause,[],[f2687,f7647]) ).
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(f7645,plain,
spl0_819,
inference(avatar_split_clause,[],[f2639,f7643]) ).
fof(f7643,plain,
( spl0_819
<=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
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(f7641,plain,
spl0_818,
inference(avatar_split_clause,[],[f2638,f7639]) ).
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(f7637,plain,
spl0_817,
inference(avatar_split_clause,[],[f2634,f7635]) ).
fof(f2634,axiom,
! [X3,X1] : c_union(X3,X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7633,plain,
spl0_816,
inference(avatar_split_clause,[],[f2633,f7631]) ).
fof(f7631,plain,
( spl0_816
<=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
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(f7629,plain,
spl0_815,
inference(avatar_split_clause,[],[f2632,f7627]) ).
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(f7625,plain,
spl0_814,
inference(avatar_split_clause,[],[f2580,f7623]) ).
fof(f7623,plain,
( spl0_814
<=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
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(f7621,plain,
spl0_813,
inference(avatar_split_clause,[],[f2576,f7619]) ).
fof(f7619,plain,
( spl0_813
<=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
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(f7617,plain,
spl0_812,
inference(avatar_split_clause,[],[f2511,f7615]) ).
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(f7613,plain,
spl0_811,
inference(avatar_split_clause,[],[f2499,f7611]) ).
fof(f7611,plain,
( spl0_811
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
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(f7609,plain,
spl0_810,
inference(avatar_split_clause,[],[f2494,f7607]) ).
fof(f7607,plain,
( spl0_810
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
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(f7605,plain,
spl0_809,
inference(avatar_split_clause,[],[f2493,f7603]) ).
fof(f7603,plain,
( spl0_809
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
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(f7601,plain,
spl0_808,
inference(avatar_split_clause,[],[f2381,f7599]) ).
fof(f7599,plain,
( spl0_808
<=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
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(f7597,plain,
spl0_807,
inference(avatar_split_clause,[],[f2380,f7595]) ).
fof(f7595,plain,
( spl0_807
<=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
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(f7593,plain,
spl0_806,
inference(avatar_split_clause,[],[f2378,f7591]) ).
fof(f7591,plain,
( spl0_806
<=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
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(f7589,plain,
spl0_805,
inference(avatar_split_clause,[],[f2370,f7587]) ).
fof(f7587,plain,
( spl0_805
<=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
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(f7585,plain,
spl0_804,
inference(avatar_split_clause,[],[f2368,f7583]) ).
fof(f7583,plain,
( spl0_804
<=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
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(f7581,plain,
spl0_803,
inference(avatar_split_clause,[],[f2344,f7579]) ).
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(f7577,plain,
spl0_802,
inference(avatar_split_clause,[],[f2269,f7575]) ).
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(f7573,plain,
spl0_801,
inference(avatar_split_clause,[],[f2156,f7570]) ).
fof(f7568,plain,
spl0_800,
inference(avatar_split_clause,[],[f2102,f7566]) ).
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(f7564,plain,
spl0_799,
inference(avatar_split_clause,[],[f2100,f7562]) ).
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(f7560,plain,
spl0_798,
inference(avatar_split_clause,[],[f2098,f7558]) ).
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(f7556,plain,
spl0_797,
inference(avatar_split_clause,[],[f2056,f7554]) ).
fof(f7554,plain,
( spl0_797
<=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
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(f7552,plain,
spl0_796,
inference(avatar_split_clause,[],[f2054,f7550]) ).
fof(f7550,plain,
( spl0_796
<=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
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(f7548,plain,
spl0_795,
inference(avatar_split_clause,[],[f2053,f7546]) ).
fof(f7546,plain,
( spl0_795
<=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
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(f7544,plain,
spl0_794,
inference(avatar_split_clause,[],[f2051,f7542]) ).
fof(f7542,plain,
( spl0_794
<=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
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(f7540,plain,
spl0_793,
inference(avatar_split_clause,[],[f2050,f7538]) ).
fof(f7538,plain,
( spl0_793
<=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
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(f7536,plain,
spl0_792,
inference(avatar_split_clause,[],[f2041,f7534]) ).
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(f7532,plain,
spl0_791,
inference(avatar_split_clause,[],[f2034,f7530]) ).
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(f7528,plain,
spl0_790,
inference(avatar_split_clause,[],[f2026,f7526]) ).
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(f7524,plain,
spl0_789,
inference(avatar_split_clause,[],[f1763,f7522]) ).
fof(f7522,plain,
( spl0_789
<=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
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(f7520,plain,
spl0_788,
inference(avatar_split_clause,[],[f1762,f7518]) ).
fof(f7518,plain,
( spl0_788
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
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(f7516,plain,
spl0_787,
inference(avatar_split_clause,[],[f1747,f7514]) ).
fof(f7514,plain,
( spl0_787
<=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
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(f7512,plain,
spl0_786,
inference(avatar_split_clause,[],[f1741,f7510]) ).
fof(f7510,plain,
( spl0_786
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
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(f7508,plain,
spl0_785,
inference(avatar_split_clause,[],[f1722,f7506]) ).
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(f7504,plain,
spl0_784,
inference(avatar_split_clause,[],[f1719,f7502]) ).
fof(f7502,plain,
( spl0_784
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
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(f7500,plain,
spl0_783,
inference(avatar_split_clause,[],[f1707,f7498]) ).
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(f7496,plain,
spl0_782,
inference(avatar_split_clause,[],[f1689,f7494]) ).
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(f7492,plain,
spl0_781,
inference(avatar_split_clause,[],[f1628,f7490]) ).
fof(f7490,plain,
( spl0_781
<=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
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(f7488,plain,
spl0_780,
inference(avatar_split_clause,[],[f1624,f7486]) ).
fof(f7486,plain,
( spl0_780
<=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
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(f7484,plain,
spl0_779,
inference(avatar_split_clause,[],[f1615,f7482]) ).
fof(f7482,plain,
( spl0_779
<=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
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(f7480,plain,
spl0_778,
inference(avatar_split_clause,[],[f1598,f7478]) ).
fof(f7478,plain,
( spl0_778
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
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(f7476,plain,
spl0_777,
inference(avatar_split_clause,[],[f1569,f7474]) ).
fof(f7474,plain,
( spl0_777
<=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
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(f7472,plain,
spl0_776,
inference(avatar_split_clause,[],[f1568,f7470]) ).
fof(f7470,plain,
( spl0_776
<=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
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(f7468,plain,
spl0_775,
inference(avatar_split_clause,[],[f1494,f7466]) ).
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(f7464,plain,
spl0_774,
inference(avatar_split_clause,[],[f1491,f7462]) ).
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(f7460,plain,
spl0_773,
inference(avatar_split_clause,[],[f1489,f7458]) ).
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(f7456,plain,
spl0_772,
inference(avatar_split_clause,[],[f1474,f7454]) ).
fof(f7454,plain,
( spl0_772
<=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
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(f7452,plain,
spl0_771,
inference(avatar_split_clause,[],[f1466,f7450]) ).
fof(f7450,plain,
( spl0_771
<=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
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(f7448,plain,
spl0_770,
inference(avatar_split_clause,[],[f1464,f7446]) ).
fof(f7446,plain,
( spl0_770
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
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(f7444,plain,
spl0_769,
inference(avatar_split_clause,[],[f1432,f7442]) ).
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(f7440,plain,
spl0_768,
inference(avatar_split_clause,[],[f1364,f7438]) ).
fof(f7438,plain,
( spl0_768
<=> ! [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_768])]) ).
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(f7436,plain,
spl0_767,
inference(avatar_split_clause,[],[f1363,f7434]) ).
fof(f7434,plain,
( spl0_767
<=> ! [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_767])]) ).
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(f7432,plain,
spl0_766,
inference(avatar_split_clause,[],[f1358,f7430]) ).
fof(f7430,plain,
( spl0_766
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
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(f7428,plain,
spl0_765,
inference(avatar_split_clause,[],[f1357,f7426]) ).
fof(f7426,plain,
( spl0_765
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
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(f7424,plain,
spl0_764,
inference(avatar_split_clause,[],[f1350,f7421]) ).
fof(f7421,plain,
( spl0_764
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
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(f7419,plain,
spl0_763,
inference(avatar_split_clause,[],[f1247,f7417]) ).
fof(f7417,plain,
( spl0_763
<=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
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(f7415,plain,
spl0_762,
inference(avatar_split_clause,[],[f1241,f7413]) ).
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(f7411,plain,
spl0_761,
inference(avatar_split_clause,[],[f1230,f7409]) ).
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(f7407,plain,
spl0_760,
inference(avatar_split_clause,[],[f1213,f7405]) ).
fof(f7405,plain,
( spl0_760
<=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
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(f7403,plain,
spl0_759,
inference(avatar_split_clause,[],[f1212,f7401]) ).
fof(f7401,plain,
( spl0_759
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
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(f7399,plain,
spl0_758,
inference(avatar_split_clause,[],[f1211,f7397]) ).
fof(f7397,plain,
( spl0_758
<=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
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(f7395,plain,
spl0_757,
inference(avatar_split_clause,[],[f1183,f7393]) ).
fof(f7393,plain,
( spl0_757
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
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(f7391,plain,
spl0_756,
inference(avatar_split_clause,[],[f1182,f7389]) ).
fof(f7389,plain,
( spl0_756
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
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(f7387,plain,
spl0_755,
inference(avatar_split_clause,[],[f1176,f7385]) ).
fof(f7385,plain,
( spl0_755
<=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
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(f7383,plain,
spl0_754,
inference(avatar_split_clause,[],[f68,f7381]) ).
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(f7379,plain,
spl0_753,
inference(avatar_split_clause,[],[f2975,f7376]) ).
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(f7374,plain,
spl0_752,
inference(avatar_split_clause,[],[f2973,f7371]) ).
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(f7368,plain,
( spl0_751
| ~ spl0_649
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f7351,f7087,f6138,f7365]) ).
fof(f7365,plain,
( spl0_751
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f7351,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_691 ),
inference(superposition,[],[f7088,f6140]) ).
fof(f7362,plain,
( ~ spl0_750
| ~ spl0_650
| ~ spl0_689 ),
inference(avatar_split_clause,[],[f7348,f7079,f6143,f7359]) ).
fof(f7359,plain,
( spl0_750
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f7079,plain,
( spl0_689
<=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f7348,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_689 ),
inference(superposition,[],[f7080,f6145]) ).
fof(f7080,plain,
( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
| ~ spl0_689 ),
inference(avatar_component_clause,[],[f7079]) ).
fof(f7357,plain,
( ~ spl0_749
| ~ spl0_649
| ~ spl0_689 ),
inference(avatar_split_clause,[],[f7347,f7079,f6138,f7354]) ).
fof(f7354,plain,
( spl0_749
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f7347,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_689 ),
inference(superposition,[],[f7080,f6140]) ).
fof(f7346,plain,
spl0_748,
inference(avatar_split_clause,[],[f3244,f7343]) ).
fof(f7343,plain,
( spl0_748
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
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(f7341,plain,
spl0_747,
inference(avatar_split_clause,[],[f3239,f7339]) ).
fof(f7339,plain,
( spl0_747
<=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
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(f7337,plain,
spl0_746,
inference(avatar_split_clause,[],[f2981,f7334]) ).
fof(f7332,plain,
spl0_745,
inference(avatar_split_clause,[],[f2923,f7330]) ).
fof(f7330,plain,
( spl0_745
<=> ! [X86] : c_in(c_Public_OshrK(X86),c_Message_OsymKeys,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
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(f7328,plain,
spl0_744,
inference(avatar_split_clause,[],[f2908,f7325]) ).
fof(f7325,plain,
( spl0_744
<=> c_0 = c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
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(f7323,plain,
spl0_743,
inference(avatar_split_clause,[],[f2907,f7320]) ).
fof(f7320,plain,
( spl0_743
<=> c_0 = c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
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(f7318,plain,
spl0_742,
inference(avatar_split_clause,[],[f2740,f7316]) ).
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(f7314,plain,
spl0_741,
inference(avatar_split_clause,[],[f2739,f7311]) ).
fof(f7311,plain,
( spl0_741
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
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(f7309,plain,
spl0_740,
inference(avatar_split_clause,[],[f2737,f7306]) ).
fof(f7306,plain,
( spl0_740
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
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(f7304,plain,
spl0_739,
inference(avatar_split_clause,[],[f2714,f7302]) ).
fof(f7302,plain,
( spl0_739
<=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
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(f7300,plain,
spl0_738,
inference(avatar_split_clause,[],[f2698,f7298]) ).
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(f7296,plain,
spl0_737,
inference(avatar_split_clause,[],[f2691,f7294]) ).
fof(f7294,plain,
( spl0_737
<=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
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(f7292,plain,
spl0_736,
inference(avatar_split_clause,[],[f2651,f7290]) ).
fof(f7290,plain,
( spl0_736
<=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f2651,axiom,
! [X1] : c_emptyset = c_Union(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f7288,plain,
spl0_735,
inference(avatar_split_clause,[],[f2649,f7286]) ).
fof(f7286,plain,
( spl0_735
<=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f2649,axiom,
! [X1] : c_UNIV = c_Union(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f7284,plain,
spl0_734,
inference(avatar_split_clause,[],[f2625,f7282]) ).
fof(f7282,plain,
( spl0_734
<=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2625,axiom,
! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f7280,plain,
spl0_733,
inference(avatar_split_clause,[],[f2619,f7278]) ).
fof(f7278,plain,
( spl0_733
<=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2619,axiom,
! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f7276,plain,
spl0_732,
inference(avatar_split_clause,[],[f2612,f7274]) ).
fof(f7274,plain,
( spl0_732
<=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f2612,axiom,
! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f7272,plain,
spl0_731,
inference(avatar_split_clause,[],[f2567,f7269]) ).
fof(f7269,plain,
( spl0_731
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
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(f7267,plain,
spl0_730,
inference(avatar_split_clause,[],[f2528,f7264]) ).
fof(f7264,plain,
( spl0_730
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
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(f7262,plain,
spl0_729,
inference(avatar_split_clause,[],[f2386,f7260]) ).
fof(f7258,plain,
spl0_728,
inference(avatar_split_clause,[],[f2164,f7255]) ).
fof(f7255,plain,
( spl0_728
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
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(f7253,plain,
spl0_727,
inference(avatar_split_clause,[],[f2163,f7250]) ).
fof(f7250,plain,
( spl0_727
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
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(f7248,plain,
spl0_726,
inference(avatar_split_clause,[],[f2152,f7246]) ).
fof(f7246,plain,
( spl0_726
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
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(f7244,plain,
spl0_725,
inference(avatar_split_clause,[],[f2151,f7242]) ).
fof(f7242,plain,
( spl0_725
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
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(f7240,plain,
spl0_724,
inference(avatar_split_clause,[],[f2135,f7238]) ).
fof(f7238,plain,
( spl0_724
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
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(f7236,plain,
spl0_723,
inference(avatar_split_clause,[],[f2130,f7234]) ).
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(f7232,plain,
spl0_722,
inference(avatar_split_clause,[],[f2115,f7230]) ).
fof(f7230,plain,
( spl0_722
<=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f7228,plain,
spl0_721,
inference(avatar_split_clause,[],[f2114,f7226]) ).
fof(f7224,plain,
spl0_720,
inference(avatar_split_clause,[],[f2106,f7221]) ).
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(f7219,plain,
spl0_719,
inference(avatar_split_clause,[],[f2105,f7216]) ).
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(f7214,plain,
spl0_718,
inference(avatar_split_clause,[],[f1866,f7211]) ).
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(f7209,plain,
spl0_717,
inference(avatar_split_clause,[],[f1785,f7207]) ).
fof(f7207,plain,
( spl0_717
<=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
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(f7205,plain,
spl0_716,
inference(avatar_split_clause,[],[f1778,f7203]) ).
fof(f7203,plain,
( spl0_716
<=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
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(f7201,plain,
spl0_715,
inference(avatar_split_clause,[],[f1751,f7199]) ).
fof(f7199,plain,
( spl0_715
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
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(f7197,plain,
spl0_714,
inference(avatar_split_clause,[],[f1736,f7195]) ).
fof(f7195,plain,
( spl0_714
<=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
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(f7193,plain,
spl0_713,
inference(avatar_split_clause,[],[f1729,f7191]) ).
fof(f7191,plain,
( spl0_713
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f7189,plain,
spl0_712,
inference(avatar_split_clause,[],[f1716,f7187]) ).
fof(f7187,plain,
( spl0_712
<=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
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(f7185,plain,
spl0_711,
inference(avatar_split_clause,[],[f1688,f7182]) ).
fof(f7182,plain,
( spl0_711
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
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(f7180,plain,
spl0_710,
inference(avatar_split_clause,[],[f1687,f7177]) ).
fof(f7177,plain,
( spl0_710
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
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(f7175,plain,
spl0_709,
inference(avatar_split_clause,[],[f1686,f7172]) ).
fof(f7172,plain,
( spl0_709
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
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(f7170,plain,
spl0_708,
inference(avatar_split_clause,[],[f1685,f7167]) ).
fof(f7167,plain,
( spl0_708
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
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(f7165,plain,
spl0_707,
inference(avatar_split_clause,[],[f1684,f7162]) ).
fof(f7162,plain,
( spl0_707
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
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(f7160,plain,
spl0_706,
inference(avatar_split_clause,[],[f1683,f7157]) ).
fof(f7157,plain,
( spl0_706
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
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(f7155,plain,
spl0_705,
inference(avatar_split_clause,[],[f1682,f7152]) ).
fof(f7152,plain,
( spl0_705
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
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(f7150,plain,
spl0_704,
inference(avatar_split_clause,[],[f1681,f7147]) ).
fof(f7147,plain,
( spl0_704
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
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(f7145,plain,
spl0_703,
inference(avatar_split_clause,[],[f1680,f7142]) ).
fof(f7142,plain,
( spl0_703
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
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(f7140,plain,
spl0_702,
inference(avatar_split_clause,[],[f1679,f7137]) ).
fof(f7137,plain,
( spl0_702
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
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(f7135,plain,
spl0_701,
inference(avatar_split_clause,[],[f1678,f7132]) ).
fof(f7132,plain,
( spl0_701
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
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(f7130,plain,
spl0_700,
inference(avatar_split_clause,[],[f1677,f7127]) ).
fof(f7127,plain,
( spl0_700
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
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(f7125,plain,
spl0_699,
inference(avatar_split_clause,[],[f1676,f7122]) ).
fof(f7122,plain,
( spl0_699
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
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(f7120,plain,
spl0_698,
inference(avatar_split_clause,[],[f1675,f7117]) ).
fof(f7117,plain,
( spl0_698
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
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(f7115,plain,
spl0_697,
inference(avatar_split_clause,[],[f1674,f7112]) ).
fof(f7112,plain,
( spl0_697
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
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(f7110,plain,
spl0_696,
inference(avatar_split_clause,[],[f1673,f7107]) ).
fof(f7107,plain,
( spl0_696
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
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(f7105,plain,
spl0_695,
inference(avatar_split_clause,[],[f1638,f7103]) ).
fof(f7103,plain,
( spl0_695
<=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
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(f7101,plain,
spl0_694,
inference(avatar_split_clause,[],[f1567,f7099]) ).
fof(f7099,plain,
( spl0_694
<=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
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(f7097,plain,
spl0_693,
inference(avatar_split_clause,[],[f1543,f7095]) ).
fof(f7095,plain,
( spl0_693
<=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
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(f7093,plain,
spl0_692,
inference(avatar_split_clause,[],[f1536,f7091]) ).
fof(f7091,plain,
( spl0_692
<=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
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(f7089,plain,
spl0_691,
inference(avatar_split_clause,[],[f1424,f7087]) ).
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(f7085,plain,
spl0_690,
inference(avatar_split_clause,[],[f1384,f7083]) ).
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(f7081,plain,
spl0_689,
inference(avatar_split_clause,[],[f1378,f7079]) ).
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(f7077,plain,
~ spl0_688,
inference(avatar_split_clause,[],[f1309,f7074]) ).
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(f7072,plain,
spl0_687,
inference(avatar_split_clause,[],[f1296,f7070]) ).
fof(f7070,plain,
( spl0_687
<=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1296,axiom,
! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f7068,plain,
spl0_686,
inference(avatar_split_clause,[],[f1295,f7066]) ).
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(f7064,plain,
spl0_685,
inference(avatar_split_clause,[],[f1278,f7062]) ).
fof(f7062,plain,
( spl0_685
<=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
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(f7060,plain,
spl0_684,
inference(avatar_split_clause,[],[f1255,f7057]) ).
fof(f7057,plain,
( spl0_684
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
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(f7055,plain,
spl0_683,
inference(avatar_split_clause,[],[f1254,f7052]) ).
fof(f7052,plain,
( spl0_683
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
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(f7050,plain,
spl0_682,
inference(avatar_split_clause,[],[f1184,f7047]) ).
fof(f7047,plain,
( spl0_682
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
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(f7045,plain,
spl0_681,
inference(avatar_split_clause,[],[f1173,f7043]) ).
fof(f7043,plain,
( spl0_681
<=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
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(f7041,plain,
spl0_680,
inference(avatar_split_clause,[],[f1172,f7039]) ).
fof(f7039,plain,
( spl0_680
<=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
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(f7037,plain,
spl0_679,
inference(avatar_split_clause,[],[f1165,f7035]) ).
fof(f7035,plain,
( spl0_679
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
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(f7033,plain,
spl0_678,
inference(avatar_split_clause,[],[f1164,f7031]) ).
fof(f7031,plain,
( spl0_678
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
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(f7029,plain,
spl0_677,
inference(avatar_split_clause,[],[f250,f7027]) ).
fof(f7027,plain,
( spl0_677
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
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(f7025,plain,
spl0_676,
inference(avatar_split_clause,[],[f128,f7023]) ).
fof(f7023,plain,
( spl0_676
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
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(f7021,plain,
spl0_675,
inference(avatar_split_clause,[],[f112,f7019]) ).
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(f7017,plain,
spl0_674,
inference(avatar_split_clause,[],[f101,f7015]) ).
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(f7013,plain,
spl0_673,
inference(avatar_split_clause,[],[f44,f7011]) ).
fof(f7011,plain,
( spl0_673
<=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
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(f7009,plain,
spl0_672,
inference(avatar_split_clause,[],[f28,f7007]) ).
fof(f7007,plain,
( spl0_672
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
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(f7005,plain,
( ~ spl0_671
| ~ spl0_650
| ~ spl0_652 ),
inference(avatar_split_clause,[],[f6995,f6153,f6143,f7002]) ).
fof(f7002,plain,
( spl0_671
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f6153,plain,
( spl0_652
<=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f6995,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_650
| ~ spl0_652 ),
inference(superposition,[],[f6154,f6145]) ).
fof(f6154,plain,
( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_652 ),
inference(avatar_component_clause,[],[f6153]) ).
fof(f7000,plain,
( ~ spl0_670
| ~ spl0_649
| ~ spl0_652 ),
inference(avatar_split_clause,[],[f6994,f6153,f6138,f6997]) ).
fof(f6997,plain,
( spl0_670
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f6994,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_649
| ~ spl0_652 ),
inference(superposition,[],[f6154,f6140]) ).
fof(f6233,plain,
spl0_669,
inference(avatar_split_clause,[],[f3254,f6230]) ).
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(f6228,plain,
spl0_668,
inference(avatar_split_clause,[],[f3235,f6226]) ).
fof(f6226,plain,
( spl0_668
<=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
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(f6224,plain,
spl0_667,
inference(avatar_split_clause,[],[f3234,f6221]) ).
fof(f6221,plain,
( spl0_667
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
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(f6219,plain,
spl0_666,
inference(avatar_split_clause,[],[f3233,f6216]) ).
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(f6214,plain,
spl0_665,
inference(avatar_split_clause,[],[f2853,f6211]) ).
fof(f2853,axiom,
c_emptyset = c_Message_Oanalz(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
fof(f6209,plain,
spl0_664,
inference(avatar_split_clause,[],[f2773,f6206]) ).
fof(f6206,plain,
( spl0_664
<=> c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
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(f6204,plain,
~ spl0_663,
inference(avatar_split_clause,[],[f2772,f6201]) ).
fof(f6201,plain,
( spl0_663
<=> c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
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(f6199,plain,
spl0_662,
inference(avatar_split_clause,[],[f2770,f6196]) ).
fof(f2770,axiom,
c_emptyset = c_Message_Oparts(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
fof(f6194,plain,
spl0_661,
inference(avatar_split_clause,[],[f2743,f6191]) ).
fof(f2743,axiom,
c_emptyset = c_Message_OkeysFor(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
fof(f6189,plain,
spl0_660,
inference(avatar_split_clause,[],[f2735,f6187]) ).
fof(f6187,plain,
( spl0_660
<=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
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(f6185,plain,
spl0_659,
inference(avatar_split_clause,[],[f2730,f6183]) ).
fof(f6183,plain,
( spl0_659
<=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
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(f6181,plain,
spl0_658,
inference(avatar_split_clause,[],[f2672,f6179]) ).
fof(f2672,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f6177,plain,
spl0_657,
inference(avatar_split_clause,[],[f2155,f6174]) ).
fof(f6174,plain,
( spl0_657
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
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(f6172,plain,
spl0_656,
inference(avatar_split_clause,[],[f2091,f6170]) ).
fof(f6170,plain,
( spl0_656
<=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2091,axiom,
! [X21] : ~ c_less(X21,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f6168,plain,
spl0_655,
inference(avatar_split_clause,[],[f2049,f6165]) ).
fof(f2049,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f6163,plain,
spl0_654,
inference(avatar_split_clause,[],[f1709,f6161]) ).
fof(f6161,plain,
( spl0_654
<=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
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(f6159,plain,
spl0_653,
inference(avatar_split_clause,[],[f1482,f6157]) ).
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(f6155,plain,
spl0_652,
inference(avatar_split_clause,[],[f1393,f6153]) ).
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(f6151,plain,
spl0_651,
inference(avatar_split_clause,[],[f1386,f6148]) ).
fof(f6148,plain,
( spl0_651
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1386,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f6146,plain,
spl0_650,
inference(avatar_split_clause,[],[f1374,f6143]) ).
fof(f6141,plain,
spl0_649,
inference(avatar_split_clause,[],[f1371,f6138]) ).
fof(f1371,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f6136,plain,
spl0_648,
inference(avatar_split_clause,[],[f1229,f6134]) ).
fof(f6134,plain,
( spl0_648
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
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(f6132,plain,
spl0_647,
inference(avatar_split_clause,[],[f1159,f6130]) ).
fof(f6130,plain,
( spl0_647
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
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(f6128,plain,
spl0_646,
inference(avatar_split_clause,[],[f1158,f6126]) ).
fof(f6126,plain,
( spl0_646
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
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(f6124,plain,
spl0_645,
inference(avatar_split_clause,[],[f1157,f6122]) ).
fof(f6122,plain,
( spl0_645
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
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(f6120,plain,
spl0_644,
inference(avatar_split_clause,[],[f1156,f6118]) ).
fof(f6118,plain,
( spl0_644
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
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(f6116,plain,
spl0_643,
inference(avatar_split_clause,[],[f1155,f6114]) ).
fof(f6114,plain,
( spl0_643
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
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(f6112,plain,
spl0_642,
inference(avatar_split_clause,[],[f1154,f6110]) ).
fof(f6110,plain,
( spl0_642
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
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(f6108,plain,
spl0_641,
inference(avatar_split_clause,[],[f1153,f6106]) ).
fof(f6106,plain,
( spl0_641
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
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(f6104,plain,
spl0_640,
inference(avatar_split_clause,[],[f1148,f6102]) ).
fof(f6102,plain,
( spl0_640
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
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(f6100,plain,
spl0_639,
inference(avatar_split_clause,[],[f1147,f6098]) ).
fof(f6098,plain,
( spl0_639
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
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(f6096,plain,
spl0_638,
inference(avatar_split_clause,[],[f1146,f6094]) ).
fof(f6094,plain,
( spl0_638
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
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(f6092,plain,
spl0_637,
inference(avatar_split_clause,[],[f1145,f6090]) ).
fof(f6090,plain,
( spl0_637
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
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(f6088,plain,
spl0_636,
inference(avatar_split_clause,[],[f1144,f6086]) ).
fof(f6086,plain,
( spl0_636
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
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(f6084,plain,
spl0_635,
inference(avatar_split_clause,[],[f1143,f6082]) ).
fof(f6082,plain,
( spl0_635
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
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(f6080,plain,
spl0_634,
inference(avatar_split_clause,[],[f1140,f6078]) ).
fof(f6078,plain,
( spl0_634
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
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(f6076,plain,
spl0_633,
inference(avatar_split_clause,[],[f1139,f6074]) ).
fof(f6074,plain,
( spl0_633
<=> ! [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_633])]) ).
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(f6072,plain,
spl0_632,
inference(avatar_split_clause,[],[f1138,f6070]) ).
fof(f6070,plain,
( spl0_632
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
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(f6068,plain,
spl0_631,
inference(avatar_split_clause,[],[f1135,f6066]) ).
fof(f6066,plain,
( spl0_631
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
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(f6064,plain,
spl0_630,
inference(avatar_split_clause,[],[f1132,f6062]) ).
fof(f6062,plain,
( spl0_630
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
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(f6060,plain,
spl0_629,
inference(avatar_split_clause,[],[f1131,f6058]) ).
fof(f6058,plain,
( spl0_629
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
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(f6056,plain,
spl0_628,
inference(avatar_split_clause,[],[f1130,f6054]) ).
fof(f6054,plain,
( spl0_628
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
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(f6052,plain,
spl0_627,
inference(avatar_split_clause,[],[f1129,f6050]) ).
fof(f6050,plain,
( spl0_627
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
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(f6048,plain,
spl0_626,
inference(avatar_split_clause,[],[f1126,f6046]) ).
fof(f6046,plain,
( spl0_626
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
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(f6044,plain,
spl0_625,
inference(avatar_split_clause,[],[f1125,f6042]) ).
fof(f6042,plain,
( spl0_625
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
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(f6040,plain,
spl0_624,
inference(avatar_split_clause,[],[f1120,f6038]) ).
fof(f6038,plain,
( spl0_624
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
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(f6036,plain,
spl0_623,
inference(avatar_split_clause,[],[f1117,f6034]) ).
fof(f6034,plain,
( spl0_623
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
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(f6032,plain,
spl0_622,
inference(avatar_split_clause,[],[f1116,f6030]) ).
fof(f6030,plain,
( spl0_622
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
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(f6028,plain,
spl0_621,
inference(avatar_split_clause,[],[f1115,f6026]) ).
fof(f6026,plain,
( spl0_621
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
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(f6024,plain,
spl0_620,
inference(avatar_split_clause,[],[f1113,f6022]) ).
fof(f6022,plain,
( spl0_620
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
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(f6020,plain,
spl0_619,
inference(avatar_split_clause,[],[f1107,f6018]) ).
fof(f6018,plain,
( spl0_619
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
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(f6016,plain,
spl0_618,
inference(avatar_split_clause,[],[f1099,f6014]) ).
fof(f6014,plain,
( spl0_618
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
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(f6012,plain,
spl0_617,
inference(avatar_split_clause,[],[f1098,f6010]) ).
fof(f6010,plain,
( spl0_617
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
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(f6008,plain,
spl0_616,
inference(avatar_split_clause,[],[f1097,f6006]) ).
fof(f6006,plain,
( spl0_616
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
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(f6004,plain,
spl0_615,
inference(avatar_split_clause,[],[f1096,f6002]) ).
fof(f6002,plain,
( spl0_615
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
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(f6000,plain,
spl0_614,
inference(avatar_split_clause,[],[f1095,f5998]) ).
fof(f5998,plain,
( spl0_614
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
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(f5996,plain,
spl0_613,
inference(avatar_split_clause,[],[f1093,f5994]) ).
fof(f5994,plain,
( spl0_613
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
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(f5992,plain,
spl0_612,
inference(avatar_split_clause,[],[f1092,f5990]) ).
fof(f5990,plain,
( spl0_612
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
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(f5988,plain,
spl0_611,
inference(avatar_split_clause,[],[f1091,f5986]) ).
fof(f5986,plain,
( spl0_611
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
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(f5984,plain,
spl0_610,
inference(avatar_split_clause,[],[f1090,f5982]) ).
fof(f5982,plain,
( spl0_610
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
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(f5980,plain,
spl0_609,
inference(avatar_split_clause,[],[f1089,f5978]) ).
fof(f5978,plain,
( spl0_609
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
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(f5976,plain,
spl0_608,
inference(avatar_split_clause,[],[f1084,f5974]) ).
fof(f5974,plain,
( spl0_608
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
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(f5972,plain,
spl0_607,
inference(avatar_split_clause,[],[f1083,f5970]) ).
fof(f5970,plain,
( spl0_607
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
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(f5968,plain,
spl0_606,
inference(avatar_split_clause,[],[f1082,f5966]) ).
fof(f5966,plain,
( spl0_606
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
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(f5964,plain,
spl0_605,
inference(avatar_split_clause,[],[f1080,f5962]) ).
fof(f5962,plain,
( spl0_605
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
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(f5960,plain,
spl0_604,
inference(avatar_split_clause,[],[f1078,f5958]) ).
fof(f5958,plain,
( spl0_604
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
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(f5956,plain,
spl0_603,
inference(avatar_split_clause,[],[f1073,f5954]) ).
fof(f5954,plain,
( spl0_603
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
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(f5952,plain,
spl0_602,
inference(avatar_split_clause,[],[f1072,f5950]) ).
fof(f5950,plain,
( spl0_602
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
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(f5948,plain,
spl0_601,
inference(avatar_split_clause,[],[f1071,f5946]) ).
fof(f5946,plain,
( spl0_601
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
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(f5944,plain,
spl0_600,
inference(avatar_split_clause,[],[f1070,f5942]) ).
fof(f5942,plain,
( spl0_600
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
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(f5940,plain,
spl0_599,
inference(avatar_split_clause,[],[f1068,f5938]) ).
fof(f5938,plain,
( spl0_599
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
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(f5936,plain,
spl0_598,
inference(avatar_split_clause,[],[f1067,f5934]) ).
fof(f5934,plain,
( spl0_598
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
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(f5932,plain,
spl0_597,
inference(avatar_split_clause,[],[f1062,f5930]) ).
fof(f5930,plain,
( spl0_597
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
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(f5928,plain,
spl0_596,
inference(avatar_split_clause,[],[f1059,f5926]) ).
fof(f5926,plain,
( spl0_596
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
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(f5924,plain,
spl0_595,
inference(avatar_split_clause,[],[f1058,f5922]) ).
fof(f5922,plain,
( spl0_595
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
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(f5920,plain,
spl0_594,
inference(avatar_split_clause,[],[f1057,f5918]) ).
fof(f5918,plain,
( spl0_594
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
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(f5916,plain,
spl0_593,
inference(avatar_split_clause,[],[f1056,f5914]) ).
fof(f5914,plain,
( spl0_593
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
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(f5912,plain,
spl0_592,
inference(avatar_split_clause,[],[f1053,f5910]) ).
fof(f5910,plain,
( spl0_592
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
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(f5908,plain,
spl0_591,
inference(avatar_split_clause,[],[f1052,f5906]) ).
fof(f5906,plain,
( spl0_591
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
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(f5904,plain,
spl0_590,
inference(avatar_split_clause,[],[f1051,f5902]) ).
fof(f5902,plain,
( spl0_590
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
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(f5900,plain,
spl0_589,
inference(avatar_split_clause,[],[f1050,f5898]) ).
fof(f5898,plain,
( spl0_589
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
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(f5896,plain,
spl0_588,
inference(avatar_split_clause,[],[f1049,f5894]) ).
fof(f5894,plain,
( spl0_588
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
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(f5892,plain,
spl0_587,
inference(avatar_split_clause,[],[f1048,f5890]) ).
fof(f5890,plain,
( spl0_587
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
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(f5888,plain,
spl0_586,
inference(avatar_split_clause,[],[f1047,f5886]) ).
fof(f5886,plain,
( spl0_586
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
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(f5884,plain,
spl0_585,
inference(avatar_split_clause,[],[f1046,f5882]) ).
fof(f5882,plain,
( spl0_585
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
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(f5880,plain,
spl0_584,
inference(avatar_split_clause,[],[f1044,f5878]) ).
fof(f5878,plain,
( spl0_584
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
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(f5876,plain,
spl0_583,
inference(avatar_split_clause,[],[f1043,f5874]) ).
fof(f5874,plain,
( spl0_583
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
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(f5872,plain,
spl0_582,
inference(avatar_split_clause,[],[f1042,f5870]) ).
fof(f5870,plain,
( spl0_582
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
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(f5868,plain,
spl0_581,
inference(avatar_split_clause,[],[f1041,f5866]) ).
fof(f5866,plain,
( spl0_581
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
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(f5864,plain,
spl0_580,
inference(avatar_split_clause,[],[f1040,f5862]) ).
fof(f5862,plain,
( spl0_580
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
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(f5860,plain,
spl0_579,
inference(avatar_split_clause,[],[f1035,f5858]) ).
fof(f5858,plain,
( spl0_579
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
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(f5856,plain,
spl0_578,
inference(avatar_split_clause,[],[f1034,f5854]) ).
fof(f5854,plain,
( spl0_578
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
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(f5852,plain,
spl0_577,
inference(avatar_split_clause,[],[f1033,f5850]) ).
fof(f5850,plain,
( spl0_577
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
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(f5848,plain,
spl0_576,
inference(avatar_split_clause,[],[f1030,f5846]) ).
fof(f5846,plain,
( spl0_576
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
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(f5844,plain,
spl0_575,
inference(avatar_split_clause,[],[f1027,f5842]) ).
fof(f5842,plain,
( spl0_575
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
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(f5840,plain,
spl0_574,
inference(avatar_split_clause,[],[f1026,f5838]) ).
fof(f5838,plain,
( spl0_574
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
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(f5836,plain,
spl0_573,
inference(avatar_split_clause,[],[f1024,f5834]) ).
fof(f5834,plain,
( spl0_573
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
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(f5832,plain,
spl0_572,
inference(avatar_split_clause,[],[f1023,f5830]) ).
fof(f5830,plain,
( spl0_572
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
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(f5828,plain,
spl0_571,
inference(avatar_split_clause,[],[f1022,f5826]) ).
fof(f5826,plain,
( spl0_571
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
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(f5824,plain,
spl0_570,
inference(avatar_split_clause,[],[f1021,f5822]) ).
fof(f5822,plain,
( spl0_570
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
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(f5820,plain,
spl0_569,
inference(avatar_split_clause,[],[f1018,f5818]) ).
fof(f5818,plain,
( spl0_569
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
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(f5816,plain,
spl0_568,
inference(avatar_split_clause,[],[f1017,f5814]) ).
fof(f5814,plain,
( spl0_568
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
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(f5812,plain,
spl0_567,
inference(avatar_split_clause,[],[f989,f5810]) ).
fof(f5810,plain,
( spl0_567
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
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(f5808,plain,
spl0_566,
inference(avatar_split_clause,[],[f987,f5806]) ).
fof(f5806,plain,
( spl0_566
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
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(f5804,plain,
spl0_565,
inference(avatar_split_clause,[],[f984,f5802]) ).
fof(f5802,plain,
( spl0_565
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
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(f5800,plain,
spl0_564,
inference(avatar_split_clause,[],[f983,f5798]) ).
fof(f5798,plain,
( spl0_564
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
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(f5796,plain,
spl0_563,
inference(avatar_split_clause,[],[f982,f5794]) ).
fof(f5794,plain,
( spl0_563
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
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(f5792,plain,
spl0_562,
inference(avatar_split_clause,[],[f981,f5790]) ).
fof(f5790,plain,
( spl0_562
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
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(f5788,plain,
spl0_561,
inference(avatar_split_clause,[],[f980,f5786]) ).
fof(f5786,plain,
( spl0_561
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
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(f5784,plain,
spl0_560,
inference(avatar_split_clause,[],[f979,f5782]) ).
fof(f5782,plain,
( spl0_560
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
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(f5780,plain,
spl0_559,
inference(avatar_split_clause,[],[f977,f5778]) ).
fof(f5778,plain,
( spl0_559
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
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(f5776,plain,
spl0_558,
inference(avatar_split_clause,[],[f976,f5774]) ).
fof(f5774,plain,
( spl0_558
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
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(f5772,plain,
spl0_557,
inference(avatar_split_clause,[],[f974,f5770]) ).
fof(f5770,plain,
( spl0_557
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
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(f5768,plain,
spl0_556,
inference(avatar_split_clause,[],[f971,f5766]) ).
fof(f5766,plain,
( spl0_556
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
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(f5764,plain,
spl0_555,
inference(avatar_split_clause,[],[f970,f5762]) ).
fof(f5762,plain,
( spl0_555
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
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(f5760,plain,
spl0_554,
inference(avatar_split_clause,[],[f968,f5758]) ).
fof(f5758,plain,
( spl0_554
<=> ! [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_554])]) ).
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(f5756,plain,
spl0_553,
inference(avatar_split_clause,[],[f967,f5754]) ).
fof(f5754,plain,
( spl0_553
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
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(f5752,plain,
spl0_552,
inference(avatar_split_clause,[],[f966,f5750]) ).
fof(f5750,plain,
( spl0_552
<=> ! [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_552])]) ).
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(f5748,plain,
spl0_551,
inference(avatar_split_clause,[],[f965,f5746]) ).
fof(f5746,plain,
( spl0_551
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
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(f5744,plain,
spl0_550,
inference(avatar_split_clause,[],[f964,f5742]) ).
fof(f5742,plain,
( spl0_550
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
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(f5740,plain,
spl0_549,
inference(avatar_split_clause,[],[f963,f5738]) ).
fof(f5738,plain,
( spl0_549
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
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(f5736,plain,
spl0_548,
inference(avatar_split_clause,[],[f962,f5734]) ).
fof(f5734,plain,
( spl0_548
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
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(f5732,plain,
spl0_547,
inference(avatar_split_clause,[],[f961,f5730]) ).
fof(f5730,plain,
( spl0_547
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
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(f5728,plain,
spl0_546,
inference(avatar_split_clause,[],[f957,f5726]) ).
fof(f5726,plain,
( spl0_546
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
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(f5724,plain,
spl0_545,
inference(avatar_split_clause,[],[f956,f5722]) ).
fof(f5722,plain,
( spl0_545
<=> ! [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_545])]) ).
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(f5720,plain,
spl0_544,
inference(avatar_split_clause,[],[f955,f5718]) ).
fof(f5718,plain,
( spl0_544
<=> ! [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_544])]) ).
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(f5716,plain,
spl0_543,
inference(avatar_split_clause,[],[f954,f5714]) ).
fof(f5714,plain,
( spl0_543
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
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(f5712,plain,
spl0_542,
inference(avatar_split_clause,[],[f949,f5710]) ).
fof(f5710,plain,
( spl0_542
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
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(f5708,plain,
spl0_541,
inference(avatar_split_clause,[],[f947,f5706]) ).
fof(f5706,plain,
( spl0_541
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
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(f5704,plain,
spl0_540,
inference(avatar_split_clause,[],[f946,f5702]) ).
fof(f5702,plain,
( spl0_540
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
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(f5700,plain,
spl0_539,
inference(avatar_split_clause,[],[f945,f5698]) ).
fof(f5698,plain,
( spl0_539
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
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(f5696,plain,
spl0_538,
inference(avatar_split_clause,[],[f944,f5694]) ).
fof(f5694,plain,
( spl0_538
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
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(f5692,plain,
spl0_537,
inference(avatar_split_clause,[],[f942,f5690]) ).
fof(f5690,plain,
( spl0_537
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
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(f5688,plain,
spl0_536,
inference(avatar_split_clause,[],[f941,f5686]) ).
fof(f5686,plain,
( spl0_536
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
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(f5684,plain,
spl0_535,
inference(avatar_split_clause,[],[f940,f5682]) ).
fof(f5682,plain,
( spl0_535
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
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(f5680,plain,
spl0_534,
inference(avatar_split_clause,[],[f939,f5678]) ).
fof(f5678,plain,
( spl0_534
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
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(f5676,plain,
spl0_533,
inference(avatar_split_clause,[],[f938,f5674]) ).
fof(f5674,plain,
( spl0_533
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
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(f5672,plain,
spl0_532,
inference(avatar_split_clause,[],[f937,f5670]) ).
fof(f5670,plain,
( spl0_532
<=> ! [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_532])]) ).
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(f5668,plain,
spl0_531,
inference(avatar_split_clause,[],[f936,f5666]) ).
fof(f5666,plain,
( spl0_531
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
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(f5664,plain,
spl0_530,
inference(avatar_split_clause,[],[f935,f5662]) ).
fof(f5662,plain,
( spl0_530
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
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(f5660,plain,
spl0_529,
inference(avatar_split_clause,[],[f934,f5658]) ).
fof(f5658,plain,
( spl0_529
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
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(f5656,plain,
spl0_528,
inference(avatar_split_clause,[],[f933,f5654]) ).
fof(f5654,plain,
( spl0_528
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
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(f5652,plain,
spl0_527,
inference(avatar_split_clause,[],[f932,f5650]) ).
fof(f5650,plain,
( spl0_527
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
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(f5648,plain,
spl0_526,
inference(avatar_split_clause,[],[f931,f5646]) ).
fof(f5646,plain,
( spl0_526
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
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(f5644,plain,
spl0_525,
inference(avatar_split_clause,[],[f930,f5642]) ).
fof(f5642,plain,
( spl0_525
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
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(f5640,plain,
spl0_524,
inference(avatar_split_clause,[],[f929,f5638]) ).
fof(f5638,plain,
( spl0_524
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
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(f5636,plain,
spl0_523,
inference(avatar_split_clause,[],[f928,f5634]) ).
fof(f5634,plain,
( spl0_523
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
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(f5632,plain,
spl0_522,
inference(avatar_split_clause,[],[f927,f5630]) ).
fof(f5630,plain,
( spl0_522
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
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(f5628,plain,
spl0_521,
inference(avatar_split_clause,[],[f926,f5626]) ).
fof(f5626,plain,
( spl0_521
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
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(f5624,plain,
spl0_520,
inference(avatar_split_clause,[],[f925,f5622]) ).
fof(f5622,plain,
( spl0_520
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
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(f5620,plain,
spl0_519,
inference(avatar_split_clause,[],[f924,f5618]) ).
fof(f5618,plain,
( spl0_519
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
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(f5616,plain,
spl0_518,
inference(avatar_split_clause,[],[f923,f5614]) ).
fof(f5614,plain,
( spl0_518
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
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(f5612,plain,
spl0_517,
inference(avatar_split_clause,[],[f922,f5610]) ).
fof(f5610,plain,
( spl0_517
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
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(f5608,plain,
spl0_516,
inference(avatar_split_clause,[],[f921,f5606]) ).
fof(f5606,plain,
( spl0_516
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
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(f5604,plain,
spl0_515,
inference(avatar_split_clause,[],[f920,f5602]) ).
fof(f5602,plain,
( spl0_515
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
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(f5600,plain,
spl0_514,
inference(avatar_split_clause,[],[f919,f5598]) ).
fof(f5598,plain,
( spl0_514
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
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(f5596,plain,
spl0_513,
inference(avatar_split_clause,[],[f918,f5594]) ).
fof(f5594,plain,
( spl0_513
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
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(f5592,plain,
spl0_512,
inference(avatar_split_clause,[],[f917,f5590]) ).
fof(f5590,plain,
( spl0_512
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
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(f5588,plain,
spl0_511,
inference(avatar_split_clause,[],[f916,f5586]) ).
fof(f5586,plain,
( spl0_511
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
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(f5584,plain,
spl0_510,
inference(avatar_split_clause,[],[f915,f5582]) ).
fof(f5582,plain,
( spl0_510
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
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(f5580,plain,
spl0_509,
inference(avatar_split_clause,[],[f914,f5578]) ).
fof(f5578,plain,
( spl0_509
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
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(f5576,plain,
spl0_508,
inference(avatar_split_clause,[],[f913,f5574]) ).
fof(f5574,plain,
( spl0_508
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
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(f5572,plain,
spl0_507,
inference(avatar_split_clause,[],[f912,f5570]) ).
fof(f5570,plain,
( spl0_507
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
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(f5568,plain,
spl0_506,
inference(avatar_split_clause,[],[f911,f5566]) ).
fof(f5566,plain,
( spl0_506
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
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(f5564,plain,
spl0_505,
inference(avatar_split_clause,[],[f910,f5562]) ).
fof(f5562,plain,
( spl0_505
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
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(f5560,plain,
spl0_504,
inference(avatar_split_clause,[],[f909,f5558]) ).
fof(f5558,plain,
( spl0_504
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
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(f5556,plain,
spl0_503,
inference(avatar_split_clause,[],[f908,f5554]) ).
fof(f5554,plain,
( spl0_503
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
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(f5552,plain,
spl0_502,
inference(avatar_split_clause,[],[f905,f5550]) ).
fof(f5550,plain,
( spl0_502
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
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(f5548,plain,
spl0_501,
inference(avatar_split_clause,[],[f903,f5546]) ).
fof(f5546,plain,
( spl0_501
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
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(f5544,plain,
spl0_500,
inference(avatar_split_clause,[],[f902,f5542]) ).
fof(f5542,plain,
( spl0_500
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
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(f5540,plain,
spl0_499,
inference(avatar_split_clause,[],[f900,f5538]) ).
fof(f5538,plain,
( spl0_499
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
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(f5536,plain,
spl0_498,
inference(avatar_split_clause,[],[f897,f5534]) ).
fof(f5534,plain,
( spl0_498
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
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(f5532,plain,
spl0_497,
inference(avatar_split_clause,[],[f896,f5530]) ).
fof(f5530,plain,
( spl0_497
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
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(f5528,plain,
spl0_496,
inference(avatar_split_clause,[],[f895,f5526]) ).
fof(f5526,plain,
( spl0_496
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
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(f5524,plain,
spl0_495,
inference(avatar_split_clause,[],[f893,f5522]) ).
fof(f5522,plain,
( spl0_495
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
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(f5520,plain,
spl0_494,
inference(avatar_split_clause,[],[f892,f5518]) ).
fof(f5518,plain,
( spl0_494
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
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(f5516,plain,
spl0_493,
inference(avatar_split_clause,[],[f891,f5514]) ).
fof(f5514,plain,
( spl0_493
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
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(f5512,plain,
spl0_492,
inference(avatar_split_clause,[],[f888,f5510]) ).
fof(f5510,plain,
( spl0_492
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
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(f5508,plain,
spl0_491,
inference(avatar_split_clause,[],[f887,f5506]) ).
fof(f5506,plain,
( spl0_491
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
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(f5504,plain,
spl0_490,
inference(avatar_split_clause,[],[f886,f5502]) ).
fof(f5502,plain,
( spl0_490
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
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(f5500,plain,
spl0_489,
inference(avatar_split_clause,[],[f885,f5498]) ).
fof(f5498,plain,
( spl0_489
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
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(f5496,plain,
spl0_488,
inference(avatar_split_clause,[],[f883,f5494]) ).
fof(f5494,plain,
( spl0_488
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
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(f5492,plain,
spl0_487,
inference(avatar_split_clause,[],[f882,f5490]) ).
fof(f5490,plain,
( spl0_487
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
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(f5488,plain,
spl0_486,
inference(avatar_split_clause,[],[f881,f5486]) ).
fof(f5486,plain,
( spl0_486
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
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(f5484,plain,
spl0_485,
inference(avatar_split_clause,[],[f880,f5482]) ).
fof(f5482,plain,
( spl0_485
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
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(f5480,plain,
spl0_484,
inference(avatar_split_clause,[],[f879,f5478]) ).
fof(f5478,plain,
( spl0_484
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
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(f5476,plain,
spl0_483,
inference(avatar_split_clause,[],[f878,f5474]) ).
fof(f5474,plain,
( spl0_483
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
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(f5472,plain,
spl0_482,
inference(avatar_split_clause,[],[f877,f5470]) ).
fof(f5470,plain,
( spl0_482
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
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(f5468,plain,
spl0_481,
inference(avatar_split_clause,[],[f876,f5466]) ).
fof(f5466,plain,
( spl0_481
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
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(f5464,plain,
spl0_480,
inference(avatar_split_clause,[],[f875,f5462]) ).
fof(f5462,plain,
( spl0_480
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
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(f5460,plain,
spl0_479,
inference(avatar_split_clause,[],[f874,f5458]) ).
fof(f5458,plain,
( spl0_479
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
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(f5456,plain,
spl0_478,
inference(avatar_split_clause,[],[f873,f5454]) ).
fof(f5454,plain,
( spl0_478
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
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(f5452,plain,
spl0_477,
inference(avatar_split_clause,[],[f872,f5450]) ).
fof(f5450,plain,
( spl0_477
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
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(f5448,plain,
spl0_476,
inference(avatar_split_clause,[],[f871,f5446]) ).
fof(f5446,plain,
( spl0_476
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
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(f5444,plain,
spl0_475,
inference(avatar_split_clause,[],[f870,f5442]) ).
fof(f5442,plain,
( spl0_475
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
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(f5440,plain,
spl0_474,
inference(avatar_split_clause,[],[f869,f5438]) ).
fof(f5438,plain,
( spl0_474
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
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(f5436,plain,
spl0_473,
inference(avatar_split_clause,[],[f868,f5434]) ).
fof(f5434,plain,
( spl0_473
<=> ! [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_473])]) ).
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(f5432,plain,
spl0_472,
inference(avatar_split_clause,[],[f867,f5430]) ).
fof(f5430,plain,
( spl0_472
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
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(f5428,plain,
spl0_471,
inference(avatar_split_clause,[],[f865,f5426]) ).
fof(f5426,plain,
( spl0_471
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
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(f5424,plain,
spl0_470,
inference(avatar_split_clause,[],[f864,f5422]) ).
fof(f5422,plain,
( spl0_470
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
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(f5420,plain,
spl0_469,
inference(avatar_split_clause,[],[f863,f5418]) ).
fof(f5418,plain,
( spl0_469
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
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(f5416,plain,
spl0_468,
inference(avatar_split_clause,[],[f862,f5414]) ).
fof(f5414,plain,
( spl0_468
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
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(f5412,plain,
spl0_467,
inference(avatar_split_clause,[],[f861,f5410]) ).
fof(f5410,plain,
( spl0_467
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
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(f5408,plain,
spl0_466,
inference(avatar_split_clause,[],[f856,f5406]) ).
fof(f5406,plain,
( spl0_466
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
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(f5404,plain,
spl0_465,
inference(avatar_split_clause,[],[f855,f5402]) ).
fof(f5402,plain,
( spl0_465
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
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(f5400,plain,
spl0_464,
inference(avatar_split_clause,[],[f854,f5398]) ).
fof(f5398,plain,
( spl0_464
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
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(f5396,plain,
spl0_463,
inference(avatar_split_clause,[],[f853,f5394]) ).
fof(f5394,plain,
( spl0_463
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
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(f5392,plain,
spl0_462,
inference(avatar_split_clause,[],[f852,f5390]) ).
fof(f5390,plain,
( spl0_462
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
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(f5388,plain,
spl0_461,
inference(avatar_split_clause,[],[f851,f5386]) ).
fof(f5386,plain,
( spl0_461
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
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(f5384,plain,
spl0_460,
inference(avatar_split_clause,[],[f850,f5382]) ).
fof(f5382,plain,
( spl0_460
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
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(f5380,plain,
spl0_459,
inference(avatar_split_clause,[],[f849,f5378]) ).
fof(f5378,plain,
( spl0_459
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
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(f5376,plain,
spl0_458,
inference(avatar_split_clause,[],[f847,f5374]) ).
fof(f5374,plain,
( spl0_458
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
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(f5372,plain,
spl0_457,
inference(avatar_split_clause,[],[f846,f5370]) ).
fof(f5370,plain,
( spl0_457
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
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(f5368,plain,
spl0_456,
inference(avatar_split_clause,[],[f845,f5366]) ).
fof(f5366,plain,
( spl0_456
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
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(f5364,plain,
spl0_455,
inference(avatar_split_clause,[],[f844,f5362]) ).
fof(f5362,plain,
( spl0_455
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
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(f5360,plain,
spl0_454,
inference(avatar_split_clause,[],[f843,f5358]) ).
fof(f5358,plain,
( spl0_454
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
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(f5356,plain,
spl0_453,
inference(avatar_split_clause,[],[f842,f5354]) ).
fof(f5354,plain,
( spl0_453
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
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(f5352,plain,
spl0_452,
inference(avatar_split_clause,[],[f840,f5350]) ).
fof(f5350,plain,
( spl0_452
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
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(f5348,plain,
spl0_451,
inference(avatar_split_clause,[],[f839,f5346]) ).
fof(f5346,plain,
( spl0_451
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
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(f5344,plain,
spl0_450,
inference(avatar_split_clause,[],[f838,f5342]) ).
fof(f5342,plain,
( spl0_450
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
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(f5340,plain,
spl0_449,
inference(avatar_split_clause,[],[f837,f5338]) ).
fof(f5338,plain,
( spl0_449
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
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(f5336,plain,
spl0_448,
inference(avatar_split_clause,[],[f836,f5334]) ).
fof(f5334,plain,
( spl0_448
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
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(f5332,plain,
spl0_447,
inference(avatar_split_clause,[],[f835,f5330]) ).
fof(f5330,plain,
( spl0_447
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
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(f5328,plain,
spl0_446,
inference(avatar_split_clause,[],[f834,f5326]) ).
fof(f5326,plain,
( spl0_446
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
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(f5324,plain,
spl0_445,
inference(avatar_split_clause,[],[f833,f5322]) ).
fof(f5322,plain,
( spl0_445
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
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(f5320,plain,
spl0_444,
inference(avatar_split_clause,[],[f832,f5318]) ).
fof(f5318,plain,
( spl0_444
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
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(f5316,plain,
spl0_443,
inference(avatar_split_clause,[],[f831,f5314]) ).
fof(f5314,plain,
( spl0_443
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
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(f5312,plain,
spl0_442,
inference(avatar_split_clause,[],[f830,f5310]) ).
fof(f5310,plain,
( spl0_442
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
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(f5308,plain,
spl0_441,
inference(avatar_split_clause,[],[f829,f5306]) ).
fof(f5306,plain,
( spl0_441
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
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(f5304,plain,
spl0_440,
inference(avatar_split_clause,[],[f828,f5302]) ).
fof(f5302,plain,
( spl0_440
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
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(f5300,plain,
spl0_439,
inference(avatar_split_clause,[],[f827,f5298]) ).
fof(f5298,plain,
( spl0_439
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
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(f5296,plain,
spl0_438,
inference(avatar_split_clause,[],[f826,f5294]) ).
fof(f5294,plain,
( spl0_438
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
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(f5292,plain,
spl0_437,
inference(avatar_split_clause,[],[f825,f5290]) ).
fof(f5290,plain,
( spl0_437
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
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(f5288,plain,
spl0_436,
inference(avatar_split_clause,[],[f824,f5286]) ).
fof(f5286,plain,
( spl0_436
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
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(f5284,plain,
spl0_435,
inference(avatar_split_clause,[],[f823,f5282]) ).
fof(f5282,plain,
( spl0_435
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
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(f5280,plain,
spl0_434,
inference(avatar_split_clause,[],[f822,f5278]) ).
fof(f5278,plain,
( spl0_434
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
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(f5276,plain,
spl0_433,
inference(avatar_split_clause,[],[f821,f5274]) ).
fof(f5274,plain,
( spl0_433
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
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(f5272,plain,
spl0_432,
inference(avatar_split_clause,[],[f820,f5270]) ).
fof(f5270,plain,
( spl0_432
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
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(f5268,plain,
spl0_431,
inference(avatar_split_clause,[],[f819,f5266]) ).
fof(f5266,plain,
( spl0_431
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
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(f5264,plain,
spl0_430,
inference(avatar_split_clause,[],[f816,f5262]) ).
fof(f5262,plain,
( spl0_430
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
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(f5260,plain,
spl0_429,
inference(avatar_split_clause,[],[f814,f5258]) ).
fof(f5258,plain,
( spl0_429
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
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(f5256,plain,
spl0_428,
inference(avatar_split_clause,[],[f812,f5254]) ).
fof(f5254,plain,
( spl0_428
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
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(f5252,plain,
spl0_427,
inference(avatar_split_clause,[],[f809,f5250]) ).
fof(f5250,plain,
( spl0_427
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
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(f5248,plain,
spl0_426,
inference(avatar_split_clause,[],[f808,f5246]) ).
fof(f5246,plain,
( spl0_426
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
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(f5244,plain,
spl0_425,
inference(avatar_split_clause,[],[f807,f5242]) ).
fof(f5242,plain,
( spl0_425
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
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(f5240,plain,
spl0_424,
inference(avatar_split_clause,[],[f806,f5238]) ).
fof(f5238,plain,
( spl0_424
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
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(f5236,plain,
spl0_423,
inference(avatar_split_clause,[],[f804,f5234]) ).
fof(f5234,plain,
( spl0_423
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
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(f5232,plain,
spl0_422,
inference(avatar_split_clause,[],[f803,f5230]) ).
fof(f5230,plain,
( spl0_422
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
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(f5228,plain,
spl0_421,
inference(avatar_split_clause,[],[f802,f5226]) ).
fof(f5226,plain,
( spl0_421
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
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(f5224,plain,
spl0_420,
inference(avatar_split_clause,[],[f801,f5222]) ).
fof(f5222,plain,
( spl0_420
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
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(f5220,plain,
spl0_419,
inference(avatar_split_clause,[],[f800,f5218]) ).
fof(f5218,plain,
( spl0_419
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
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(f5216,plain,
spl0_418,
inference(avatar_split_clause,[],[f799,f5214]) ).
fof(f5214,plain,
( spl0_418
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
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(f5212,plain,
spl0_417,
inference(avatar_split_clause,[],[f798,f5210]) ).
fof(f5210,plain,
( spl0_417
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
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(f5208,plain,
spl0_416,
inference(avatar_split_clause,[],[f797,f5206]) ).
fof(f5206,plain,
( spl0_416
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
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(f5204,plain,
spl0_415,
inference(avatar_split_clause,[],[f796,f5202]) ).
fof(f5202,plain,
( spl0_415
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
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(f5200,plain,
spl0_414,
inference(avatar_split_clause,[],[f732,f5198]) ).
fof(f5198,plain,
( spl0_414
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
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(f5196,plain,
spl0_413,
inference(avatar_split_clause,[],[f729,f5194]) ).
fof(f5194,plain,
( spl0_413
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
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(f5192,plain,
spl0_412,
inference(avatar_split_clause,[],[f728,f5190]) ).
fof(f5190,plain,
( spl0_412
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
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(f5188,plain,
spl0_411,
inference(avatar_split_clause,[],[f727,f5186]) ).
fof(f5186,plain,
( spl0_411
<=> ! [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_411])]) ).
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(f5184,plain,
spl0_410,
inference(avatar_split_clause,[],[f726,f5182]) ).
fof(f5182,plain,
( spl0_410
<=> ! [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_410])]) ).
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(f5180,plain,
spl0_409,
inference(avatar_split_clause,[],[f725,f5178]) ).
fof(f5178,plain,
( spl0_409
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
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(f5176,plain,
spl0_408,
inference(avatar_split_clause,[],[f724,f5174]) ).
fof(f5174,plain,
( spl0_408
<=> ! [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_408])]) ).
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(f5172,plain,
spl0_407,
inference(avatar_split_clause,[],[f723,f5170]) ).
fof(f5170,plain,
( spl0_407
<=> ! [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_407])]) ).
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(f5168,plain,
spl0_406,
inference(avatar_split_clause,[],[f722,f5166]) ).
fof(f5166,plain,
( spl0_406
<=> ! [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_406])]) ).
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(f5164,plain,
spl0_405,
inference(avatar_split_clause,[],[f721,f5162]) ).
fof(f5162,plain,
( spl0_405
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
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(f5160,plain,
spl0_404,
inference(avatar_split_clause,[],[f720,f5158]) ).
fof(f5158,plain,
( spl0_404
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
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(f5156,plain,
spl0_403,
inference(avatar_split_clause,[],[f719,f5154]) ).
fof(f5154,plain,
( spl0_403
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
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(f5152,plain,
spl0_402,
inference(avatar_split_clause,[],[f718,f5150]) ).
fof(f5150,plain,
( spl0_402
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
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(f5148,plain,
spl0_401,
inference(avatar_split_clause,[],[f716,f5146]) ).
fof(f5146,plain,
( spl0_401
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
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(f5144,plain,
spl0_400,
inference(avatar_split_clause,[],[f715,f5142]) ).
fof(f5142,plain,
( spl0_400
<=> ! [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_400])]) ).
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(f5140,plain,
spl0_399,
inference(avatar_split_clause,[],[f714,f5138]) ).
fof(f5138,plain,
( spl0_399
<=> ! [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_399])]) ).
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(f5136,plain,
spl0_398,
inference(avatar_split_clause,[],[f713,f5134]) ).
fof(f5134,plain,
( spl0_398
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
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(f5132,plain,
spl0_397,
inference(avatar_split_clause,[],[f712,f5130]) ).
fof(f5130,plain,
( spl0_397
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
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(f5128,plain,
spl0_396,
inference(avatar_split_clause,[],[f711,f5126]) ).
fof(f5126,plain,
( spl0_396
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
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(f5124,plain,
spl0_395,
inference(avatar_split_clause,[],[f710,f5122]) ).
fof(f5122,plain,
( spl0_395
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
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(f5120,plain,
spl0_394,
inference(avatar_split_clause,[],[f709,f5118]) ).
fof(f5118,plain,
( spl0_394
<=> ! [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_394])]) ).
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(f5116,plain,
spl0_393,
inference(avatar_split_clause,[],[f706,f5114]) ).
fof(f5114,plain,
( spl0_393
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
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(f5112,plain,
spl0_392,
inference(avatar_split_clause,[],[f705,f5110]) ).
fof(f5110,plain,
( spl0_392
<=> ! [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_392])]) ).
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(f5108,plain,
spl0_391,
inference(avatar_split_clause,[],[f704,f5106]) ).
fof(f5106,plain,
( spl0_391
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
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(f5104,plain,
spl0_390,
inference(avatar_split_clause,[],[f703,f5102]) ).
fof(f5102,plain,
( spl0_390
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
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(f5100,plain,
spl0_389,
inference(avatar_split_clause,[],[f702,f5098]) ).
fof(f5098,plain,
( spl0_389
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
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(f5096,plain,
spl0_388,
inference(avatar_split_clause,[],[f701,f5094]) ).
fof(f5094,plain,
( spl0_388
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
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(f5092,plain,
spl0_387,
inference(avatar_split_clause,[],[f700,f5090]) ).
fof(f5090,plain,
( spl0_387
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
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(f5088,plain,
spl0_386,
inference(avatar_split_clause,[],[f698,f5086]) ).
fof(f5086,plain,
( spl0_386
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
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(f5084,plain,
spl0_385,
inference(avatar_split_clause,[],[f697,f5082]) ).
fof(f5082,plain,
( spl0_385
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
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(f5080,plain,
spl0_384,
inference(avatar_split_clause,[],[f696,f5078]) ).
fof(f5078,plain,
( spl0_384
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
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(f5076,plain,
spl0_383,
inference(avatar_split_clause,[],[f695,f5074]) ).
fof(f5074,plain,
( spl0_383
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
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(f5072,plain,
spl0_382,
inference(avatar_split_clause,[],[f694,f5070]) ).
fof(f5070,plain,
( spl0_382
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
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(f5068,plain,
spl0_381,
inference(avatar_split_clause,[],[f693,f5066]) ).
fof(f5066,plain,
( spl0_381
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
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(f5064,plain,
spl0_380,
inference(avatar_split_clause,[],[f692,f5062]) ).
fof(f5062,plain,
( spl0_380
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
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(f5060,plain,
spl0_379,
inference(avatar_split_clause,[],[f691,f5058]) ).
fof(f5058,plain,
( spl0_379
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
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(f5056,plain,
spl0_378,
inference(avatar_split_clause,[],[f688,f5054]) ).
fof(f5054,plain,
( spl0_378
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
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(f5052,plain,
spl0_377,
inference(avatar_split_clause,[],[f686,f5050]) ).
fof(f5050,plain,
( spl0_377
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
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(f5048,plain,
spl0_376,
inference(avatar_split_clause,[],[f685,f5046]) ).
fof(f5046,plain,
( spl0_376
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
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(f5044,plain,
spl0_375,
inference(avatar_split_clause,[],[f683,f5042]) ).
fof(f5042,plain,
( spl0_375
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
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(f5040,plain,
spl0_374,
inference(avatar_split_clause,[],[f680,f5038]) ).
fof(f5038,plain,
( spl0_374
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
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(f5036,plain,
spl0_373,
inference(avatar_split_clause,[],[f679,f5034]) ).
fof(f5034,plain,
( spl0_373
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
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(f5032,plain,
spl0_372,
inference(avatar_split_clause,[],[f678,f5030]) ).
fof(f5030,plain,
( spl0_372
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
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(f5028,plain,
spl0_371,
inference(avatar_split_clause,[],[f677,f5026]) ).
fof(f5026,plain,
( spl0_371
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
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(f5024,plain,
spl0_370,
inference(avatar_split_clause,[],[f676,f5022]) ).
fof(f5022,plain,
( spl0_370
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
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(f5020,plain,
spl0_369,
inference(avatar_split_clause,[],[f675,f5018]) ).
fof(f5018,plain,
( spl0_369
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
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(f5016,plain,
spl0_368,
inference(avatar_split_clause,[],[f674,f5014]) ).
fof(f5014,plain,
( spl0_368
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
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(f5012,plain,
spl0_367,
inference(avatar_split_clause,[],[f673,f5010]) ).
fof(f5010,plain,
( spl0_367
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
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(f5008,plain,
spl0_366,
inference(avatar_split_clause,[],[f672,f5006]) ).
fof(f5006,plain,
( spl0_366
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
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(f5004,plain,
spl0_365,
inference(avatar_split_clause,[],[f671,f5002]) ).
fof(f5002,plain,
( spl0_365
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
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(f5000,plain,
spl0_364,
inference(avatar_split_clause,[],[f670,f4998]) ).
fof(f4998,plain,
( spl0_364
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
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(f4996,plain,
spl0_363,
inference(avatar_split_clause,[],[f668,f4994]) ).
fof(f4994,plain,
( spl0_363
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
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(f4992,plain,
spl0_362,
inference(avatar_split_clause,[],[f666,f4990]) ).
fof(f4990,plain,
( spl0_362
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
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(f4988,plain,
spl0_361,
inference(avatar_split_clause,[],[f663,f4986]) ).
fof(f4986,plain,
( spl0_361
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
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(f4984,plain,
spl0_360,
inference(avatar_split_clause,[],[f661,f4982]) ).
fof(f4982,plain,
( spl0_360
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
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(f4980,plain,
spl0_359,
inference(avatar_split_clause,[],[f659,f4978]) ).
fof(f4978,plain,
( spl0_359
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
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(f4976,plain,
spl0_358,
inference(avatar_split_clause,[],[f656,f4974]) ).
fof(f4974,plain,
( spl0_358
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
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(f4972,plain,
spl0_357,
inference(avatar_split_clause,[],[f655,f4970]) ).
fof(f4970,plain,
( spl0_357
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
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(f4968,plain,
spl0_356,
inference(avatar_split_clause,[],[f654,f4966]) ).
fof(f4966,plain,
( spl0_356
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
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(f4964,plain,
spl0_355,
inference(avatar_split_clause,[],[f653,f4962]) ).
fof(f4962,plain,
( spl0_355
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
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(f4960,plain,
spl0_354,
inference(avatar_split_clause,[],[f651,f4958]) ).
fof(f4958,plain,
( spl0_354
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
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(f4956,plain,
spl0_353,
inference(avatar_split_clause,[],[f650,f4954]) ).
fof(f4954,plain,
( spl0_353
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
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(f4952,plain,
spl0_352,
inference(avatar_split_clause,[],[f649,f4950]) ).
fof(f4950,plain,
( spl0_352
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
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(f4948,plain,
spl0_351,
inference(avatar_split_clause,[],[f648,f4946]) ).
fof(f4946,plain,
( spl0_351
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
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(f4944,plain,
spl0_350,
inference(avatar_split_clause,[],[f647,f4942]) ).
fof(f4942,plain,
( spl0_350
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
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(f4940,plain,
spl0_349,
inference(avatar_split_clause,[],[f646,f4938]) ).
fof(f4938,plain,
( spl0_349
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
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(f4936,plain,
spl0_348,
inference(avatar_split_clause,[],[f645,f4934]) ).
fof(f4934,plain,
( spl0_348
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
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(f4932,plain,
spl0_347,
inference(avatar_split_clause,[],[f644,f4930]) ).
fof(f4930,plain,
( spl0_347
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
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(f4928,plain,
spl0_346,
inference(avatar_split_clause,[],[f643,f4926]) ).
fof(f4926,plain,
( spl0_346
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
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(f4924,plain,
spl0_345,
inference(avatar_split_clause,[],[f607,f4922]) ).
fof(f4922,plain,
( spl0_345
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
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(f4920,plain,
spl0_344,
inference(avatar_split_clause,[],[f606,f4918]) ).
fof(f4918,plain,
( spl0_344
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
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(f4916,plain,
spl0_343,
inference(avatar_split_clause,[],[f605,f4914]) ).
fof(f4914,plain,
( spl0_343
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
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(f4912,plain,
spl0_342,
inference(avatar_split_clause,[],[f604,f4910]) ).
fof(f4910,plain,
( spl0_342
<=> ! [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_342])]) ).
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(f4908,plain,
spl0_341,
inference(avatar_split_clause,[],[f603,f4906]) ).
fof(f4906,plain,
( spl0_341
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
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(f4904,plain,
spl0_340,
inference(avatar_split_clause,[],[f601,f4902]) ).
fof(f4902,plain,
( spl0_340
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
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(f4900,plain,
spl0_339,
inference(avatar_split_clause,[],[f600,f4898]) ).
fof(f4898,plain,
( spl0_339
<=> ! [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_339])]) ).
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(f4896,plain,
spl0_338,
inference(avatar_split_clause,[],[f599,f4894]) ).
fof(f4894,plain,
( spl0_338
<=> ! [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_338])]) ).
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(f4892,plain,
spl0_337,
inference(avatar_split_clause,[],[f598,f4890]) ).
fof(f4890,plain,
( spl0_337
<=> ! [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_337])]) ).
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(f4888,plain,
spl0_336,
inference(avatar_split_clause,[],[f597,f4886]) ).
fof(f4886,plain,
( spl0_336
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
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(f4884,plain,
spl0_335,
inference(avatar_split_clause,[],[f596,f4882]) ).
fof(f4882,plain,
( spl0_335
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
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(f4880,plain,
spl0_334,
inference(avatar_split_clause,[],[f595,f4878]) ).
fof(f4878,plain,
( spl0_334
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
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(f4876,plain,
spl0_333,
inference(avatar_split_clause,[],[f592,f4874]) ).
fof(f4874,plain,
( spl0_333
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
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(f4872,plain,
spl0_332,
inference(avatar_split_clause,[],[f591,f4870]) ).
fof(f4870,plain,
( spl0_332
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
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(f4868,plain,
spl0_331,
inference(avatar_split_clause,[],[f586,f4866]) ).
fof(f4866,plain,
( spl0_331
<=> ! [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_331])]) ).
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(f4864,plain,
spl0_330,
inference(avatar_split_clause,[],[f585,f4862]) ).
fof(f4862,plain,
( spl0_330
<=> ! [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_330])]) ).
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(f4860,plain,
spl0_329,
inference(avatar_split_clause,[],[f582,f4858]) ).
fof(f4858,plain,
( spl0_329
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
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(f4856,plain,
spl0_328,
inference(avatar_split_clause,[],[f581,f4854]) ).
fof(f4854,plain,
( spl0_328
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
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(f4852,plain,
spl0_327,
inference(avatar_split_clause,[],[f579,f4850]) ).
fof(f4850,plain,
( spl0_327
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
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(f4848,plain,
spl0_326,
inference(avatar_split_clause,[],[f578,f4846]) ).
fof(f4846,plain,
( spl0_326
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
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(f4844,plain,
spl0_325,
inference(avatar_split_clause,[],[f577,f4842]) ).
fof(f4842,plain,
( spl0_325
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
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(f4840,plain,
spl0_324,
inference(avatar_split_clause,[],[f576,f4838]) ).
fof(f4838,plain,
( spl0_324
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
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(f4836,plain,
spl0_323,
inference(avatar_split_clause,[],[f575,f4834]) ).
fof(f4834,plain,
( spl0_323
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
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(f4832,plain,
spl0_322,
inference(avatar_split_clause,[],[f574,f4830]) ).
fof(f4830,plain,
( spl0_322
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
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(f4828,plain,
spl0_321,
inference(avatar_split_clause,[],[f570,f4826]) ).
fof(f4826,plain,
( spl0_321
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
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(f4824,plain,
spl0_320,
inference(avatar_split_clause,[],[f568,f4822]) ).
fof(f4822,plain,
( spl0_320
<=> ! [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_320])]) ).
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(f4820,plain,
spl0_319,
inference(avatar_split_clause,[],[f565,f4818]) ).
fof(f4818,plain,
( spl0_319
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
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(f4816,plain,
spl0_318,
inference(avatar_split_clause,[],[f562,f4814]) ).
fof(f4814,plain,
( spl0_318
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
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(f4812,plain,
spl0_317,
inference(avatar_split_clause,[],[f561,f4810]) ).
fof(f4810,plain,
( spl0_317
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
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(f4808,plain,
spl0_316,
inference(avatar_split_clause,[],[f559,f4806]) ).
fof(f4806,plain,
( spl0_316
<=> ! [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_316])]) ).
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(f4804,plain,
spl0_315,
inference(avatar_split_clause,[],[f558,f4802]) ).
fof(f4802,plain,
( spl0_315
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
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(f4800,plain,
spl0_314,
inference(avatar_split_clause,[],[f557,f4798]) ).
fof(f4798,plain,
( spl0_314
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
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(f4796,plain,
spl0_313,
inference(avatar_split_clause,[],[f554,f4794]) ).
fof(f4794,plain,
( spl0_313
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
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(f4792,plain,
spl0_312,
inference(avatar_split_clause,[],[f553,f4790]) ).
fof(f4790,plain,
( spl0_312
<=> ! [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_312])]) ).
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(f4788,plain,
spl0_311,
inference(avatar_split_clause,[],[f551,f4786]) ).
fof(f4786,plain,
( spl0_311
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
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(f4784,plain,
spl0_310,
inference(avatar_split_clause,[],[f545,f4782]) ).
fof(f4782,plain,
( spl0_310
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
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(f4780,plain,
spl0_309,
inference(avatar_split_clause,[],[f544,f4778]) ).
fof(f4778,plain,
( spl0_309
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
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(f4776,plain,
spl0_308,
inference(avatar_split_clause,[],[f542,f4774]) ).
fof(f4774,plain,
( spl0_308
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
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(f4772,plain,
spl0_307,
inference(avatar_split_clause,[],[f541,f4770]) ).
fof(f4770,plain,
( spl0_307
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
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(f4768,plain,
spl0_306,
inference(avatar_split_clause,[],[f534,f4766]) ).
fof(f4766,plain,
( spl0_306
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
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(f4764,plain,
spl0_305,
inference(avatar_split_clause,[],[f533,f4762]) ).
fof(f4762,plain,
( spl0_305
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
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(f4760,plain,
spl0_304,
inference(avatar_split_clause,[],[f531,f4758]) ).
fof(f4758,plain,
( spl0_304
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
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(f4756,plain,
spl0_303,
inference(avatar_split_clause,[],[f530,f4754]) ).
fof(f4754,plain,
( spl0_303
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
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(f4752,plain,
spl0_302,
inference(avatar_split_clause,[],[f529,f4750]) ).
fof(f4750,plain,
( spl0_302
<=> ! [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_302])]) ).
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(f4748,plain,
spl0_301,
inference(avatar_split_clause,[],[f527,f4746]) ).
fof(f4746,plain,
( spl0_301
<=> ! [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_301])]) ).
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(f4744,plain,
spl0_300,
inference(avatar_split_clause,[],[f526,f4742]) ).
fof(f4742,plain,
( spl0_300
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
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(f4740,plain,
spl0_299,
inference(avatar_split_clause,[],[f525,f4738]) ).
fof(f4738,plain,
( spl0_299
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
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(f4736,plain,
spl0_298,
inference(avatar_split_clause,[],[f524,f4734]) ).
fof(f4734,plain,
( spl0_298
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
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(f4732,plain,
spl0_297,
inference(avatar_split_clause,[],[f523,f4730]) ).
fof(f4730,plain,
( spl0_297
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
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(f4728,plain,
spl0_296,
inference(avatar_split_clause,[],[f522,f4726]) ).
fof(f4726,plain,
( spl0_296
<=> ! [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_296])]) ).
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(f4724,plain,
spl0_295,
inference(avatar_split_clause,[],[f521,f4722]) ).
fof(f4722,plain,
( spl0_295
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
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(f4720,plain,
spl0_294,
inference(avatar_split_clause,[],[f520,f4718]) ).
fof(f4718,plain,
( spl0_294
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
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(f4716,plain,
spl0_293,
inference(avatar_split_clause,[],[f519,f4714]) ).
fof(f4714,plain,
( spl0_293
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
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(f4712,plain,
spl0_292,
inference(avatar_split_clause,[],[f518,f4710]) ).
fof(f4710,plain,
( spl0_292
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
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(f4708,plain,
spl0_291,
inference(avatar_split_clause,[],[f515,f4706]) ).
fof(f4706,plain,
( spl0_291
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
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(f4704,plain,
spl0_290,
inference(avatar_split_clause,[],[f513,f4702]) ).
fof(f4702,plain,
( spl0_290
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
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(f4700,plain,
spl0_289,
inference(avatar_split_clause,[],[f511,f4698]) ).
fof(f4698,plain,
( spl0_289
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
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(f4696,plain,
spl0_288,
inference(avatar_split_clause,[],[f508,f4694]) ).
fof(f4694,plain,
( spl0_288
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
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(f4692,plain,
spl0_287,
inference(avatar_split_clause,[],[f507,f4690]) ).
fof(f4690,plain,
( spl0_287
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
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(f4688,plain,
spl0_286,
inference(avatar_split_clause,[],[f506,f4686]) ).
fof(f4686,plain,
( spl0_286
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
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(f4684,plain,
spl0_285,
inference(avatar_split_clause,[],[f503,f4682]) ).
fof(f4682,plain,
( spl0_285
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
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(f4680,plain,
spl0_284,
inference(avatar_split_clause,[],[f500,f4678]) ).
fof(f4678,plain,
( spl0_284
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
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(f4676,plain,
spl0_283,
inference(avatar_split_clause,[],[f499,f4674]) ).
fof(f4674,plain,
( spl0_283
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
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(f4672,plain,
spl0_282,
inference(avatar_split_clause,[],[f497,f4670]) ).
fof(f4670,plain,
( spl0_282
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
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(f4668,plain,
spl0_281,
inference(avatar_split_clause,[],[f496,f4666]) ).
fof(f4666,plain,
( spl0_281
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
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(f4664,plain,
spl0_280,
inference(avatar_split_clause,[],[f495,f4662]) ).
fof(f4662,plain,
( spl0_280
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
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(f4660,plain,
spl0_279,
inference(avatar_split_clause,[],[f494,f4658]) ).
fof(f4658,plain,
( spl0_279
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
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(f4656,plain,
spl0_278,
inference(avatar_split_clause,[],[f493,f4654]) ).
fof(f4654,plain,
( spl0_278
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
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(f4652,plain,
spl0_277,
inference(avatar_split_clause,[],[f491,f4650]) ).
fof(f4650,plain,
( spl0_277
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
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(f4648,plain,
spl0_276,
inference(avatar_split_clause,[],[f488,f4646]) ).
fof(f4646,plain,
( spl0_276
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
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(f4644,plain,
spl0_275,
inference(avatar_split_clause,[],[f487,f4642]) ).
fof(f4642,plain,
( spl0_275
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
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(f4640,plain,
spl0_274,
inference(avatar_split_clause,[],[f483,f4638]) ).
fof(f4638,plain,
( spl0_274
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
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(f4636,plain,
spl0_273,
inference(avatar_split_clause,[],[f481,f4634]) ).
fof(f4634,plain,
( spl0_273
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
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(f4632,plain,
spl0_272,
inference(avatar_split_clause,[],[f473,f4630]) ).
fof(f4630,plain,
( spl0_272
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
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(f4628,plain,
spl0_271,
inference(avatar_split_clause,[],[f472,f4626]) ).
fof(f4626,plain,
( spl0_271
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
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(f4624,plain,
spl0_270,
inference(avatar_split_clause,[],[f471,f4622]) ).
fof(f4622,plain,
( spl0_270
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
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(f4620,plain,
spl0_269,
inference(avatar_split_clause,[],[f470,f4618]) ).
fof(f4618,plain,
( spl0_269
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
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(f4616,plain,
spl0_268,
inference(avatar_split_clause,[],[f469,f4614]) ).
fof(f4614,plain,
( spl0_268
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
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(f4612,plain,
spl0_267,
inference(avatar_split_clause,[],[f468,f4610]) ).
fof(f4610,plain,
( spl0_267
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
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(f4608,plain,
spl0_266,
inference(avatar_split_clause,[],[f467,f4606]) ).
fof(f4606,plain,
( spl0_266
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f467,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4604,plain,
spl0_265,
inference(avatar_split_clause,[],[f466,f4602]) ).
fof(f4602,plain,
( spl0_265
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
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(f4600,plain,
spl0_264,
inference(avatar_split_clause,[],[f465,f4598]) ).
fof(f4598,plain,
( spl0_264
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
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(f4596,plain,
spl0_263,
inference(avatar_split_clause,[],[f464,f4594]) ).
fof(f4594,plain,
( spl0_263
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
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(f4592,plain,
spl0_262,
inference(avatar_split_clause,[],[f463,f4590]) ).
fof(f4590,plain,
( spl0_262
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
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(f4588,plain,
spl0_261,
inference(avatar_split_clause,[],[f462,f4586]) ).
fof(f4586,plain,
( spl0_261
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
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(f4584,plain,
spl0_260,
inference(avatar_split_clause,[],[f461,f4582]) ).
fof(f4582,plain,
( spl0_260
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
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(f4580,plain,
spl0_259,
inference(avatar_split_clause,[],[f460,f4578]) ).
fof(f4578,plain,
( spl0_259
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
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(f4576,plain,
spl0_258,
inference(avatar_split_clause,[],[f459,f4574]) ).
fof(f4574,plain,
( spl0_258
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
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(f4572,plain,
spl0_257,
inference(avatar_split_clause,[],[f458,f4570]) ).
fof(f4570,plain,
( spl0_257
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
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(f4568,plain,
spl0_256,
inference(avatar_split_clause,[],[f457,f4566]) ).
fof(f4566,plain,
( spl0_256
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
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(f4564,plain,
spl0_255,
inference(avatar_split_clause,[],[f454,f4562]) ).
fof(f4562,plain,
( spl0_255
<=> ! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f454,axiom,
! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4560,plain,
spl0_254,
inference(avatar_split_clause,[],[f453,f4558]) ).
fof(f4558,plain,
( spl0_254
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f453,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4556,plain,
spl0_253,
inference(avatar_split_clause,[],[f452,f4554]) ).
fof(f4554,plain,
( spl0_253
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f452,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4552,plain,
spl0_252,
inference(avatar_split_clause,[],[f451,f4550]) ).
fof(f4550,plain,
( spl0_252
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
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(f4548,plain,
spl0_251,
inference(avatar_split_clause,[],[f450,f4546]) ).
fof(f4546,plain,
( spl0_251
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
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(f4544,plain,
spl0_250,
inference(avatar_split_clause,[],[f449,f4542]) ).
fof(f4542,plain,
( spl0_250
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f449,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4540,plain,
spl0_249,
inference(avatar_split_clause,[],[f446,f4538]) ).
fof(f4538,plain,
( spl0_249
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
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(f4536,plain,
spl0_248,
inference(avatar_split_clause,[],[f445,f4534]) ).
fof(f4534,plain,
( spl0_248
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
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(f4532,plain,
spl0_247,
inference(avatar_split_clause,[],[f441,f4530]) ).
fof(f4530,plain,
( spl0_247
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
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(f4528,plain,
spl0_246,
inference(avatar_split_clause,[],[f440,f4526]) ).
fof(f4526,plain,
( spl0_246
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
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(f4524,plain,
spl0_245,
inference(avatar_split_clause,[],[f439,f4522]) ).
fof(f4522,plain,
( spl0_245
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
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(f4520,plain,
spl0_244,
inference(avatar_split_clause,[],[f436,f4518]) ).
fof(f4518,plain,
( spl0_244
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
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(f4516,plain,
spl0_243,
inference(avatar_split_clause,[],[f434,f4514]) ).
fof(f4514,plain,
( spl0_243
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
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(f4512,plain,
spl0_242,
inference(avatar_split_clause,[],[f433,f4510]) ).
fof(f4510,plain,
( spl0_242
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
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(f4508,plain,
spl0_241,
inference(avatar_split_clause,[],[f432,f4506]) ).
fof(f4506,plain,
( spl0_241
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
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(f4504,plain,
spl0_240,
inference(avatar_split_clause,[],[f431,f4502]) ).
fof(f4502,plain,
( spl0_240
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
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(f4500,plain,
spl0_239,
inference(avatar_split_clause,[],[f430,f4498]) ).
fof(f4498,plain,
( spl0_239
<=> ! [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_239])]) ).
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(f4496,plain,
spl0_238,
inference(avatar_split_clause,[],[f426,f4494]) ).
fof(f4494,plain,
( spl0_238
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
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(f4492,plain,
spl0_237,
inference(avatar_split_clause,[],[f425,f4490]) ).
fof(f4490,plain,
( spl0_237
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
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(f4488,plain,
spl0_236,
inference(avatar_split_clause,[],[f424,f4486]) ).
fof(f4486,plain,
( spl0_236
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
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(f4484,plain,
spl0_235,
inference(avatar_split_clause,[],[f421,f4482]) ).
fof(f4482,plain,
( spl0_235
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
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(f4480,plain,
spl0_234,
inference(avatar_split_clause,[],[f419,f4478]) ).
fof(f4478,plain,
( spl0_234
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
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(f4476,plain,
spl0_233,
inference(avatar_split_clause,[],[f417,f4474]) ).
fof(f4474,plain,
( spl0_233
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
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(f4472,plain,
spl0_232,
inference(avatar_split_clause,[],[f416,f4470]) ).
fof(f4470,plain,
( spl0_232
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
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(f4468,plain,
spl0_231,
inference(avatar_split_clause,[],[f415,f4466]) ).
fof(f4466,plain,
( spl0_231
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
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(f4464,plain,
spl0_230,
inference(avatar_split_clause,[],[f414,f4462]) ).
fof(f4462,plain,
( spl0_230
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
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(f4460,plain,
spl0_229,
inference(avatar_split_clause,[],[f413,f4458]) ).
fof(f4458,plain,
( spl0_229
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
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(f4456,plain,
spl0_228,
inference(avatar_split_clause,[],[f411,f4454]) ).
fof(f4454,plain,
( spl0_228
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
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(f4452,plain,
spl0_227,
inference(avatar_split_clause,[],[f410,f4450]) ).
fof(f4450,plain,
( spl0_227
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
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(f4448,plain,
spl0_226,
inference(avatar_split_clause,[],[f407,f4446]) ).
fof(f4446,plain,
( spl0_226
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
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(f4444,plain,
spl0_225,
inference(avatar_split_clause,[],[f405,f4442]) ).
fof(f4442,plain,
( spl0_225
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
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(f4440,plain,
spl0_224,
inference(avatar_split_clause,[],[f404,f4438]) ).
fof(f4438,plain,
( spl0_224
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
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(f4436,plain,
spl0_223,
inference(avatar_split_clause,[],[f403,f4434]) ).
fof(f4434,plain,
( spl0_223
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
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(f4432,plain,
spl0_222,
inference(avatar_split_clause,[],[f402,f4430]) ).
fof(f4430,plain,
( spl0_222
<=> ! [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_222])]) ).
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(f4428,plain,
spl0_221,
inference(avatar_split_clause,[],[f401,f4426]) ).
fof(f4426,plain,
( spl0_221
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
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(f4424,plain,
spl0_220,
inference(avatar_split_clause,[],[f400,f4422]) ).
fof(f4422,plain,
( spl0_220
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
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(f4420,plain,
spl0_219,
inference(avatar_split_clause,[],[f399,f4418]) ).
fof(f4418,plain,
( spl0_219
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
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(f4416,plain,
spl0_218,
inference(avatar_split_clause,[],[f398,f4414]) ).
fof(f4414,plain,
( spl0_218
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
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(f4412,plain,
spl0_217,
inference(avatar_split_clause,[],[f397,f4410]) ).
fof(f4410,plain,
( spl0_217
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
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(f4408,plain,
spl0_216,
inference(avatar_split_clause,[],[f394,f4406]) ).
fof(f4406,plain,
( spl0_216
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
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(f4404,plain,
spl0_215,
inference(avatar_split_clause,[],[f393,f4402]) ).
fof(f4402,plain,
( spl0_215
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
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(f4400,plain,
spl0_214,
inference(avatar_split_clause,[],[f392,f4398]) ).
fof(f4398,plain,
( spl0_214
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
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(f4396,plain,
spl0_213,
inference(avatar_split_clause,[],[f391,f4394]) ).
fof(f4394,plain,
( spl0_213
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
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(f4392,plain,
spl0_212,
inference(avatar_split_clause,[],[f390,f4390]) ).
fof(f4390,plain,
( spl0_212
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
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(f4388,plain,
spl0_211,
inference(avatar_split_clause,[],[f389,f4386]) ).
fof(f4386,plain,
( spl0_211
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
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(f4384,plain,
spl0_210,
inference(avatar_split_clause,[],[f387,f4382]) ).
fof(f4382,plain,
( spl0_210
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
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(f4380,plain,
spl0_209,
inference(avatar_split_clause,[],[f385,f4378]) ).
fof(f4378,plain,
( spl0_209
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
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(f4376,plain,
spl0_208,
inference(avatar_split_clause,[],[f384,f4374]) ).
fof(f4374,plain,
( spl0_208
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
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(f4372,plain,
spl0_207,
inference(avatar_split_clause,[],[f383,f4370]) ).
fof(f4370,plain,
( spl0_207
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
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(f4368,plain,
spl0_206,
inference(avatar_split_clause,[],[f382,f4366]) ).
fof(f4366,plain,
( spl0_206
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
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(f4364,plain,
spl0_205,
inference(avatar_split_clause,[],[f379,f4362]) ).
fof(f4362,plain,
( spl0_205
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
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(f4360,plain,
spl0_204,
inference(avatar_split_clause,[],[f377,f4358]) ).
fof(f4358,plain,
( spl0_204
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
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(f4356,plain,
spl0_203,
inference(avatar_split_clause,[],[f376,f4354]) ).
fof(f4354,plain,
( spl0_203
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
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(f4352,plain,
spl0_202,
inference(avatar_split_clause,[],[f375,f4350]) ).
fof(f4350,plain,
( spl0_202
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
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(f4348,plain,
spl0_201,
inference(avatar_split_clause,[],[f374,f4346]) ).
fof(f4346,plain,
( spl0_201
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
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(f4344,plain,
spl0_200,
inference(avatar_split_clause,[],[f373,f4342]) ).
fof(f4342,plain,
( spl0_200
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
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(f4340,plain,
spl0_199,
inference(avatar_split_clause,[],[f372,f4338]) ).
fof(f4338,plain,
( spl0_199
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
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(f4336,plain,
spl0_198,
inference(avatar_split_clause,[],[f371,f4334]) ).
fof(f4334,plain,
( spl0_198
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
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(f4332,plain,
spl0_197,
inference(avatar_split_clause,[],[f370,f4330]) ).
fof(f4330,plain,
( spl0_197
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
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(f4328,plain,
spl0_196,
inference(avatar_split_clause,[],[f368,f4326]) ).
fof(f4326,plain,
( spl0_196
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
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(f4324,plain,
spl0_195,
inference(avatar_split_clause,[],[f366,f4322]) ).
fof(f4322,plain,
( spl0_195
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
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(f4320,plain,
spl0_194,
inference(avatar_split_clause,[],[f365,f4318]) ).
fof(f4318,plain,
( spl0_194
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
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(f4316,plain,
spl0_193,
inference(avatar_split_clause,[],[f364,f4314]) ).
fof(f4314,plain,
( spl0_193
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
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(f4312,plain,
spl0_192,
inference(avatar_split_clause,[],[f363,f4310]) ).
fof(f4310,plain,
( spl0_192
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
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(f4308,plain,
spl0_191,
inference(avatar_split_clause,[],[f360,f4306]) ).
fof(f4306,plain,
( spl0_191
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
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(f4304,plain,
spl0_190,
inference(avatar_split_clause,[],[f358,f4302]) ).
fof(f4302,plain,
( spl0_190
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
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(f4300,plain,
spl0_189,
inference(avatar_split_clause,[],[f357,f4298]) ).
fof(f4298,plain,
( spl0_189
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
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(f4296,plain,
spl0_188,
inference(avatar_split_clause,[],[f356,f4294]) ).
fof(f4294,plain,
( spl0_188
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
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(f4292,plain,
spl0_187,
inference(avatar_split_clause,[],[f355,f4290]) ).
fof(f4290,plain,
( spl0_187
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
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(f4288,plain,
spl0_186,
inference(avatar_split_clause,[],[f354,f4286]) ).
fof(f4286,plain,
( spl0_186
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
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(f4284,plain,
spl0_185,
inference(avatar_split_clause,[],[f353,f4282]) ).
fof(f4282,plain,
( spl0_185
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
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(f4280,plain,
spl0_184,
inference(avatar_split_clause,[],[f352,f4278]) ).
fof(f4278,plain,
( spl0_184
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
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(f4276,plain,
spl0_183,
inference(avatar_split_clause,[],[f350,f4274]) ).
fof(f4274,plain,
( spl0_183
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
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(f4272,plain,
spl0_182,
inference(avatar_split_clause,[],[f348,f4270]) ).
fof(f4270,plain,
( spl0_182
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
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(f4268,plain,
spl0_181,
inference(avatar_split_clause,[],[f347,f4266]) ).
fof(f4266,plain,
( spl0_181
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
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(f4264,plain,
spl0_180,
inference(avatar_split_clause,[],[f346,f4262]) ).
fof(f4262,plain,
( spl0_180
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
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(f4260,plain,
spl0_179,
inference(avatar_split_clause,[],[f345,f4258]) ).
fof(f4258,plain,
( spl0_179
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
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(f4256,plain,
spl0_178,
inference(avatar_split_clause,[],[f344,f4254]) ).
fof(f4254,plain,
( spl0_178
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
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(f4252,plain,
spl0_177,
inference(avatar_split_clause,[],[f343,f4250]) ).
fof(f4250,plain,
( spl0_177
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
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(f4248,plain,
spl0_176,
inference(avatar_split_clause,[],[f340,f4246]) ).
fof(f4246,plain,
( spl0_176
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
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(f4244,plain,
spl0_175,
inference(avatar_split_clause,[],[f338,f4242]) ).
fof(f4242,plain,
( spl0_175
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
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(f4240,plain,
spl0_174,
inference(avatar_split_clause,[],[f337,f4238]) ).
fof(f4238,plain,
( spl0_174
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
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(f4236,plain,
spl0_173,
inference(avatar_split_clause,[],[f336,f4234]) ).
fof(f4234,plain,
( spl0_173
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
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(f4232,plain,
spl0_172,
inference(avatar_split_clause,[],[f335,f4230]) ).
fof(f4230,plain,
( spl0_172
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
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(f4228,plain,
spl0_171,
inference(avatar_split_clause,[],[f334,f4226]) ).
fof(f4226,plain,
( spl0_171
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
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(f4224,plain,
spl0_170,
inference(avatar_split_clause,[],[f333,f4222]) ).
fof(f4222,plain,
( spl0_170
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
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(f4220,plain,
spl0_169,
inference(avatar_split_clause,[],[f332,f4218]) ).
fof(f4218,plain,
( spl0_169
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
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(f4216,plain,
spl0_168,
inference(avatar_split_clause,[],[f330,f4214]) ).
fof(f4214,plain,
( spl0_168
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
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(f4212,plain,
spl0_167,
inference(avatar_split_clause,[],[f328,f4210]) ).
fof(f4210,plain,
( spl0_167
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
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(f4208,plain,
spl0_166,
inference(avatar_split_clause,[],[f327,f4206]) ).
fof(f4206,plain,
( spl0_166
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
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(f4204,plain,
spl0_165,
inference(avatar_split_clause,[],[f326,f4202]) ).
fof(f4202,plain,
( spl0_165
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
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(f4200,plain,
spl0_164,
inference(avatar_split_clause,[],[f323,f4198]) ).
fof(f4198,plain,
( spl0_164
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
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(f4196,plain,
spl0_163,
inference(avatar_split_clause,[],[f321,f4194]) ).
fof(f4194,plain,
( spl0_163
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
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(f4192,plain,
spl0_162,
inference(avatar_split_clause,[],[f320,f4190]) ).
fof(f4190,plain,
( spl0_162
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
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(f4188,plain,
spl0_161,
inference(avatar_split_clause,[],[f319,f4186]) ).
fof(f4186,plain,
( spl0_161
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
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(f4184,plain,
spl0_160,
inference(avatar_split_clause,[],[f318,f4182]) ).
fof(f4182,plain,
( spl0_160
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
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(f4180,plain,
spl0_159,
inference(avatar_split_clause,[],[f314,f4178]) ).
fof(f4178,plain,
( spl0_159
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
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(f4176,plain,
spl0_158,
inference(avatar_split_clause,[],[f307,f4174]) ).
fof(f4174,plain,
( spl0_158
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
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(f4172,plain,
spl0_157,
inference(avatar_split_clause,[],[f299,f4170]) ).
fof(f4170,plain,
( spl0_157
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
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(f4168,plain,
spl0_156,
inference(avatar_split_clause,[],[f298,f4166]) ).
fof(f4166,plain,
( spl0_156
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
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(f4164,plain,
spl0_155,
inference(avatar_split_clause,[],[f293,f4162]) ).
fof(f4162,plain,
( spl0_155
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
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(f4160,plain,
spl0_154,
inference(avatar_split_clause,[],[f291,f4158]) ).
fof(f4158,plain,
( spl0_154
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
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(f4156,plain,
spl0_153,
inference(avatar_split_clause,[],[f289,f4154]) ).
fof(f4154,plain,
( spl0_153
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
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(f4152,plain,
spl0_152,
inference(avatar_split_clause,[],[f288,f4150]) ).
fof(f4150,plain,
( spl0_152
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
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(f4148,plain,
spl0_151,
inference(avatar_split_clause,[],[f285,f4146]) ).
fof(f4146,plain,
( spl0_151
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
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(f4144,plain,
spl0_150,
inference(avatar_split_clause,[],[f283,f4142]) ).
fof(f4142,plain,
( spl0_150
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
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(f4140,plain,
spl0_149,
inference(avatar_split_clause,[],[f282,f4138]) ).
fof(f4138,plain,
( spl0_149
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
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(f4136,plain,
spl0_148,
inference(avatar_split_clause,[],[f281,f4134]) ).
fof(f4134,plain,
( spl0_148
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
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(f4132,plain,
spl0_147,
inference(avatar_split_clause,[],[f280,f4130]) ).
fof(f4130,plain,
( spl0_147
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
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(f4128,plain,
spl0_146,
inference(avatar_split_clause,[],[f279,f4126]) ).
fof(f4126,plain,
( spl0_146
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
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(f4124,plain,
spl0_145,
inference(avatar_split_clause,[],[f278,f4122]) ).
fof(f4122,plain,
( spl0_145
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
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(f4120,plain,
spl0_144,
inference(avatar_split_clause,[],[f277,f4118]) ).
fof(f4118,plain,
( spl0_144
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
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(f4116,plain,
spl0_143,
inference(avatar_split_clause,[],[f276,f4114]) ).
fof(f4114,plain,
( spl0_143
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
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(f4112,plain,
spl0_142,
inference(avatar_split_clause,[],[f275,f4110]) ).
fof(f4110,plain,
( spl0_142
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
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(f4108,plain,
spl0_141,
inference(avatar_split_clause,[],[f274,f4106]) ).
fof(f4106,plain,
( spl0_141
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
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(f4104,plain,
spl0_140,
inference(avatar_split_clause,[],[f272,f4102]) ).
fof(f4102,plain,
( spl0_140
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
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(f4100,plain,
spl0_139,
inference(avatar_split_clause,[],[f271,f4098]) ).
fof(f4098,plain,
( spl0_139
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
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(f4096,plain,
spl0_138,
inference(avatar_split_clause,[],[f270,f4094]) ).
fof(f4094,plain,
( spl0_138
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
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(f4092,plain,
spl0_137,
inference(avatar_split_clause,[],[f269,f4090]) ).
fof(f4090,plain,
( spl0_137
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
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(f4088,plain,
spl0_136,
inference(avatar_split_clause,[],[f268,f4086]) ).
fof(f4086,plain,
( spl0_136
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
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(f4084,plain,
spl0_135,
inference(avatar_split_clause,[],[f267,f4082]) ).
fof(f4082,plain,
( spl0_135
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
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(f4080,plain,
spl0_134,
inference(avatar_split_clause,[],[f266,f4078]) ).
fof(f4078,plain,
( spl0_134
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
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(f4076,plain,
spl0_133,
inference(avatar_split_clause,[],[f264,f4074]) ).
fof(f4074,plain,
( spl0_133
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
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(f4072,plain,
spl0_132,
inference(avatar_split_clause,[],[f263,f4070]) ).
fof(f4070,plain,
( spl0_132
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
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(f4068,plain,
spl0_131,
inference(avatar_split_clause,[],[f260,f4066]) ).
fof(f4066,plain,
( spl0_131
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
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(f4064,plain,
spl0_130,
inference(avatar_split_clause,[],[f259,f4062]) ).
fof(f4062,plain,
( spl0_130
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
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(f4060,plain,
spl0_129,
inference(avatar_split_clause,[],[f258,f4058]) ).
fof(f4058,plain,
( spl0_129
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
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(f4056,plain,
spl0_128,
inference(avatar_split_clause,[],[f257,f4054]) ).
fof(f4054,plain,
( spl0_128
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f257,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f4052,plain,
spl0_127,
inference(avatar_split_clause,[],[f256,f4050]) ).
fof(f4050,plain,
( spl0_127
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f256,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f4048,plain,
spl0_126,
inference(avatar_split_clause,[],[f255,f4046]) ).
fof(f4046,plain,
( spl0_126
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
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(f4044,plain,
spl0_125,
inference(avatar_split_clause,[],[f254,f4042]) ).
fof(f4042,plain,
( spl0_125
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
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(f4040,plain,
spl0_124,
inference(avatar_split_clause,[],[f253,f4038]) ).
fof(f4038,plain,
( spl0_124
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
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(f4036,plain,
spl0_123,
inference(avatar_split_clause,[],[f98,f4034]) ).
fof(f98,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f4032,plain,
spl0_122,
inference(avatar_split_clause,[],[f66,f4030]) ).
fof(f66,axiom,
! [X21] : ~ c_less(X21,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f4028,plain,
spl0_121,
inference(avatar_split_clause,[],[f64,f4026]) ).
fof(f64,axiom,
! [X21] : c_lessequals(c_0,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f4024,plain,
spl0_120,
inference(avatar_split_clause,[],[f40,f4022]) ).
fof(f4022,plain,
( spl0_120
<=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
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(f4020,plain,
spl0_119,
inference(avatar_split_clause,[],[f39,f4018]) ).
fof(f4018,plain,
( spl0_119
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
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(f4016,plain,
spl0_118,
inference(avatar_split_clause,[],[f23,f4014]) ).
fof(f4014,plain,
( spl0_118
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
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(f4012,plain,
spl0_117,
inference(avatar_split_clause,[],[f2974,f4010]) ).
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(f4008,plain,
~ spl0_116,
inference(avatar_split_clause,[],[f2903,f4005]) ).
fof(f4005,plain,
( spl0_116
<=> c_Public_Okeymode_OSignature = c_Public_Okeymode_OEncryption ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
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(f4003,plain,
~ spl0_115,
inference(avatar_split_clause,[],[f2733,f4000]) ).
fof(f4000,plain,
( spl0_115
<=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
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(f3998,plain,
~ spl0_114,
inference(avatar_split_clause,[],[f2629,f3995]) ).
fof(f3995,plain,
( spl0_114
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f2629,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3993,plain,
~ spl0_113,
inference(avatar_split_clause,[],[f2310,f3990]) ).
fof(f3990,plain,
( spl0_113
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f2310,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3988,plain,
spl0_112,
inference(avatar_split_clause,[],[f2303,f3985]) ).
fof(f3985,plain,
( spl0_112
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3983,plain,
spl0_111,
inference(avatar_split_clause,[],[f2290,f3980]) ).
fof(f3980,plain,
( spl0_111
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3978,plain,
~ spl0_110,
inference(avatar_split_clause,[],[f2159,f3975]) ).
fof(f3975,plain,
( spl0_110
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
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(f3973,plain,
spl0_109,
inference(avatar_split_clause,[],[f1706,f3971]) ).
fof(f3971,plain,
( spl0_109
<=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
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(f3969,plain,
spl0_108,
inference(avatar_split_clause,[],[f1551,f3967]) ).
fof(f3967,plain,
( spl0_108
<=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
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(f3965,plain,
~ spl0_107,
inference(avatar_split_clause,[],[f1370,f3962]) ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3960,plain,
~ spl0_106,
inference(avatar_split_clause,[],[f1251,f3957]) ).
fof(f3957,plain,
( spl0_106
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
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(f3955,plain,
spl0_105,
inference(avatar_split_clause,[],[f249,f3953]) ).
fof(f3953,plain,
( spl0_105
<=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f249,axiom,
! [X37] : class_Orderings_Oorder(tc_set(X37)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3951,plain,
spl0_104,
inference(avatar_split_clause,[],[f248,f3949]) ).
fof(f3949,plain,
( spl0_104
<=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f248,axiom,
! [X37] : class_Orderings_Oord(tc_set(X37)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3947,plain,
spl0_103,
inference(avatar_split_clause,[],[f126,f3944]) ).
fof(f3944,plain,
( spl0_103
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
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(f3942,plain,
spl0_102,
inference(avatar_split_clause,[],[f124,f3939]) ).
fof(f3939,plain,
( spl0_102
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
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(f3937,plain,
spl0_101,
inference(avatar_split_clause,[],[f123,f3935]) ).
fof(f3935,plain,
( spl0_101
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
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(f3933,plain,
spl0_100,
inference(avatar_split_clause,[],[f244,f3930]) ).
fof(f3930,plain,
( spl0_100
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f244,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3928,plain,
spl0_99,
inference(avatar_split_clause,[],[f243,f3925]) ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3923,plain,
spl0_98,
inference(avatar_split_clause,[],[f242,f3920]) ).
fof(f3920,plain,
( spl0_98
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f242,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3918,plain,
spl0_97,
inference(avatar_split_clause,[],[f241,f3915]) ).
fof(f241,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3913,plain,
spl0_96,
inference(avatar_split_clause,[],[f239,f3910]) ).
fof(f3910,plain,
( spl0_96
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f239,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3908,plain,
spl0_95,
inference(avatar_split_clause,[],[f238,f3905]) ).
fof(f238,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3903,plain,
spl0_94,
inference(avatar_split_clause,[],[f236,f3900]) ).
fof(f3900,plain,
( spl0_94
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3898,plain,
spl0_93,
inference(avatar_split_clause,[],[f235,f3895]) ).
fof(f3895,plain,
( spl0_93
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f235,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3893,plain,
spl0_92,
inference(avatar_split_clause,[],[f234,f3890]) ).
fof(f3890,plain,
( spl0_92
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f234,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3888,plain,
spl0_91,
inference(avatar_split_clause,[],[f233,f3885]) ).
fof(f3885,plain,
( spl0_91
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f233,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3883,plain,
spl0_90,
inference(avatar_split_clause,[],[f232,f3880]) ).
fof(f232,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3878,plain,
spl0_89,
inference(avatar_split_clause,[],[f231,f3875]) ).
fof(f3875,plain,
( spl0_89
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f231,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3873,plain,
spl0_88,
inference(avatar_split_clause,[],[f230,f3870]) ).
fof(f3870,plain,
( spl0_88
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f230,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3868,plain,
spl0_87,
inference(avatar_split_clause,[],[f229,f3865]) ).
fof(f3865,plain,
( spl0_87
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f229,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3863,plain,
spl0_86,
inference(avatar_split_clause,[],[f228,f3860]) ).
fof(f3860,plain,
( spl0_86
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3858,plain,
spl0_85,
inference(avatar_split_clause,[],[f227,f3855]) ).
fof(f3855,plain,
( spl0_85
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3853,plain,
spl0_84,
inference(avatar_split_clause,[],[f226,f3850]) ).
fof(f3850,plain,
( spl0_84
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f226,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3848,plain,
spl0_83,
inference(avatar_split_clause,[],[f225,f3845]) ).
fof(f3845,plain,
( spl0_83
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f225,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3843,plain,
spl0_82,
inference(avatar_split_clause,[],[f224,f3840]) ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3838,plain,
spl0_81,
inference(avatar_split_clause,[],[f223,f3835]) ).
fof(f3835,plain,
( spl0_81
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f223,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3833,plain,
spl0_80,
inference(avatar_split_clause,[],[f222,f3830]) ).
fof(f3830,plain,
( spl0_80
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f222,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3828,plain,
spl0_79,
inference(avatar_split_clause,[],[f221,f3825]) ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3823,plain,
spl0_78,
inference(avatar_split_clause,[],[f220,f3820]) ).
fof(f3820,plain,
( spl0_78
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f220,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3818,plain,
spl0_77,
inference(avatar_split_clause,[],[f219,f3815]) ).
fof(f3815,plain,
( spl0_77
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f219,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3813,plain,
spl0_76,
inference(avatar_split_clause,[],[f218,f3810]) ).
fof(f3810,plain,
( spl0_76
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f218,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3808,plain,
spl0_75,
inference(avatar_split_clause,[],[f217,f3805]) ).
fof(f3805,plain,
( spl0_75
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f217,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3803,plain,
spl0_74,
inference(avatar_split_clause,[],[f216,f3800]) ).
fof(f3800,plain,
( spl0_74
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f216,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3798,plain,
spl0_73,
inference(avatar_split_clause,[],[f215,f3795]) ).
fof(f3795,plain,
( spl0_73
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f215,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3793,plain,
spl0_72,
inference(avatar_split_clause,[],[f214,f3790]) ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3788,plain,
spl0_71,
inference(avatar_split_clause,[],[f213,f3785]) ).
fof(f3785,plain,
( spl0_71
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f213,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3783,plain,
spl0_70,
inference(avatar_split_clause,[],[f212,f3780]) ).
fof(f3780,plain,
( spl0_70
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f212,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3778,plain,
spl0_69,
inference(avatar_split_clause,[],[f211,f3775]) ).
fof(f3775,plain,
( spl0_69
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3773,plain,
spl0_68,
inference(avatar_split_clause,[],[f210,f3770]) ).
fof(f3770,plain,
( spl0_68
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3768,plain,
spl0_67,
inference(avatar_split_clause,[],[f209,f3765]) ).
fof(f3765,plain,
( spl0_67
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f209,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3763,plain,
spl0_66,
inference(avatar_split_clause,[],[f208,f3760]) ).
fof(f3760,plain,
( spl0_66
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f208,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3758,plain,
spl0_65,
inference(avatar_split_clause,[],[f203,f3755]) ).
fof(f3755,plain,
( spl0_65
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3753,plain,
spl0_64,
inference(avatar_split_clause,[],[f198,f3750]) ).
fof(f3750,plain,
( spl0_64
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f198,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3748,plain,
spl0_63,
inference(avatar_split_clause,[],[f195,f3745]) ).
fof(f3745,plain,
( spl0_63
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f195,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3743,plain,
spl0_62,
inference(avatar_split_clause,[],[f194,f3740]) ).
fof(f3740,plain,
( spl0_62
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f194,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3738,plain,
spl0_61,
inference(avatar_split_clause,[],[f189,f3735]) ).
fof(f189,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3733,plain,
spl0_60,
inference(avatar_split_clause,[],[f186,f3730]) ).
fof(f186,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3728,plain,
spl0_59,
inference(avatar_split_clause,[],[f184,f3725]) ).
fof(f3725,plain,
( spl0_59
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f184,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3723,plain,
spl0_58,
inference(avatar_split_clause,[],[f183,f3720]) ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3718,plain,
spl0_57,
inference(avatar_split_clause,[],[f182,f3715]) ).
fof(f3715,plain,
( spl0_57
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f182,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3713,plain,
spl0_56,
inference(avatar_split_clause,[],[f181,f3710]) ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3708,plain,
spl0_55,
inference(avatar_split_clause,[],[f180,f3705]) ).
fof(f3705,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
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(f3703,plain,
spl0_54,
inference(avatar_split_clause,[],[f178,f3700]) ).
fof(f3700,plain,
( spl0_54
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f178,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3698,plain,
spl0_53,
inference(avatar_split_clause,[],[f177,f3695]) ).
fof(f3695,plain,
( spl0_53
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f177,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3693,plain,
spl0_52,
inference(avatar_split_clause,[],[f176,f3690]) ).
fof(f3690,plain,
( spl0_52
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f176,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3688,plain,
spl0_51,
inference(avatar_split_clause,[],[f175,f3685]) ).
fof(f175,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3683,plain,
spl0_50,
inference(avatar_split_clause,[],[f174,f3680]) ).
fof(f3680,plain,
( spl0_50
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f174,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3678,plain,
spl0_49,
inference(avatar_split_clause,[],[f173,f3675]) ).
fof(f3675,plain,
( spl0_49
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f173,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3673,plain,
spl0_48,
inference(avatar_split_clause,[],[f172,f3670]) ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3668,plain,
spl0_47,
inference(avatar_split_clause,[],[f171,f3665]) ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3663,plain,
spl0_46,
inference(avatar_split_clause,[],[f170,f3660]) ).
fof(f3660,plain,
( spl0_46
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
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(f3658,plain,
spl0_45,
inference(avatar_split_clause,[],[f169,f3655]) ).
fof(f3655,plain,
( spl0_45
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
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(f3653,plain,
spl0_44,
inference(avatar_split_clause,[],[f168,f3650]) ).
fof(f3650,plain,
( spl0_44
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
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(f3648,plain,
spl0_43,
inference(avatar_split_clause,[],[f167,f3645]) ).
fof(f3645,plain,
( spl0_43
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
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(f3643,plain,
spl0_42,
inference(avatar_split_clause,[],[f166,f3640]) ).
fof(f3640,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
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(f3638,plain,
spl0_41,
inference(avatar_split_clause,[],[f165,f3635]) ).
fof(f3635,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
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(f3633,plain,
spl0_40,
inference(avatar_split_clause,[],[f164,f3630]) ).
fof(f3630,plain,
( spl0_40
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f164,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3628,plain,
spl0_39,
inference(avatar_split_clause,[],[f162,f3625]) ).
fof(f3625,plain,
( spl0_39
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
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(f3623,plain,
spl0_38,
inference(avatar_split_clause,[],[f161,f3620]) ).
fof(f3620,plain,
( spl0_38
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
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(f3618,plain,
spl0_37,
inference(avatar_split_clause,[],[f160,f3615]) ).
fof(f3615,plain,
( spl0_37
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
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(f3613,plain,
spl0_36,
inference(avatar_split_clause,[],[f159,f3610]) ).
fof(f3610,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3608,plain,
spl0_35,
inference(avatar_split_clause,[],[f158,f3605]) ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3603,plain,
spl0_34,
inference(avatar_split_clause,[],[f157,f3600]) ).
fof(f3600,plain,
( spl0_34
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f157,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3598,plain,
spl0_33,
inference(avatar_split_clause,[],[f156,f3595]) ).
fof(f156,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3593,plain,
spl0_32,
inference(avatar_split_clause,[],[f155,f3590]) ).
fof(f155,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3588,plain,
spl0_31,
inference(avatar_split_clause,[],[f154,f3585]) ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3583,plain,
spl0_30,
inference(avatar_split_clause,[],[f153,f3580]) ).
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(f3578,plain,
spl0_29,
inference(avatar_split_clause,[],[f151,f3575]) ).
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(f3573,plain,
spl0_28,
inference(avatar_split_clause,[],[f150,f3570]) ).
fof(f3570,plain,
( spl0_28
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f150,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3568,plain,
spl0_27,
inference(avatar_split_clause,[],[f149,f3565]) ).
fof(f3565,plain,
( spl0_27
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
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(f3563,plain,
spl0_26,
inference(avatar_split_clause,[],[f148,f3560]) ).
fof(f3560,plain,
( spl0_26
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
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(f3558,plain,
spl0_25,
inference(avatar_split_clause,[],[f147,f3555]) ).
fof(f3555,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f147,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3553,plain,
spl0_24,
inference(avatar_split_clause,[],[f146,f3550]) ).
fof(f3550,plain,
( spl0_24
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f146,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3548,plain,
spl0_23,
inference(avatar_split_clause,[],[f145,f3545]) ).
fof(f145,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3543,plain,
spl0_22,
inference(avatar_split_clause,[],[f144,f3540]) ).
fof(f3540,plain,
( spl0_22
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
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(f3538,plain,
spl0_21,
inference(avatar_split_clause,[],[f143,f3535]) ).
fof(f3535,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f143,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3533,plain,
spl0_20,
inference(avatar_split_clause,[],[f142,f3530]) ).
fof(f3530,plain,
( spl0_20
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
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(f3528,plain,
spl0_19,
inference(avatar_split_clause,[],[f140,f3525]) ).
fof(f3525,plain,
( spl0_19
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f140,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3523,plain,
spl0_18,
inference(avatar_split_clause,[],[f139,f3520]) ).
fof(f3520,plain,
( spl0_18
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
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(f3518,plain,
spl0_17,
inference(avatar_split_clause,[],[f138,f3515]) ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3513,plain,
spl0_16,
inference(avatar_split_clause,[],[f137,f3510]) ).
fof(f3510,plain,
( spl0_16
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f137,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3508,plain,
spl0_15,
inference(avatar_split_clause,[],[f136,f3505]) ).
fof(f3505,plain,
( spl0_15
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f136,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3503,plain,
spl0_14,
inference(avatar_split_clause,[],[f135,f3500]) ).
fof(f3500,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
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(f3498,plain,
spl0_13,
inference(avatar_split_clause,[],[f134,f3495]) ).
fof(f3495,plain,
( spl0_13
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f134,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3493,plain,
spl0_12,
inference(avatar_split_clause,[],[f133,f3490]) ).
fof(f133,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3488,plain,
spl0_11,
inference(avatar_split_clause,[],[f132,f3485]) ).
fof(f3485,plain,
( spl0_11
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f132,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3483,plain,
spl0_10,
inference(avatar_split_clause,[],[f131,f3480]) ).
fof(f3480,plain,
( spl0_10
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f131,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3478,plain,
spl0_9,
inference(avatar_split_clause,[],[f130,f3475]) ).
fof(f3475,plain,
( spl0_9
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f130,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3473,plain,
~ spl0_8,
inference(avatar_split_clause,[],[f2976,f3470]) ).
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(f3468,plain,
~ spl0_7,
inference(avatar_split_clause,[],[f2971,f3465]) ).
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(f3463,plain,
spl0_6,
inference(avatar_split_clause,[],[f2970,f3460]) ).
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(f3458,plain,
spl0_5,
inference(avatar_split_clause,[],[f2977,f3455]) ).
fof(f2977,axiom,
c_in(v_Aa,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
fof(f3453,plain,
spl0_4,
inference(avatar_split_clause,[],[f2972,f3450]) ).
fof(f2972,axiom,
c_in(v_KAB,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3448,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f2969,f3445]) ).
fof(f2969,axiom,
~ c_in(v_Ba,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_11) ).
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
% 0.06/0.12 % Problem : SWV362-1 : TPTP v8.2.0. Released v3.2.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 08:21:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (7439)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.46 % (7446)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)
% 0.21/0.46 % (7442)WARNING: value z3 for option sas not known
% 0.21/0.47 % (7440)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.47 % (7441)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.47 % (7443)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.47 % (7442)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.47 % (7444)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)
% 0.21/0.47 % (7445)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 1.97/0.73 TRYING [1]
% 4.07/1.01 TRYING [2]
% 5.65/1.31 TRYING [1]
% 6.78/1.41 % (7444)First to succeed.
% 7.33/1.48 % (7444)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7439"
% 7.33/1.49 % (7444)Refutation found. Thanks to Tanya!
% 7.33/1.49 % SZS status Unsatisfiable for theBenchmark
% 7.33/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 7.54/1.53 % (7444)------------------------------
% 7.54/1.53 % (7444)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.54/1.53 % (7444)Termination reason: Refutation
% 7.54/1.53
% 7.54/1.53 % (7444)Memory used [KB]: 21697
% 7.54/1.53 % (7444)Time elapsed: 1.016 s
% 7.54/1.53 % (7444)Instructions burned: 2786 (million)
% 7.54/1.53 % (7439)Success in time 1.168 s
%------------------------------------------------------------------------------